Question

For the given frequency distribution, if 2 < a ≤ 8, then median is equal to

Class interval	Frequency
0-10	8
10-20	6
20-30	a
30-40	10
40-50	4

• A. 22
• B. 25
• C. 26
• D. 30

Answer 1

The correct option is B 25

Class interval	Frequency	Cumulative Frequency
0-10	8	8
10-20	6	14
20-30	a	14+a
30-40	10	24+a
40-50	4	28+a

Given that 2 < a ≤ 8.
Adding 28 to all sides, we get
$\Rightarrow$ 30 < 28 + a ≤ 36

$\Rightarrow 15<14+\frac{a}{2}\le 18$

Also, $\frac{N}{2}=\frac{28+a}{2}=14+\frac{a}{2}$

$\Rightarrow \frac{N}{2}$ lies in class interval 20 – 30

Here,
Lower limit, (l) = 20
Cumulative frequency of class preceding the median class, (cf) = 14
Frequency of the median class (f) = a
Class size (h) = 10
$\therefore Median=l+\left(\frac{\frac{N}{2}-cf}{f}\right)\times h$
$=20+\left(\frac{14+\frac{a}{2}-14}{a}\right)\times 10$
$=20+(\frac{1}{2}\times 10)$
$=25$
Hence, the correct answer option b.