Question

If the mode of the following data is 36, then the value of P is

Class Interval	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	7	6	10	16	P	8	10

• A. 11
• B. 12
• C. 14
• D. 15

Answer 1

The correct option is B 12

Class Interval	Frequency
0-10	7
10-20	6
20-30	10
30-40	16
40-50	P
50-60	8
60-70	10

Since, the mode lies in the interval 30 - 40.
So, the modal class is 30 – 40.

Here,
Lower limit (l) of modal class = 30
Class size (h) = 40 – 30 = 10
Frequency ($f_1$) of the modal class = 16
Frequency ($f_0$) of the class preceding to the modal class = 10
Frequency ($f_2$) of class succeeding to the modal class = P

$\therefore Mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

$\Rightarrow 36=30+\left[\frac{16-10}{2\left(16\right)-10-P}\right]\times 10$

$\Rightarrow 36=30+\left[\frac{6}{32-10-P}\right]\times 10$

$\Rightarrow 6=\frac{6}{22-P}\times 10$

$\Rightarrow 22-P=10$

$\Rightarrow P=12$

Hence, the correct answer is option b.