Question

A random sample of voters from New Delhi, is classified by age group, as shown by the

following data : (10)

Age Group Frequency

18 – under 24 17

24 – under 30 22

30 – under 36 26

36 – under 42 35

42 – under 48 33

48 – under 54 30

54 – under 60 32

60 – under 66 21

66 – under 72 15

a. Calculate the mean for this data.

b. Calculate the mode for this data.

c. Calculate the standard deviation for this data.

Answer 1

Following table shows the calculation:

a. Mean of grouped data:

$\bar{x}=\frac{\Sigma fx}{\Sigma f}$

$\bar{x}=\frac{10371}{231}=44.90\approx45$

b. Mode of grouped data:

$Mode=L+(\frac{f_1-f_0}{2(f_1)-f_0-f_2})\times h$

$Mode=36+(\frac{35-26}{2(35)-26-33})\times 6=40.91\approx41$

c. Standard deviation of grouped data:

$S=\sqrt{\frac{\Sigma f(x-\bar{x})^2}{\Sigma f-1}}$

$S=\sqrt{\frac{43056}{231-1}}=13.68$