Question

If the median of the following distribution is $46$, find the missing frequencies $p$ and $q$.

class interval	10-20	20-30	30-40	40-50	50-60	60-70	70-80	Total
Frequency	12	30	p	65	q	25	18	230

• A. $4$ and $46$
• B. $34$ and $46$
• C. $34$ and $6$
• D. None of these

Answer 1

The correct option is B $34$ and $46$

Solution -

Median class is $40-50$

L = Lower limit of median class = 40

B = C.F of classes before median class = 42+P

G = Frequency of median class = 65

W = class width = 10

n = 230 (Total frequency)

Median $L+\frac{(n/2-8)}{G}\times W$

$46=40+\frac{(115-42-1)}{65}\times 10$

$\frac{3}{5}=\frac{73-P}{65}$

$39=73-P$

$P=34$

Now, Total Frequency = 230

$12+30+34+65+q+25+18=230$

$q=230-184=46$