Question

Class-intervals	0-10	10-20	20-30	30-40	40-50
Frequency	12	11	14	10	13

Find the arithmetic mean for the given grouped frequency distribution.

• A. $15\frac{1}{6}$
• B. $25\frac{1}{6}$
• C. $35\frac{1}{6}$
• D. $45\frac{1}{6}$

Answer 1

Answer: (B)

$25\frac{1}{6}$

Consider the following table, to calculate mean:

$ci$	$f_i$	$x_i$	$f_i{x}_i$
0-10	12	5	60
10-20	11	15	165
20-30	14	25	350
30-40	10	35	350
40-50	13	45	585

$N=\Sigma f_i=60$

$\Sigma f_i{x}_i=1510$

Mean $\overline{x}=\frac{\Sigma f_i{x}_i}{N}$

$\therefore \overline{x}=\frac{1510}{60}=25\frac{1}{6}$

Hence, option $B$ is correct.