Question

The 2006 General Social Survey asked respondents about the number of children that they have. Consider the following hypothetical sub-sample: 2, 7, 4, 4, 1, 2, 2, 3, 1, 2, 4, 5. calculate and interpret the values of mean, median, range and standard deviation.

Answer 1

Solution:

x	x2
2	4
7	49
4	16
4	16
1	1
2	4
2	4
3	9
1	1
2	4
4	16
5	25
∑x=37	∑x2=149

Mean ˉx=∑xn

=2+7+4+4+1+2+2+3+1+2+4+5/12

=37/12

=3.0833

Median :
Observations in the ascending order are :
1,1,2,2,2,2,3,4,4,4,5,7

Here, n=12 is even.

M=Value of(n/2)thobservation+Value of(n2+1)thobservation/2

=Value of(12/2)thobservation+Value of(12/2+1)thobservation/2

=Value of6thobservation+Value of7thobservation/2

=2+32

=2.5
Range = Maximum value - Minimum value

= 7 - 2

= 5
Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√149-(37)212/11

=√149-114.0833/11

=√34.9167/11

=√3.1742

=1.7816