Statistics
4 solved SSC CGL Quantitative Aptitude previous year questions on Statistics, each with the correct answer and a full explanation.
Q1
The marks obtained by 15 students out of a maximum of 25 in a test are given as 13,11, 16, 15, 18, 12, 13, 14, 10, 22, 15, 21, 20, 17 and24. Find the product of the modes of this set of data.
✓ Correct answer: d) 195
ExplanationMode is the number that appears most frequently in a data set we count the frequency of each mark 10= 1 time 11=1 time 12=1 time 13=2 times 14=1 time 15 =2 times 16= 1 time 17= 1 time 18= 1 time 20= 1 time 21= 1 time 22= 1 time 24= 1 time The modes of this set of data are 13 and 15, as these marks appear most frequently.Product of modes The product of the modes of this set of data is 195. Hence, Option D is the correct answer.
Q2
A set of data presented in the form of a frequency distribution table with class intervals and their respective frequencies had a mode of 48.5 . The lower boundary of the modal class was 46.5 ; the frequency of the modal class was 34 ; the frequency of the class interval just preceding the modal class was 32 and the frequency of the class interval just succeeding the modal class was 25 . What was the width of the modal class?
✓ Correct answer: c) 11
ExplanationThe formula for the mode in a grouped data is: Mode= Where, L = Lower boundary of the modal class. fm = Frequency of the modal class. f1= Frequency of the class preceding the modal class, f2 = Frequency of the class succeeding the modal class, h = 1 of the modal class, Mode Given mode.Therefore, Given mode= 48.5 fm = 34 f1= 25 f2 = 32 Substituting the given values into the formula: Hence, Option C is the correct answer.
Q3
Find the standard deviation of the following data (rounded off to two decimal places). 5,3,4,7
✓ Correct answer: a) 1. 48
ExplanationStandard deviation= Total of numbers= (5+3+4+7)= 19 Mean= Now, Standard deviation = Hence, Option A is the correct answer
Q4
The median of a set of 11 distinct observations is 73.2 . If each of the largest five observations of the set is increased by 3 , then the median of the new set:
✓ Correct answer: c) remains the same as that of the original set
ExplanationSince the median of the original set is 73.2, we know that there are 5 observations less than 73.2 and 5 observations greater than 73.2. Let's call the largest observation in the original set x. Then we have The median is 73.2 There are 5 observations less than 73.2 and 5 observations greater than 73.2 The largest observation is x When we increase the largest five observations by 3, the new largest observation will be x+3. However, this will not change the position of the median in the ordered set.The median will still be the middle value, which is still 73.2 Therefore, The median of the new set remains the same as that of the original set.Hence, Option C is the correct answer.
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