Question

The General Social Survey asked respondents about the age at which they had their first child. Consider the following hypothetical sub-sample: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20, 14

Using the above data, calculate the interquartile range (IQR).

Using the above data, calculate the range.

Using the above data, calculate the variance.

Using the above data, calculate the standard deviation.

Answer 1

24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20, 14

Put the numbers in order

14,18,20,21,22,24,24,25,27,28,31,35,36

Find the median.

14,18,20,21,22,24,24,25,27,28,31,35,36

MEdian is 24

(14,18,20,21,22,24),24,(25,27,28,31,35,36)

Find Q1 and Q3

(14,18,20,21,22,24),24,(25,27,28,31,35,36)

Q1 = 20

Q3 = 27

Subtract Q1 from Q3 to find the interquartile range.

27-20 = 7

interquartile range (IQR) is 7

calculate the range

Maximum value - minimum value is called as range

MAximum = 36 and Minimun = 14. so the range is 36-14 = 22

Range is 22

Calculating variance in excel with the formula of VAR.S(range)

so here assume our data set in the range of A1:A14

Formula is VAR.S(A2:A14)

answer is 41

Standard deviation

=STDEV.S(A2:A14)

answer is 6.403