Question

The median for the following distibution class

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	5	10	20	7	8	5

is

• A. $26$
• B. $25$
• C. $26.25$
• D. $27$

Answer 1

The correct option is C $26.25$

Answer:-

Taking cumulation frequency(C. F.)

Class	Frequency	Cumulative frequency
0-10	5	5
10-20	10	15
20-30	20	35
30-40	7	42
40-50	8	50
50-60	5	55

N = 55 $\Rightarrow \frac{N}{2}=\frac{55}{2}=27.5$

35 is greater than 27.5

$\therefore$ Median class is 20-30.

Now, median = $L+\frac{\frac{N}{2}-C}{f}\times w$

L = lower limit of median class

f = fraquency of median class

w = width of median class

C = C.F. of previous class

$\frac{N}{2}=27.5$, L = 20, f = 20, C = 15, w = 30 - 20 = 10

Median = $L+\frac{\frac{N}{2}-C}{f}\times w$

Median = $20+\frac{27.5-15}{20}\times 10$

= $20+\frac{12.5}{20}\times 10$

= $20+6.25=26.25$