3.1.1 Sampling Methods

Added: 2026-06-02

[00:00:00]in this section of notes we're gonna look at some basics on how to conduct surveys and how to get the people in your sample for those surveys so there's a lot of vocabulary here so the first word is population and that is like the entire group that you want to try to find out about the census would be if you are trying to try to collect data from all of those people which we typically don't do for many reasons because it's pretty challenging to try to track down everybody and then there's also a sample which is more common which is where you try to take some subset of the population and you want to collect information from them so your population is the whole group the sample is a subgroup and we want to collect data from the sample so that we can apply the same findings of the sample to the population one thing to add here there's also another group in here called a sampling frame a sampling frame is like a list of people that you're choosing your sample from so for example let's say you wanted to try to make some predictions about how people might vote in the next presidential election while your population would be all of the registered voters in the country your sampling frame would be some sort of a list of those people and then your sample would be the people that you picked from that list now a lot of times the sampling frame is the same as the population sometimes you don't have a list of everyone so sometimes your sampling frame is limited in that there are fewer people on the list than there are in the population now two other vocabulary terms that are important here are the idea of a statistic and a parameter statistics and parameters are essentially similar things they're summaries so like maybe you find the mean or maybe you find a proportion and then the statistic is just the mean of the sample or the proportion of the sample and then the parameter is the mean or the proportion of the population so if we're talking about the who you're gonna vote for example again with an election if we maybe set our statistic was we took a sample of a hundred people and 60% of them said they were going to vote for the current president to be reelected that 60% is a statistic if I think that's also true for the population then that 60% would be the parameter so a statistic and a perimeter are similar it's just that the statistic described a sample and the parameter describes an entire population so next we'll take a look at how you go about taking a sample so there's three steps here the first thing you have to do is you have to define the population that you're interested in and then you want to find out exactly what do you want to measure so do you want to know what percent are going to vote for the current president to be re-elected or you might ask what is the average number of steps that high-school students take per day since everyone's measuring their steps with their pedometers in their their smartwatches and phones and then a sample survey is our method of data collection for this type of question where we would just ask people what it is that that they're gonna do so how are they gonna vote how many steps did they take on average over the last week something like that and then last you're gonna describe how you're going to pick your people so how are you going to do that you've still got it you've got maybe a thousand people in the high school if you're gonna try to estimate the average number of steps per day taken by a member of our school community how are you gonna pick say 50 of them now there we'll start with some things that you don't want to do so there are some bad ways to do a survey and then there are some good ways to do a survey one bad way to do a survey is to do a convenience sample a convenience sample is just asking people who are easy to find so maybe if you wanted to estimate the average number of steps that someone in our high school takes every day and you just ask everyone in your 1st block class that would be a convenient sample and that results in biased responses so it's not necessarily representative because maybe you're a senior and your first block is filled with zine with seniors and maybe seniors take more or less steps than say freshmen or then teachers so you want to make sure that however you get your sample the whole population is somehow representing otherwise you get bias in your results which means that the answer you get from your survey doesn't match the true answer so maybe you asked all of your 1st block classes and they said on average we take 8,000 steps per day but then if you were to really look at everyone maybe that number could possibly be different more or less than 8,000 that would be bias another bad way to do a survey is voluntary response this is when participants choose whether or not they are going to be in the sample a common example of this is a lot of times grocery stores or other stores sometimes will print off a receipt for you when you shop there and then at the end of the receipt it says call in and take this survey and you have the choice of whether or not you call in and do that the reason that this is biased is because people who either had a really great experience that day at the store or really bad experience they're more likely to call in than someone that just had an average experience so you end up getting again a biased result so now we'll look at how to sample well so what you want to do is you want to do something random so you want to make sure that everyone has an equal chance of being selected and if that's the case then your sample is and that helps to reduce bias there are lots of types of random samples and then there are subtypes that are specific kinds of random sampling so the first kind of subgroup the first type of random sampling that we'll talk about is a simple random sample of size N and is going to be a number so maybe you'll say a sample of size 10 which means you're going to pick 10 people at random or a sample of size 50 those would be the lower case n whatever however many people you're picking is your sample size now there is a separate video that I'll have you watch later on how to do a simple random sample on your graphing calculator but for now we're going to start with how to use the table of random digits this is located at the end of your formula packet and we'll look at how to do that first so if you're using technology that would be where you're using your calculator again there's another video for that or you could do a website like random org they have ways to pick random numbers and what you would do is you would take all the people in your population and you would label them from 1 to capital n capital n is the number of people in your population and then you would use the calculator or use random.org or some other digital way to do it and that's how you would pick your lowercase in your sample size number of people versus if we're going to use table D which is our table of random digits you still kind of start by labeling everyone and when we say use as few digits as possible for example if you are gonna pick from a population of 20 people then that's two digit numbers so you have to have like 1 would be 0 1 2 would be 0 2 so you want to try to reduce things as much as you can that way you're not skipping digits so for example if you were only picking a number within two digits you wouldn't want to go to three digits because you to skip more you'll see what I mean here in a moment picking some way to do this at random so you'll pick a random place in your table to start and then you'll read straight across the table you'll want to skip repeats if it doesn't make sense for your problem and you'll want to skip over numbers that don't match up with a person in your sample and then you'll keep doing that process until you have the number of people that you need so again that's a little weird just to see the the description but let's look at an example to make more sense of that so here are a bunch of hotels there are 28 of them and I want to pick four of them the line that you see and kind of the pink pinkish purplish box that's like a line from your random number table it's from line 130 so I picked a random place to start and that's the line from my random digit table so since I have 28 hotels I'm gonna be working with two-digit numbers so I'm taking this list of numbers and splitting them up into two digits at a time notice how the space after the fifth digit so there's like a 5-1 and then there's a space and then there's a six for that space doesn't really matter you can see the one that was the fifth number and the six that was the six number come together and make us 16 so you take all of these values here and you make them into two-digit numbers because our list goes from 0 1 2 to 8 so I'm working with two-digit numbers there next I would start going across so 69 is not a number on my list my number my numbers only go up to 28 5 is a number on my list and it corresponds with the beach Castle Hotel so I'm going to pick that one as one of my 4 and then I'm gonna keep doing this until I get a total of four hotels skipping over numbers that don't make sense and if I would happen to get a repeat like here I get 17 again so I'm gonna skip over that repeat and then I keep going into eventually I'd get one that's not a repeat and I have my four total hotels now in terms of your random number table sometimes you might have to wrap around to the next row of your table that is a possibility so our C our random sample ends up being Beach Castle Radisson Ramada NC Club don't forget to watch the video on how to do a simple random sample on your graphing calculator and then try the practice problems before moving on to the next section of notes