ASO STATISTICS | PYQ | IMPORTANT QUESTIONS | ASSISTANT STATISTICAL OFFICER | ASO ONLINE CLASSES|RSB

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[00:00:09]Hi Andy. So previous year's question pap if two observations are 10 and minus 10 their arithmetic mean is okay. So arithmetic mean formula summation x i / n okay formula. So two observations. So sum of observations.

[00:00:39]So first value for when you remove the summation you have to take the plus sign divided by observations 1 2. Okay. So 10 plus into minus min - 10 by 2. So 10 - 10 is 0 0 by 2 0 by 2 is 0. Okay. So arithmetic mean two given two observations. Okayus options option one 10 option two five option three one and option four zero.

[00:01:20]So option four. So option four zero is the correct answer for this question. Okay.

[00:01:29]Next.

[00:01:32]Okay. If all the observations in the data are the same then okay.

[00:01:42]So option meanal is equal to mode. Next is greater than or equal to is greater than or equal to mode. Next mean is less than or equal to median is less than or equal to mode. Next median is less than or equal to mean is less than or equal to mode. Okay. So already same data med and for the same data I have calculated the mode and I got the answer is zero.

[00:02:25]So in these cases mean equal to median is equal to mode which is equal to zero.

[00:02:31]So if all the observations in the data are the same okay same value.

[00:02:46]So option same option a meanal to median is equal to mode. So option greater than positively mean.

[00:03:04]Okay.

[00:03:12]So types of symmetrical equal mood values that is symmetrical.

[00:03:26]Okay. So mean median mode values are equal means there is a symmetrical. So mean value greater than median greater than mode there is a positively skewed less negatively skewed. So okay three types of so option one is the correct answer for this question. Okay next pick out pick out the wrong statement from among the alternative given below.

[00:03:58]So wrong statement.

[00:04:01]So pick out pick out the wrong statement.

[00:04:06]Sorry options. The arithmetic mean depends on all the observations.

[00:04:15]So we are adding all the observations right. So observations.

[00:04:30]So the correct statement arithmetic mean is depend on the all observations and this is the correct statement. Okay.

[00:04:37]Next the median is an average of position.

[00:04:44]So median we divide the data into two equal parts and we are focusing on the only mid values. Okay. So this is also a character statement.

[00:04:54]Okay. Med is also a an average of the position. position bas.

[00:05:10]So position meanal average. Okay, arithmetic is the calculated average. Median is the positional average. So median and the position. So correct next mode is the value which has a greatest frequency. So three cases two only series.

[00:05:38]So more definition the highest frequency will consider as that mean the highest frequency corresponding variable will consider as a mode. So answer the arithmetic mean is least affected by extreme observations in the data. So this is very wrong.

[00:06:08]So we are involving the every observations.

[00:06:11]Okay.

[00:06:14]First option. So we are involving the every observations. So when the data is hugeffected least affected it is affected. Okay. So effect and that median mode.

[00:06:44]So this is a wrong statement. So for the given data this is the correct answer and the fourth one is the correct option. Okay. So wrong statement correct statements wrong statement or fourth statement. So option four is the correct answer for this question. Okay.

[00:07:02]Next in a moderated skewed distribution.

[00:07:08]Okay. Mean minus mode equal to three mean minus median. So option student option two mode is equal to 3 mean minus 2 median. Uh median is equal to 3 mean minus 2 median. Uh mean is equal to median is equal to mode.

[00:07:26]Okay. So moderately skewed distributions relationship between the mean median mode. Okay distribution formula z is equal to three median minus 2 mean the formula. Okay moderately skewed distribution. So option one is mean minus mode is equal to 3 into mean minus median. So did I get this condition?

[00:07:59]Okay. So multiply three meanus median.

[00:08:06]Okay. So okay minus sign minus mode is equal to so three meanus.

[00:08:33]Okay. So, so three mean plus signus. So, two mean two meanus median.

[00:08:45]Okay. minus mode equal to so minus both the sides mode equal to sorry mode equal to so first minus first three median plus 2 meanus 3 and 2 mean xar so condition.

[00:09:16]Okay. So, option A is the correct answer. Okay.

[00:09:24]This is the formula. Z is equal to 3 median minus 2 mean. Okay. So, option one option one is the correct opt correct answer for this question. Okay. Next.

[00:09:40]The sum of n observations is 630 and their mean is 42. The value of n is okay n 630 42 x iid.

[00:10:05]Okay.

[00:10:07]The sum of n observations sum total value sum of n observations observations summation x value. So summation x value sorry 630.

[00:10:25]Okay. So sum of observations observations.

[00:10:34]Okay. Next and mean xar and value of n.

[00:10:44]So this is the formula.

[00:10:49]So xar 42 and summation 630 divided by n. So cross multiplication. So cross multiplication say n is equal to 630 divided by 42. So cancel just the 15. Okay. So option student sorry uh option one 21, option two 30, option three 20, option four 15.

[00:11:14]So option four is the correct answer for this question. Okay. Next.

[00:11:23]Given a data the sum of squares of deviation is minimum when the deviations are taken about. Okay.

[00:11:42]Okay. options geometric meanyam uh option two median myagam option three mode bahulam and option D none of the above okay so sum of the squares of the deviation is minimum so sum of squares of deviations when you taken from the arithmetic mean okay generally when you take the sum of the squares of deviation from the arithmetic mean the value should be minimum. Okay. So that is the point in the arithmetic means options but sum of the squares of the deviations taken from the arithmetic mean. Okay. So option four is the correct answer that is none of the above.

[00:12:36]Okay. Option four is correct. Next.

[00:12:43]In a class there are five boys and 10 girls. Okay. Okay. Class five girls.

[00:12:48]Yeah. Sorry. Five boys, 10 girls. Okay.

[00:12:52]The average marks of boys is 60 and that of girls is 55. Okay. So boys average 60 and 10 mess.

[00:13:09]The average marks for the whole class is okay.

[00:13:32]So combined mean okay boys.

[00:13:42]Okay boys five members and girls 10. Okay. So next x1 bar 60 and x2 bar 55.

[00:14:05]Okay.

[00:14:07]Total average of the whole class X12 bar combined main formula already discussed N1 X1 bar plus N_sub_2 X2 bar divided by N_sub_1 + N_sub_2. So this is the formula. Okay. So for substitute n1 5 into x1 bar 60 plus n_sub_2 n 10 into 55 divided by n1 and 5 + 10. So 5 uh 5 into 6 30 and 0 plus 10 into 55 5 divided by 15. So 50 550 + 300 850 850 divided by 15. So when you cancel this you will get 56.66 around. Okay. So options check the options. Option one is 57.5.

[00:15:17]Option two 58.5 and option three 56.66.

[00:15:23]Option four 56.55.

[00:15:26]So option three is the correct answer for this question. So combined mean formula. Okay. Next question.

[00:15:37]A student scored 55 marks in English, 80 marks in mathematics, 60 marks in science and 65 marks in social studies.

[00:15:47]Please stop. Given that mathematics and science is twice as important as the other subject, the average marks taking into consideration uh consideration the importance also is. Okay. Okay.

[00:16:03]foreign.

[00:16:27]Okay.

[00:16:30]Okay. a person okay students English mathematics science social okay four subjects so English mathematics science and social four subjects so mathematics particular person average.

[00:17:02]Okay. So, first uh 55 plus 80 55 80 into 80.

[00:17:16]Next uh mathematics 80 60 marks in science.

[00:17:21]So mathematics and science science 2 into 60 plus 65.

[00:17:31]Okay. So 55 + 160 120 + 65. Okay. Total length 400.

[00:17:44]Okay.

[00:17:46]Next uh mark 1 + 2 + 2 + 1. So 3 3 6. Okay.

[00:17:57]So 400 / 6 cancel.