Introduction to Quantitative Methods: Statistics, Variables, Data, Population, Sample

Hinzugefügt: 2026-06-02

[00:00:00]Thank you very much. So, this is quantitative methods. Okay? Quantitative methods as all of you are aware of.

[00:00:07]Um what I plan to do today, I'll walk you through the the course outline and then maybe set some general expectations for the course.

[00:00:17]And then we would we would do a few things by way of foundational concepts. Okay? To be able to build our understanding before we jump into computations a bit later on in the course.

[00:00:35]Now with regards to the course outline, I think I would make that available on the on the virtual class platform, right?

[00:00:43]What you call the LMS. And so maybe that's something that we can look forward to. But in general, as as you may be you may have been exposed to, right?

[00:00:53]The the the quantitative methods course encompasses some general numerical skills that are important for secretaryship, managerial people, administrative people, you know, to have as part of their training.

[00:01:16]All right? So typically people would ask, I mean, I'm reading secretaryship and maybe administrative practice, right? But but what what has this got to do with quantitative methods? It's simply because we're living in a big data world.

[00:01:33]All right? And and because data is all around us and it's almost impossible to do anything significant these days without doing some data analysis. So, it's very important that regardless of your background, regardless of your preferences or anything, you still need to be equipped with some vital skill sets when it comes to analyzing and then understanding data.

[00:02:02]All right? It's not enough to just say that I am I am an admin person. So, this data-related issues have nothing to do with me. No, it has everything to do with you. All right? [snorts] Now, the second thing is maybe by way of setting expectations for the course.

[00:02:21]A lot of people come into the course with with with a closed mindset. What I mean by a closed mindset is once you begin to say things like, "As for me, I don't like calculations. As for me, anything calculation is not for me."

[00:02:38]That's That's an outright failure, okay?

[00:02:41]That That's That's like failing in advance.

[00:02:44]All right?

[00:02:46]Everything can be taught and everything can be learned if you if only you're open to.

[00:02:52]All right? So, I I want to disabuse your minds of some of these presumptions that you make of yourselves, right? I do understand yes, for most of you, the last time you did anything relating to calculation maybe sometime in senior high school, where you were forced to do some core maths.

[00:03:09]All right? After core maths, you've not touched anything related to calculations. And so, I do understand that there will be some challenge. So, in that regard, you need to recognize that challenge.

[00:03:23]Okay, embrace that challenge and then now Now that you know the reality, put in a lot of work, right? Another thing I would say is you cannot study or read this course like one of your other vanilla courses.

[00:03:39]All right? This is not a reading course, where you can lie on your bed and cross your legs and then read and then hope that you will get it. All right? You You You can only sail through this course with practice and actually working things out.

[00:03:55]All right? Actually writing and solving problems. That's the only way that you can get ahead.

[00:04:00]All right? It's not just about reading solutions. No.

[00:04:04]Okay? So, these are just a few things that I would leave you with before I I begin. So, typically typically when I come to class whether in person or virtual I would normally like to especially in person sessions, I normally like to do manual teaching.

[00:04:24]So, I don't I hardly use PowerPoint presentations for especially when I am inside, you know, the lecture hall. The only time I may use a PowerPoint presentation is when we're doing virtual sessions. Okay? Like online sessions.

[00:04:37]And even with that I would complement it with writing. Okay? Writing, doing digital writing.

[00:04:45]And this is because if I just focus on PowerPoint slides, right? Everything is solved and then I'm just walking you through.

[00:04:53]It's very easy to look at the slides and say that oh yes, so you do it this way or X becomes this or you take it you transpose the matrix, you go here. It's very easy to just tell a narrative. But at the end of the day when I give you a problem that okay, now do this on your own, you'd you'd realize that you really have not understood it. Okay? So, there's something about writing there's something about writing that helps a person to learn and and to understand. Okay? So, it's that's something I would want to encourage all of you to do.

[00:05:28]Especially as you are we are doing these Zoom sessions. Well, I'll come to these Zoom sessions. But even in in the class.

[00:05:34]Okay?

[00:05:36]Whatever I'm writing, follow through and and write as well.

[00:05:40]Okay? Most of you like to just take pictures.

[00:05:43]You know, like paparazzis.

[00:05:45]And then you tell yourself that you'll find time and then transcribe it into your notes. But you and I know that you'll never make that time to transcribe. And by the end of the semester, the only notes that you have are screenshots.

[00:06:01]And and and you're tickling yourself that you're learning, right? I I don't think that's the way to go.

[00:06:07]So, when we come to class, there'll be a lot of writing that you can expect, okay?

[00:06:13]So, I'm just setting the expectation right now. Also, in cases where we're having Zoom classes, like I said, with Zoom, we may decide to convert some of the Zoom sessions to in-person sessions, okay?

[00:06:27]When the course progresses and things become a bit more intense.

[00:06:31]All right? However, in instances where we're still having Zoom, I want you to take it with the seriousness of an in-person session.

[00:06:40]Okay? Most students see virtual sessions as less important. Oh, I mean, if if it's an online week, it's a free week for us.

[00:06:51]You know, the lecture is not going to be so serious. And after all, even if, you know, we can just tell the lecture that uh we were losing connection within here, so if he can repeat. Please keep in mind, whatever I teach virtually or online, I will not repeat in class the next time.

[00:07:09]I take Zoom sessions and virtual sessions as if they are in-person sessions. It is a class. It is also a lecture. And it has to be treated with the same level of importance.

[00:07:21]All right? So, I don't want you to think of virtual sessions as less important.

[00:07:26]Okay? They are equally important.

[00:07:29]>> [clears throat] >> Okay?

[00:07:32]So, I think with that being said, I think with that being said, if I mean, if anything else comes to mind, I'll do all to to let you know. But I think these are the ground for for now. So, for example, with today with regards to what I had wanted to do, I have some slides that of course I'll share later on. But, um at the beginning I will be doing a bit more writing, okay? Because I want to actually walk you through you know, we we kind of building ourselves from ground up. Okay? So, by way of the course outline I'll retrieve that later on and then I I I think I'll just make that available.

[00:08:13]But, in general, we'll start by looking at in general what quantitative methods is.

[00:08:20]You know, its importance and we would move into We'll talk a bit about statistics.

[00:08:28]We'll talk about the framework of statistics.

[00:08:32]We'll talk about population and sampling.

[00:08:39]We'll talk about measures of central tendency.

[00:08:44]We'll talk about measures of dispersion.

[00:08:47]We'll talk about coefficients of variabilities.

[00:08:51]We'll talk about quartiles. We'll talk about correlation analysis. We'll talk about regression analysis.

[00:08:59]Okay? These are all very very crucial topics that if you take seriously I think you would you would do well, all right? So, I also want you to come into the course with a certain mindset, a mindset of possibility, right? A mindset that says that yes maybe math or statistics is nothing is is not really my stronghold, but I'm willing to put in the effort.

[00:09:27]Okay? And just to give you a sense of how the difficulty the difficulty level of this course. This is like um if you take all the mathematical sciences, all right, and let's say you take 1%.

[00:09:44]Okay, 1% is what? 1 over 100, right?

[00:09:50]Okay. Now, the level of difficulty of this course is like this 1%. Okay, take another 1% of this.

[00:09:57]So, it's like 1% of 1%.

[00:10:06]Okay, that's a very small number. 1% of 1% is I think is what? 0.001.

[00:10:19]Right?

[00:10:26]Okay. So, this like 0.0001.

[00:10:29]So, this simply means that if you divide the mathematical sciences into or the statistical sciences into 10,000 parts, okay, quantitative methods is like just one part. Okay, 0.001 is just one over what? 10,000.

[00:10:48]So, quantitative methods is like 1,000th parts of the statistical science 1/10,000th part of the statistical science. So, it's it's just watered down statistics, right? It's nothing extraordinary, nothing to be scared of, right? It's just very basic. So, if you if you decide that, okay, it's something you're willing to put in the effort, I I don't see why you shouldn't do well.

[00:11:12]Okay, so, I'm about to start the lecture now. As we move on, if there are any questions, uh just show by hand, okay, using the the the emoticons and then or if if it's a a passive concern that you have or or a question that you think you can type into the chat area, you can also do so.

[00:11:32]But if it's something that you want to voice out, just show by hand and then you can you can talk. All right?

[00:11:39]Good. So, with that being said, I think let's just jump right into it and do something.

[00:11:46]Let's start by we're looking at quantitative methods.

[00:11:50]Oh, here we're looking at what the the approaches.

[00:11:56]Okay, we're looking at um number one We're looking at principles.

[00:12:13]theories and modalities.

[00:12:29]Okay.

[00:12:35]for studying for studying and comprehending quantities.

[00:13:01]Okay, in quant methods we're going to study the principles, the theories, and the modalities for studying and for comprehending quantities.

[00:13:11]All right? For comprehending quantities.

[00:13:13]Now, the quantities here that we're talking about, when we say quantities, what are quantities? Quantities are uh measures of values.

[00:13:23]Okay, measures of values.

[00:13:26]Measures of value. So, as we move on in the course, you would realize that the measures of values that we're actually talking about are simply data.

[00:13:43]Okay? So, essentially in quantitative methods, we're going to be studying the principles, the theories, and the modalities for studying and for understanding data. Okay? That's really, you know, the the end goal at the end of the day.

[00:14:00]Now, in studying quantitative methods, we need to employ some tools.

[00:14:06]Okay?

[00:14:08]We need to employ some tools. And one of those tools, okay, is statistics.

[00:14:24]Okay.

[00:14:25]So, now let's look at what statistics All of you may have heard about statistics in one [clears throat] way or the other.

[00:14:34]Okay? Now, statistics is a very broad area. It's a broad subfield of mathematics.

[00:14:42]All right?

[00:14:43]And it constitutes different aspects. So, first of all, statistics, what is it?

[00:14:50]It's It's a mathematical science.

[00:14:53]Okay?

[00:15:03]It's a mathematical science which is composed of five different phases. Number one, collection.

[00:15:18]Number two, organization.

[00:15:29]Number three analysis Number four interpretation And then number five is presentation of data.

[00:16:20]All right, for informed decision-making.

[00:16:53]Okay.

[00:16:54]So, statistics, first of all, is a mathematical science, meaning that we statistics uses mathematical elements.

[00:17:02]>> [clears throat] >> All right?

[00:17:04]And it's it's a science as well, so it's a mathematical science which involves the collection organization the analysis, the interpretation, and the presentation of data for informed decision-making, right? So, the goal of statistics is essentially to help stakeholders in academe and then in industry to be able to make informed decisions. When we say informed decisions, we mean evidence-based decisions, okay? You're making decisions based on based on credible based on a credible basis.

[00:17:48]Okay? You are not making a decision simply because I feel like we should do this. We I think we should. For example, if you take a government a government that wants to implement some developmental initiatives, right?

[00:18:04]The the government cannot just do like a a cookie-cutter approach, all right? Where randomly the government will just say, "Okay, we I think our people need this. I I I feel they need this. They Right?" When you do that, you will you will misappropriate resources.

[00:18:25]Okay? And you will end up not allocating it's already scarce resources to to to to to where they rightfully belong.

[00:18:36]Okay? Because resources are scarce, every decision that we're making as a government, as a university, as as a as a city, as a municipality, as as as a family, as a household, or as individuals has to be informed.

[00:18:57]Okay?

[00:18:59]Yeah.

[00:19:00]So, it's just like it's an individual, right? You know your means of income. I mean, you you know your income.

[00:19:06]And you can't afford not to Whether you're buying something or you're investing in something, you need to think critically and then gather some data points, right? You need to have a basis for the action that you're taking.

[00:19:19]So, that's essentially it, all right?

[00:19:21]So, normally we call this the statistical pipeline.

[00:19:26]The statistical pipeline, okay? These are five things. So, as we move on in the course, when I say statistical pipeline, I want you to think about these five different phases.

[00:19:37]All right? The collection of data, the organization of data, the analysis of data, the interpretation of data, and then the presentation of data. Okay? And again, why are we doing all this?

[00:19:51]To help stakeholders like yourselves and I make informed decisions. And like I said, informed decision means evidence-based decisions, decisions that are data-driven.

[00:20:04]Okay? Data-driven decisions.

[00:20:08]So, let's take them one by one. I mean, as we move on in the course, we'll actually spend a lot more time talking through each each one of them.

[00:20:16]But, for for now, let me just give a a quick overview of each one of them.

[00:20:22]When we take collection of data, all right?

[00:20:26]You're collecting data. Collection of data simply means or simply involves the the process of obtaining the process of obtaining data from its origins or sources.

[00:20:47]All right? The process of obtaining data from its origins or sources.

[00:20:54]Now, we know what data is.

[00:20:58]Although, if we move as we move along, I'll give you a more technical perspective of what data is, but I'm sure at this point, if I'm to ask the class, what is data? All of you will tell me one thing. Data is raw information.

[00:21:14]But then the question is, what if I ask you what is information? Then you will tell me information is processed data.

[00:21:21]Then again, what is data? Data is raw information. Then again, what is information? Information is processed data. So in other words, you're using information, which is also another big word. You're using information to explain data.

[00:21:38]And you're also using data to explain information. And it's like this unending pendulum, you know, that that just keeps swinging back and forth.

[00:21:47]But as since this is the very beginning, it is fine for now to think of data as raw information, okay? Unprocessed, unrefined information. For now, it is it is all right to think of data that way.

[00:22:01]All right? But as we move ahead, you would you would appreciate data in a more holistic sense.

[00:22:08]All right?

[00:22:09]Good. So again, collection of data involves the process of obtaining this data, okay, from its raw sources or origins.

[00:22:22]All right?

[00:22:23]And as we when we talk about as we move on, we'll understand a bit more as to what we mean by the origins and then the sources. All right?

[00:22:35]Number two. When you collect that data, normally, the data is is raw. I mean, that's why it is data, right? It's raw.

[00:22:46]So anything that's raw is a bit dirty, right? It's it's not clean.

[00:22:54]So what do you do? You need to do some cleaning. You need to do some laundry.

[00:22:57]You need to do some washing to to to to to it look good.

[00:23:03]All right? It it it's in very late times. So, organization of data involves the classification or categorization or sorting of data into refined forms for further processing.

[00:23:22]Okay? Organization in in in in involves the the process of categorizing, classifying, or sorting data into refined forms for further processing.

[00:23:35]So, let me give you an example. Let's suppose that a political agency or party comes to campus, right?

[00:23:43]ATU, and decides to meet with the student body.

[00:23:49]And the reason for coming to see you is to take your opinions, take your concerns about what you would like the next government to do for tertiary students.

[00:24:04]All right.

[00:24:05]Now, ATU is about 20 25,000 thereabouts.

[00:24:12]Supposing that they're able to engage with all 20 25,000 people, Kwame will say this, Ama will say this, Fosuaa will say this, Kwame and I will say this. So, all the 20,000 people would have their turn and and say something.

[00:24:29]Okay? You see, that is raw information.

[00:24:32]So, they've come to collect data. So, that is raw information. It is raw because these are these are thoughts of individuals and they've not been refined. They are not filtered in any way. Okay? And you are the sources. The university is therefore the source.

[00:24:46]Okay?

[00:24:47]Now, the question is for this political party to actually make sense of all the 20,000 views, it's it's impracticable for them to just take the 20,000 views and and and and run with it and say that they want to implement it. No.

[00:25:08]What they have to do is to organize the data, okay? So, by organization, they would do some classification or some some categorization and then some sorting.

[00:25:23]Okay? So, you would realize that at the end of the day, 20,000 people have spoken, but you may realize that oh, I can actually bottle their views into, let's say, just three silos.

[00:25:40]Right? Maybe a part of the student body uh more interested in let's say, infrastructure.

[00:25:49]They say that the next government, when when we come, infrastructure ture.

[00:25:58]Right? They're saying that the next government, when we come, we should build a lot more, you know, infrastructure and then uh so, this could mean maybe even more institutions, more departments, more faculties, more hostels, and so on and so forth. All right?

[00:26:15]Then, after looking at the data from 20,000 people, you may also realize that though it's 20,000 views, but there's also a section which is basically saying the same thing. Maybe these people, they're more interested in let's say, educational let's say, financial aids.

[00:26:40]Financial aids.

[00:26:51]So, by financial aids, I mean things like maybe scholarships, bursaries, some advances, educational sponsorship schemes, and so on and so forth. All right? Just to alleviate the plights of the economic plight of students.

[00:27:10]Then, if you read through the 20,000 maybe comments or or or views, you may also realize that, okay, maybe this So, maybe we have what? Group A, Group B, and then Group C. Okay, you may also realize that there's one group which is also interested in let's say um So, let's say infrastructure, financial aids. What what else are students having interested in?

[00:27:48]What what is the other group?

[00:27:50]Say it again.

[00:27:52]Bundle. Bundle.

[00:27:54]What? Bundle?

[00:27:58]Did you say bundle?

[00:28:03]I want to find I'm not I'm not hearing you, but anyway.

[00:28:07]So, So, so interesting. So, we well, let's say bundle all those things can be part of infrastructure, right? Because it means that when the government comes, they need to build more telecommunication masts and things like that. So, so bundle can come under under the infrastructure, and then financial aids, and then let's say general um maybe let let's call this well-being.

[00:28:43]All right? Let's make it industrial industrial corporations.

[00:29:02]Okay, students want students want industry to participate in their curriculums as much as possible.

[00:29:09]So, by that, meaning that because of the the the the the the unemployment situation, students would like every now and then for industries, right? Companies and so on and so forth, to come to campus to give talks and to to to to to to do symposiums and things like that. Okay, so the students can get the chance to build networks ahead of their graduation or completion. Okay? So, you realize that the raw data set, once you are doing organization, you're able to bottle them into some groupings. So, in that regard, as a as a as a government, it's very easy for you to prioritize, okay, and and focus on them than to look at 20,000 views and opinions individually.

[00:30:07]Okay? So, we're saying that after collecting the data, the 20,000 views, now organization involves the process of classifying, categorizing, or sorting of the collected data into refined forms.

[00:30:24]But, this is not the end point, okay?

[00:30:26]So, for further processing, okay, for further processing.

[00:30:30]>> [snorts] >> Good. Now, let's look at analysis.

[00:30:34]Analysis simply is the investigate in investigation or so the in-depth investigation or interrogation of data to uncover insights.

[00:30:52]Okay, that the interrogation or in-depth investigation of data to uncover relevant insights.

[00:31:03]All right. So, now that you have done some refinements, you know, by way of organizing your data, you now want to understand what the data is telling you.

[00:31:16]Right? So, you are interrogating the data as if to say the data is is a is a human being standing in front of you.

[00:31:24]Okay, so you're you're interrogating the data or you are investigating the the data to see if you can uncover insights.

[00:31:35]Okay? You see, the whole point of research is to solve a problem.

[00:31:41]All right, we're trying to solve a problem or we're trying to understand a certain phenomenon.

[00:31:47]Okay, we're trying to answer a question of why is something happening?

[00:31:52]Why is something the case?

[00:31:54]Why are we facing a particular situation as a country?

[00:31:59]Why is this happening?

[00:32:00]And so on and so forth. So, you can only answer these questions when you subject the data to scrutiny.

[00:32:09]Okay, you're scrutinizing the data.

[00:32:13]And this is where quantitative methods comes in heavily. Okay, because there are methods there are methods that we'll be studying to help us investigate, to help us interrogate, to help us scrutinize the data. Okay, so that we can understand or we can uncover these insights from the data.

[00:32:35]All right, good.

[00:32:38]Now, now that you've collected the data, you've done some organization, you've done some analysis, keep in mind, you are the technical person.

[00:32:50]But we don't What typically when you carry out research and you do the analysis, you come up with some findings.

[00:32:58]All right? But we need to understand these findings, okay? So interpretation is key. Interpretation is key for both yourself as the researcher and then also for your target audience.

[00:33:10]If you yourself don't understand what you've analyzed, how can you explain it to someone else?

[00:33:16]All right?

[00:33:17]So, interpretation involved is the process of deducing meanings.

[00:33:26]Okay, is the process of deducing meanings from the findings of the analysis.

[00:33:33]Or is the process of deducing meanings from the outcomes of the analysis.

[00:33:39]All right? So, that that's that's just about it.

[00:33:45]Then, we come to a very vital part, which is presentation.

[00:33:50]We don't conduct a research to sit on it or to put it under our beds and and sleep on it. Okay? Research is for the consumption or research is meant for human good.

[00:34:03]Okay? We conduct research to help us understand a particular problem in our society, in our governance, in our institutions, and so on and so forth. All right? In our companies or organizations of work, et cetera.

[00:34:21]So, you've collected data, you've done some organization, you've done the analysis, you've done the interpretation.

[00:34:28]We now need to disseminate the findings so that it could be widely consumed.

[00:34:37]Okay, for for societal benefit.

[00:34:40]So, for example, let's say you wake up one of these days and you are the the the board secretary the board secretary for let's say Tullow Oil.

[00:34:54]Or you are the board secretary for AngloGold Ashanti.

[00:34:57]All right?

[00:34:59]Now, they have an annual meeting coming up.

[00:35:02]Let's say sometime in December.

[00:35:07]And you need to you need to you done some research on the company's productive capacities over the past quarters. Okay, from January from the first quarter, second quarter, third quarter into the final quarter.

[00:35:23]All right? But you see, you are the technical person. You are using so many technical tools and quantitative methods to do your analysis and everything. But the people that you're going to that will benefit from your work may not be as technical as you. So, you need to find a very intelligent, a very understandable way of explaining what your findings are without being too complicated. So, that's why interpretation is key. Now, presentation here presentation here, right? has to do with It's not just about wearing a suit or wearing you know, dressing nicely to go stand in in front of people with a PowerPoint slides, you know, beautifully animated and then you say you're doing a presentation. Yes, that is a presentation but that is not the only definition for a presentation. Here, what we say presentation, we mean disseminating.

[00:36:26]Okay?

[00:36:27]The process of disseminating the findings of the research.

[00:36:32]Okay, disseminating the findings of the research. When you're disseminating something, you are making it widespread.

[00:36:38]You're making it publicly available.

[00:36:41]All right?

[00:36:42]So, presentation can be a physical presentation, like a formal or a corporate presentation where you're standing in front of people to deliver a presentation. It can also be in the form of a written report.

[00:36:57]Okay?

[00:36:59]It can be in the form of coming to radio stations and television stations to explain a certain finding.

[00:37:08]And so on and so forth.

[00:37:10]All right?

[00:37:11]So, that's just about it for the statistical pipeline. So, we do all these things to help us make informed decisions. Are there any questions?

[00:37:41]Are there any questions or general comments?

[00:37:46]No, sir.

[00:37:48]It goes.

[00:37:49]No, sir.

[00:37:51]No, okay.

[00:37:52]Okay, that's fine. So, then we would proceed.

[00:38:11]Okay.

[00:38:13]So, the next thing that we would look at is the the various aspects of statistics.

[00:38:38]Uh what you would call uh the types of statistics.

[00:38:43]All right?

[00:38:45]Or the schools of thought in statistics.

[00:39:00]So, we have You know, all statistics can be categorized into two. Okay? So, we can we we have Just a second.

[00:39:50]Okay. So, we have types. Okay? Or or aspects of statistics. So, we have >> So, we have number one.

[00:40:41]We have descriptive statistics.

[00:41:05]Descriptive statistics and then we have inferential statistics.

[00:41:35]All right, descriptive and inferential statistics.

[00:41:39]What is descriptive statistics?

[00:41:46]So, with descriptive statistics, right, we uh So, with descriptive statistics, it it involves the summarization of data.

[00:42:07]Okay, so, involves >> summarization of data.

[00:42:28]Okay?

[00:42:29]Using using quantities.

[00:42:47]Or using verifiable quantities, okay? Or objective quantities.

[00:42:52]All right, so you can insert it there.

[00:42:53]It involves the summarization of data using verifiable quantities or objective quantities such as such as means such as means and medians.

[00:43:31]Or if you like, I can make it a bit more uh technical. So, we'll look at means and medians and all that, okay? But, let me just maybe refine it a little bit.

[00:43:42]So, it involves the summarization of data using quantities such as central tendency and >> dispersional measures.

[00:44:18]And central tendency and dispersional measures actually is a is a topic, okay, that we would we would treat together.

[00:44:25]But I just want to, you know, give you a heads-up.

[00:44:29]So, with descriptive statistics, okay, we are basically using We we're basically interested in summarizing data using quantities.

[00:44:42]Okay?

[00:44:43]So, for example, for example, if I if I come to class right now and then I collect all of your ages, all right? Let's say there are about 50 people in the class. So, when I collect all of your ages and I strike the average, okay? When I strike the average, I would say X bar. And don't worry about these things, right? I mean, when when we start doing the calculations, you would understand what these things mean. So, when I say X bar into brackets, so, X bar subscript age, okay? So, this into bracket means the average age.

[00:45:28]Or let me say the mean age.

[00:45:43]So, when I say, you know, so, when I collect the data and then I find the average and I I I I come up with a number, I say X bar is, let's say, 25.

[00:45:57]This is a descriptive statistic.

[00:46:01]Okay? Because it is a data summary and I'm using a central tendency measure.

[00:46:06]Okay, this X bar is a mean. Mean is a central tendency.

[00:46:11]All right. So, this is descriptive statistic.

[00:46:17]All right.

[00:46:19]So, basically, descriptive statistic is very objective.

[00:46:25]All right, it's very objective. So, whether I am the one who comes to class to measure the the the age of members in the class and then find the average or somebody else comes would all arrive at the same 25 years if only we're doing the computation correctly.

[00:46:42]Okay, so descriptive statistics basically is telling the situation as it is.

[00:46:48]All right. So, descriptive statistics is the is the aspect of statistics which involves the summarization of data using quantities.

[00:46:57]And examples of those quantities are what central tendencies and dispersionary measures. Okay, and I've given you an example of a descriptive statistical statements. Okay, when I say X bar is equal to 25 or an example, if I say um X bar um income we normally use Y for income, right?

[00:47:24]So, X bar income or let me just write it in full.

[00:47:27]Just so that in case you are taking notes you you you're not be confused later on.

[00:47:34]Where So, let's say X bar income.

[00:47:40]Okay, so this is what average or let's say mean income.

[00:47:49]Supposing you were a company and I come to class, I take all of you your your salaries or for incomes and then I find the average or the mean.

[00:47:58]Okay? And then let's say I come up with a value.

[00:48:02]Let's say the average is 3,000 Ghana cedis.

[00:48:06]For example.

[00:48:11]Okay? This is also a descriptive statistical statement.

[00:48:16]All right? You are you are you are using a quantity you are using quantities, okay? To summarize some data in a given situation.

[00:48:28]Okay? So, these are two examples of descriptive statistical statements.

[00:48:34]All right? Now, let's move on to talk about inferential statistics.

[00:48:41]Can I can I move to the next page? I think we've run out of Can I move on?

[00:48:59]Now, let's look look at inferential statistics.

[00:49:55]>> Okay, so with inferential statistics that involves Yes, sir.

[00:50:01]Okay.

[00:50:03]Now, the next thing I want us to talk about is you see so far everything that we've been saying is revolving around data, data, data, data, data.

[00:50:12]All right, data.

[00:50:15]Now, what are the the decompositions of data?

[00:50:21]Right? What are the constituent parts of data?

[00:50:26]So, I want us to look at that next.

[00:50:28]In the way that you know data to be raw or unprocessed information, but as we go on as we go on your understanding would would expand. Okay, on on exactly what constitutes data.

[00:50:40]So, let's first start by looking at characteristics. I mean, the what a variable is. Right? So, a variable is a characteristic that possesses different numerical values.

[00:50:54]Different numerical values. So, for example, if I say I want to write in this area. Uh just a second.

[00:51:04]Yeah.

[00:51:05]So, if I say for example X Wait, that thing is too it's too big.

[00:51:25]Okay.

[00:51:26]So, if I say that If I say for example X is equal to 95,000 for example X is a variable. All right. X is a variable, or tomorrow. Maybe today X is 95,000. Tomorrow X will be 15. Tomorrow X will be 72 and so on and so forth. All right. But instead of even using X, let's say that we're collecting some data, okay? And typically when you collect data, there are different variables in there.

[00:52:09]All right. So let's say you have I'm collecting some data on members of you know, the SMS 209 class, okay? So let's say I'll have I'll collect data on your ages.

[00:52:24]Uh what other information can I collect on you? Let's say age, weights, heights.

[00:52:45]Okay. And then well, let's say temperature.

[00:52:49]complexion Okay.

[00:53:03]Good.

[00:53:04]So, it could be So let's say if there are Let Let Let's assume there are five people in the class. So, individual one, two, three, four, five. Maybe Kwame Owusu, uh you Memuna and so on and so forth.

[00:53:23]Okay, five people. So, somebody may be 19, 21, 25, 24, and then 20.

[00:53:39]Okay.

[00:53:40]Somebody's weight can be what? 60 at 19 years old. Let's say you are about I don't know. Well, it depends on your feeding.

[00:53:51]So, let's say 50 kg. This might be 60.

[00:53:58]This 25 might be let's say 75.

[00:54:02]Let's say 74.

[00:54:05]And then let's make this 55.

[00:54:11]Okay, height.

[00:54:13]Uh at 19 years old depending on your genetic makeup, maybe you're about 5.

[00:54:23]Uh or sometimes 4.9, 5.23 there about.

[00:54:27]Anyway, so you get the drift. I can populate this area. Okay, let's say we have some heights.

[00:54:36]We have some heights.

[00:54:40]Okay, for all these people.

[00:54:42]You realize that for individual one, individual one, individual two, individual three, individual four, individual five, they all have age, weight, height, and then temperature.

[00:54:54]But you realize that it changes. Age is not just one thing.

[00:54:59]Okay, and weight is not just one thing.

[00:55:01]Height is not just one thing.

[00:55:03]Temperature is not just one thing. Okay, so we call these things the age, the weight, the height, the temperature. We call them variables.

[00:55:13]We call them variables. Okay, that's why we are saying that a variable is a characteristic that possesses different numerical values or categories.

[00:55:25]Okay, so the same age is it's change it's changing from 19 to 25. Okay, the same weight it's changing across different people. The same height is changing. So, because it's not static and changes, we call it variable.

[00:55:41]Variable meaning it varies, okay? It changes.

[00:55:45]Okay? So, different numerical values or categories. In fact, we can even add this another variable, uh gender.

[00:55:52]Okay, gender.

[00:55:59]Okay, gender.

[00:56:01]So, maybe the person one is a male, the second person is also a male, we have a female, male, and then finally another female.

[00:56:17]So, you realize that the same gender, but it is not one thing. The moment you have just one thing, then we can't even call it a variable, then that becomes a constant.

[00:56:28]Okay?

[00:56:30]So, once there is some alternation in the value, then we call it a variable.

[00:56:37]I hope it makes sense. So, what I want us to look at is Now, think about it. Variables contain data.

[00:56:47]All right? The 19, it is a data. 21 is a data. 25 is data. 24 is data. 20 is data.

[00:56:55]All right? So, the this variable is storing a series of data.

[00:57:00]The weight is storing a series of data.

[00:57:02]The height is storing a series of data.

[00:57:04]Temperature is storing a series of data.

[00:57:05]Gender is storing what a series of data.

[00:57:08]Okay?

[00:57:09]So, the the variables are like the storage points of data. Therefore, when we are studying the types of variables, at the back of your mind, I also want you to know that the types of variables are the same as the types of data.

[00:57:24]Okay? So, let me do like a stroke here.

[00:57:27]So, variable stroke data.

[00:57:34]Okay, so when we're studying types of variables is the same as types of data.

[00:57:43]Okay, because variables contain data and data are contained within variables. So, their types will be the same. Just that when we're explaining, we we will explain it a bit differently, but that the types structurally are the same. So, let's just look at them.

[00:57:59]Now, every data or variable, okay, in the world can be grouped into two parts.

[00:58:05]We have qualitative data and then quantitative data.

[00:58:11]Okay, we have qualitative data and then quantitative data.

[00:58:15]Now, qualitative data can also be broken down into two parts, nominal data and then ordinal data.

[00:58:24]And then quantitative data can also be broken down into two parts. We have discrete data and then continuous data.

[00:58:32]Right? Let's Let's understand what these what these different decompositions mean.

[00:58:39]Let's start with qualitative data.

[00:58:43]We're saying that qualitative data generally described is generally described by words or letters.

[00:58:52]Okay, words or letters.

[00:58:54]So, normally you see I want you to think of this word qualitative qualities.

[00:59:04]Okay, what are qualities? Qualities are attributes.

[00:59:07]Okay, so normally qualitative data are are are are are data that describe attributes. Okay, and normally attributes are described using words and letters. Okay, so for example, let me even say let me collect data on your names. Okay, if I decide that I'm collecting data.

[00:59:35]Let's say let me create names of members in the class.

[00:59:46]All right, so the main names of members in the class there is There is Kofi.

[00:59:56]There is There is Ama, there is Ya, there is There is some Biffy and then and so on and so forth.

[01:00:14]Right? These are [clears throat] attributes. These are These are These are letters. These are labels. Okay, these are words.

[01:00:21]But they are data.

[01:00:22]Okay? So, whenever you collect data and realize that they can be described or they are describable by words and letters, all right? Then you have qualitative data.

[01:00:35]Okay? So, for example, color, ethnic groups. Let's say if I I can create another data set containing ethnicities of members of the class.

[01:00:43]So, I can create ethnicity.

[01:00:53]So, ethnicities, right? Let's say if somebody is is um uh Let's say Dagomba.

[01:01:08]Dagomba Let's say Ewe.

[01:01:15]Let's say Fante.

[01:01:21]Let's say Asante or or is it Akan?

[01:01:28]Let's say four.

[01:01:30]All right. Again, these are traits.

[01:01:32]These are These are things that are are describing where where group of people come from or or who certain people are.

[01:01:41]All right. And these are all letters and words.

[01:01:45]Let's look at quantitative data.

[01:02:01]Let's look at quantitative data.

[01:02:04]Now, with quantitative data, as the name depicts, we're talking about what quantities.

[01:02:11]Okay, we're talking about quantities.

[01:02:14]So, when you hear quantities, what comes to mind? We're talking about numerical values.

[01:02:21]We're talking of numerical values. So, quantitative data involves numbers and are the result of counting or measuring.

[01:02:32]All right.

[01:02:35]So, for example, So, for example, we have more specific examples. So, again, age.

[01:03:06]Ages of members in a class. So, 24 years old.

[01:03:12]25.

[01:03:14]21. Somebody's study.

[01:03:19]And then maybe so that five members of the class and then let's say someone is two, three.

[01:03:34]All right, two, three.

[01:03:36]So, this is quantitative data.

[01:03:40]Okay, quantitative data.

[01:03:43]Or the the number of the number of buildings in a city.

[01:03:52]Okay, it is a number.

[01:03:54]Okay, so let's say if I have cities, maybe number of buildings in in in different cities in Ghana.

[01:04:06]So, let's say I'm taking five cities.

[01:04:08]All right, so let's say in in in city A, there are 500 buildings. In city B, there are 450.

[01:04:19]In city C, there are 700.

[01:04:23]In city D, there are 1,000.

[01:04:28]And then in city E, there are 890.

[01:04:34]Okay, all these are values, okay? So, what whenever you have a a numerical components in the data set or when the data set is is constitutes numerical values, then you have quantitative data. They are quantities, all right?

[01:04:52]Good.

[01:04:54]Now, let's look at quantitative data. Like I said that that we have two breakdowns.

[01:05:11]Oh, I shouldn't have even erased this example because I would have needed it, but I mean, I'm sure you were taking notes, so I can always refer to it.

[01:05:20]Now, quantitative data can be discrete or continuous depending on two things.

[01:05:27]It depends on countability or measurability.

[01:05:32]Okay? Now, you realize that I can give you two data points. They're all numbers, but still they are different in the sense that the question is if you look at a particular quantitative data, the question is are you able to count or you are only able to measure it?

[01:05:54]So, I'm giving examples here. The number of students in a given class.

[01:06:00]For example, your class, right? If you have 50 students or or 60 students, 60 is a quantitative data point. But how do we get 60? The 60 can be obtained by counting.

[01:06:12]Or the number of books on the shelf, or the number of tables, or the number of chairs in the lecture hall.

[01:06:18]All right? These are countable quantitative values. So, whenever you have a countable quantitative data point, we call it a discrete data.

[01:06:32]On the other hand, you may have some quantitative data points which are not countable.

[01:06:38]Yes, they are quantitative, but they're not countable.

[01:06:40]For example, I mean, in that case, they are they are continuous. Okay? So, for example, if I say what is your height?

[01:06:50]Height, you will tell me, "Well, maybe I am 5'9" or I am 6.1 or you are 4.2.

[01:06:57]Okay? Or you are 6.3.

[01:07:02]But these values, although they are quantitative, but they're not countable. They're only measurable, right? You can only measure heights or let's say your your body weight or body mass.

[01:07:13]You tell me you're 60 kg, 40 kg, 72 kg.

[01:07:19]These are not countable values. You cannot tell me that I am going to count my height or I'm going to count my weight. You only measure. They are measurable.

[01:07:29]Or let's take your body temperature.

[01:07:31]Nobody counts temperature. We measure temperature.

[01:07:34]Okay?

[01:07:36]The atmospheric temperature, the atmospheric pressure. All these things are measurable, although they are values. All right? So so think about it this way.

[01:07:45]Count I mean discreetness or continuity of the data is is based on countability or measurability.

[01:07:52]All right? And you should be able [clears throat] to give examples.

[01:08:06]So I mean these things are readables. I I wanted to So I need to explain now the nominal and then ordinal.

[01:08:16]All right? Nominal and then ordinal. Let Let me explain it this way.

[01:08:23]So think about this. You see nominal, nom nom.

[01:08:28]Anything nom has to do with names, okay?

[01:08:30]It's like French, les noms.

[01:08:32]All right?

[01:08:33]So when we say nominal data nominal data is definitely qualitative data, but it's nominal because it's simply a collection of attributes or names.

[01:08:46]And when I say names, I mean labels.

[01:08:50]Okay? So for example, if you walk into a restaurant, let's say I walk into your your class, your restaurant, SMS 209 Restaurant and Hotel and Services Limited. And then they serve me with a menu.

[01:09:06]Right, I'm served with a menu.

[01:09:13]So let let's create a data set on menu. Let Let me actually go back and use the the the screen.

[01:09:21]Okay. Now, let's suppose that we go to a restaurant.

[01:09:30]And then you are served with a menu.

[01:09:37]All right, you're served with a menu.

[01:09:39]So, you have What kind of foods do you serve in the in your in your restaurant? So, let's say Let's say it's a local restaurant. So, we have fufu.

[01:09:56]Let's say TZ.

[01:10:03]What else?

[01:10:27]The lady who just said fufu that she I can tell you are really Your your your your your your tongue your tongue says a lot. It looks like your tongue has been having a lot of fufu that she the way you actually the way you pronounce it Yeah, you you really you really pronounced it with a with a traditional tongue.

[01:10:50]Okay.

[01:10:51]>> [laughter] >> I see. So, what else? Maybe let's just add uh uh you know, just for just to make it fine.

[01:11:03]This really not local, but anyway. So, if we look at this, okay, for example, if you look at this this menu, the menu contains five different meals. Now, when we say nominal data, nominal data is a type of qualitative data, which constitutes names or labels without any sense of hierarchy in the data set. So, listen very carefully. We're saying that nominal data is qualitative data, which constitutes labels or names without recourse to hierarchy or order.

[01:11:48]All right. So, what do I mean? If you look at this data set, you cannot look at this data set and tell me that fufu, because it comes first, all of a sudden fufu is more important than apple pie, right? Or Sorry. Or let's say Yes, is someone talking?

[01:12:09]Uh sir, please thank you the definition of nominal data.

[01:12:13]Can I ask again? Can I do what?

[01:12:16]The definition of nominal data.

[01:12:18]Of nominal data. Oh, yeah. Yeah, I'm just saying that nominal data is qualitative data, which constitutes names or labels without recourse to order or hierarchy.

[01:12:39]All right. Quantitative data is is quality Sorry.

[01:12:43]Nominal data is qualitative data, which constitutes names or labels without recourse to hierarchy or order.

[01:12:55]All right? So, in other words, if you look at the data, inherently, there is no sense of importance. There's no sense of relative importance, all right?

[01:13:04]They're all the same.

[01:13:06]Okay? Being Being Banku is not all of a sudden more important than beans or beans is not more important than tizi or, right?

[01:13:14]They're all foods that people like. So, depending on who you are, you would choose or you'd have preferences.

[01:13:21]All right? Yeah.

[01:13:23]On the other hand, if we take ordinal data, okay? So, here, you see the keyword is the the num, okay? So, nominal, num.

[01:13:33]Now, here the keyword is ordinal, so ordinal, ord.

[01:13:37]Okay? So, this is the opposite. Ordinal data is qualitative data, which constitutes labels, also constitutes labels, but with recourse to order or hierarchy.

[01:14:00]Okay? With recourse to order or hierarchy.

[01:14:04]And And I'll give you an example, so you understand.

[01:14:23]Let's take Let's take for example, now that you've gone to the menu, right?

[01:14:29]You've gone to the the the restaurant, they've given you, you know, this menu, you've taken your meal, you are done, and then all of a sudden, you know, a a lady or a gentleman walks up to you, and they say, "Thank you for patronizing our services.

[01:14:44]Uh we We you to rate us." Okay? And then maybe they give you a customer satisfaction form.

[01:14:50]Okay, so on the customer satisfaction form, they have the following.

[01:14:54]So, let's call this a ratings data.

[01:15:05]All right, so let's call this a ratings data and then they have let's say average, excellent, average, excellent, what else?

[01:15:30]Poor.

[01:15:35]Sorry.

[01:15:41]Poor.

[01:15:45]Good.

[01:15:50]And then fair.

[01:16:04]Okay.

[01:16:05]Now here, without even you being told, you realize that there is Yes, they are they are qualitative in nature, but there is a sense of hierarchy.

[01:16:15]No matter how shuffled they are, there's a sense of order.

[01:16:19]You and I know that excellent is better than good.

[01:16:27]And then what? Good is better than average.

[01:16:31]And average is better than fair.

[01:16:35]And fair is also better than what? Poor.

[01:16:38]Right?

[01:16:40]So, here because there is a sense of order, there's a sense of order.

[01:16:45]There's a sense of hierarchy.

[01:16:47]Or, there's a sense of relative importance.

[01:16:52]So, we call this ordinal data, ord- ord- ord for order, okay? Just to help you remember. And nominal is just nom- is just the names. It There's no sense of importance, right?

[01:17:08]I believe it makes sense.

[01:17:13]Yes, sir.

[01:17:14]Okay. Let us just take one example. So, another one is, for example, um Let's even take academic qualifications.

[01:17:43]Academic qualifications.

[01:17:46]All right. Academic qualifications, I mean, there are lots.

[01:17:52]Let's say, if I if I create a data set containing uh let's say, let's say, a bachelor's degree.

[01:18:06]So, a BTech, a BSc, a BA, a BB, okay? These are all types of bachelor's degrees. Uh a BEng, okay? So, we have BEngs, also. So, but let me constitute them and just make bachelor's, okay? So, if I put everything in there, um in general, there there are so many academic qualifications, but we know that in general, a a paper is is a bit lower than a certificate.

[01:18:43]And then also a certificate is lower than a diploma.

[01:18:47]And a diploma is lower than a higher national diploma.

[01:18:52]And a higher national diploma is lower than a what you call it, a bachelor's degree.

[01:18:58]Okay?

[01:19:00]And then a bachelor's degree is also lower than a master's degree.

[01:19:05]And a master's degree is also, you know, PhD is is higher than a master's degree.

[01:19:12]Okay? So, if I write all these things in here, master's, bachelor's, all these degrees, though they are words, though they are qualitative, but they are inherently connoting a sense of relative importance or order or relative hierarchy.

[01:19:34]All right?

[01:19:35]Yeah. That's also another another example. An another example I can also give is, you know, you're doing organizational Are you doing a course in organization?

[01:19:47]organizational management or something?

[01:19:49]Are you doing something like that?

[01:19:52]Yes, sir.

[01:19:53]Yes, sir.

[01:19:55]Okay. So, so have you done Do you know about an organogram?

[01:20:01]Have you heard of >> Yes, sir. Yes, I have.

[01:20:03]Have you heard of organogram?

[01:20:06]What is organogram? It's not that thing.

[01:20:10]It's organizational structure.

[01:20:14]Do you Have you seen this word before?

[01:20:19]No, sir.

[01:20:20]Okay. So, maybe maybe you'll come across it in due course of your studies.

[01:20:25]An organic An organogram is simply um a hierarchical structure of an organization. So, normally it looks something like this.

[01:20:35]Let me erase the screen.

[01:20:54]All right.

[01:20:55]So, an organogram looks something like this.

[01:21:00]Okay, normally in organizations you have what? The chief executive officer, you know, maybe coming at the top. So, let's say CEO, followed by let's say the managing director.

[01:21:14]Then these are directors.

[01:21:23]Okay, then maybe you have line managers, the LMs.

[01:21:33]Line managers.

[01:21:36]Then you have maybe staff.

[01:21:44]I mean, this is a this is a this is an overly simplistic version. Normally a typical organizational structure would go all the way maybe about eight or nine steps. Okay, so maybe even So, let let instead of staff, let's call the supervisors, okay? Then I can I can break this down further.

[01:22:03]Maybe every supervisor is is supervising maybe some team lead. Okay, TL.

[01:22:19]And the team leads have what? Staff.

[01:22:29]All right, so it goes on and on and on and on. This is a an organizational structure. We call it an organogram. Okay? So, for example, if I create a data set, all right, and I call it org structure or my org or my organogram, and then I put in CEO, MD, director, supervisor.

[01:22:50]Though these are words, they are qualitative, but they have a sense of hierarchical attributes. And so therefore, they would be ordinal data.

[01:23:02]Okay? So, so that's just about it on the classifications for data and variable.

[01:23:10]Now, recall, okay? Recall that we said the first point in the statistical pipeline is what? Data collection.

[01:23:21]All right, data collection. And we said that data collection is the process of obtaining the data from its origin or source, its origins or sources.

[01:23:34]All right? So, where is that origin or where is that source? Where will we will we go and collect that data from?

[01:23:41]All right? We call that place a population.

[01:23:45]Okay? The population.

[01:23:47]So, I I think everybody knows what a population is, but normally when I ask you, you tell me that a population is what the uh the total number of people living in the country. Well, that's correct. However, that's only that's a limited definition.

[01:24:02]In the in in in in the context of quantitative methods, when we say a population, we're not just talking about human beings.

[01:24:12]All right? Not just human beings. We're talking about human beings and non-humans.

[01:24:19]All right? So, in general, a population is a is is the totality, okay, or the collection of units or elements within a domain.

[01:24:33]Okay, typically over a period of time.

[01:24:36]Okay, it's it's the it's the collection or the totality of units or elements within a domain over a given period of time. So, you realize that in this particular statement I did not say anything about country or people, but a country or people can still fit in there.

[01:24:54]All right, because the units or elements that I made mention of uh the if it's a country, they will be the individuals. Right? And then the domain that I I made mention of would would be a country if you know, that's what we're referring to. But, it could also mean everything else.

[01:25:15]All right? So, we can talk about the population of a country. We can talk about the population of a university. We can talk about the population of cars in the ATU parking lots.

[01:25:26]We can talk about the population of of of bees in a hive. We can talk about the population of trees in a forest.

[01:25:35]We can talk about the population of What else?

[01:25:43]Population of buildings in a city.

[01:25:53]Okay.

[01:25:55]Hello.

[01:25:56]Yeah. We can talk about populations of buildings in a city.

[01:26:01]We can talk about the population of chairs in a class. We can talk about the population of I mean, tables in in a particular building and so on and so forth. Okay?

[01:26:12]So, these are all things that we can we can attribute to population.

[01:26:18]So, these are some examples that I'm giving here.

[01:26:22]Now, a population can either be finite or infinite. When you have a finite population, it means that it's it's limited in the number of units. Okay, it's countable.

[01:26:32]Okay, for example, like countries or or or university populations or even class populations. It's possible to count. So, these are finite populations.

[01:26:44]Infinite populations are limitless in number.

[01:26:49]Okay.

[01:26:51]Like we say the infinitude of the wisdom of God. It means that you cannot place a boundary on on the on the majesty of of the almighty. Okay, this is wisdom and you know, is infinite. You know, beyond the expanse of the universe. So, anything that's infinite is boundless or limitless. So, in the same way when we say we have an infinite population, this is this is a population which is composed of a limitless number of elementary units.

[01:27:20]Okay. So, for example, sea, you know, fishes in the sea, it's not possible to count.

[01:27:28]At least not now with the current technology available.

[01:27:31]Grains of sand.

[01:27:33]Okay. Grains of sand in a particular from a shore.

[01:27:37]You know, other particulates matter.

[01:27:40]So, these are the different types of populations. But often times in this course, in fact, in this course, we'll be dealing predominantly with finite populations.

[01:27:51]Okay. Now, the final thing I would say then I would draw down the curtains is this.

[01:27:56]You see, if we're collecting data, okay, we ideally we should go to the population. But think about it. Let's say that in ATU there are about 20,000 students. You're going there to collect data. Even if it takes one Ghana CD to print a questionnaire for each participant, that means you need about 20,000 Ghana CDs just for data collection, right? Are you following? You need 20,000 CDs just for data collection.

[01:28:25]Which one will be prudent? If you're spending 20,000 on data collection, how much would you actually spend on establishing the business for which you're collecting the data? Okay? So, because of this, we have to resource to something called a sample.

[01:28:42]A sample is a subselection, a representative subselection from a population.

[01:28:49]Okay? Now, we select samples in such a way that it gives us a reduced number, a reduced number, but we can use that reduced number to still draw meaningful inferences about the population at hand.

[01:29:03]In other words, instead of going to engage with 20,000 people and waste money and also waste time, statistically, it is possible for us to use a smaller number of people to save time, to save money, but also derive credible insights.

[01:29:23]So, we call that a sample, and the process of deriving this subselection is what we call sampling.

[01:29:30]All right? So, in our next meeting, in our next meeting, we'll be studying sampling techniques.

[01:29:37]Okay? Sampling methodologies. Exactly how do we do the sampling?

[01:29:41]Okay? So, we'll look at probabilistic sampling and then non-probabilistic sampling, and then we'll look at the different types, okay, of probabilistic sampling and then non-probabilistic sampling, and then we we move on and on.

[01:29:52]So, if there are no questions, I thank you very much. I'll meet you next week, okay, as the Lord wills.

[01:29:58]Have a pleasant day.

[01:30:01]I mean, I just say Okay. Bye.

[01:30:05]Bye.

[01:30:06]Bye.

[01:30:07]Have a nice day. love you, baby.

[01:30:11]I love you, baby.