The mean of the following distribution is $15$ . Find the value of $a$ .
Class Interval $5$ $10$ $15$ $20$ $25$
Frequency $6$ $a$ $6$ $10$ $5$

Open in App

Solution

Class Interval $5$ $10$ $15$ $20$ $25$
Frequency $6$ $a$ $6$ $10$ $5$
Given, Mean $= 15$ .
The number of observations $= 5$ .

We know, Mean is given by,
$Mean = \frac{Sum of the elements}{Total number of elements}$ .
$⟹$ Mean $= \frac{(5 \times 6) + (10 \times a) + (15 \times 6) + (20 \times 10) + (25 \times 5)}{6 + a + 6 + 10 + 5}$

$⟹$ Mean $= \frac{30 + 10 a + 90 + 200 + 125}{6 + a + 6 + 10 + 5}$

$⟹$ $15 = \frac{445 + 10 a}{27 + a}$

$⟹$ $15 (27 + a) = 445 + 10 a$

$⟹$ $405 + 15 a = 445 + 10 a$

$⟹$ $5 a = 40$

$⟹$ $a = \frac{40}{5} = 8$ .

Therefore, $8$ is the required answer.

Suggest Corrections

Similar questions

25

p

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$5$	$18$	$15$	$p$	$6$

x < 6

17.5

Class interval	0-5	5-10	10-15	15-20	20-25
Frequency	5	2	3	6	x

x

Class interval	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Frequency	$8$	$11$	$6$	$13$	$12$

Join BYJU'S Learning Program