In the following distribution, calculate mean $¯ ¯ ¯ x$ :
Class-interval $10 - 25$ $25 - 40$ $40 - 55$ $55 - 70$ $70 - 85$ $85 - 100$
Frequency $2$ $3$ $7$ $5$ $6$ $7$
If $¯ x = a b$ , then $a + b$ is :

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Solution

Mean is calculated as:
$¯ ¯ ¯ x = \frac{\sum x_{i} n_{i}}{\sum n_{i}}$
$⟹$ $¯ ¯ ¯ x = \frac{17.5 \times 2 + 32.5 \times 3 + 47.5 \times 7 + 62.5 \times 5 + 77.5 \times 6 + 92.5 \times 7}{2 + 3 + 7 + 5 + 6 + 7}$
$⟹$ $¯ ¯ ¯ x = \frac{1890}{30}$
$⟹$ $¯ ¯ ¯ x = 63 = a b$ .

We know, $¯ ¯ ¯ x = a b$ .
Comparing, $a = 6, b = 3$ .
Then, $a + b = 6 + 3 = 9$ .

Hence, the required answer is $9$ .

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Class-interval of marks	$10 - 25$	$25 - 40$	$40 - 55$	$55 - 70$	$70 - 85$	$85 - 100$
Number of students	$2$	$3$	$7$	$6$	$6$	$6$

Class Interval	40−45	45−50	50−55	55−60	60−65	65−70	70−75	75−80	80−85
Frequency	4	6	8	10	7	6	5	3	1

Rent (in Rs)	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$	$75 - 85$	$85 - 95$
No. of Houses	$8$	$10$	$15$	$25$	$40$	$20$	$15$	$7$

Find the mean of the following using step deviation method.

Class intervals / Frequency

15-25. 6

25-35. 11

35-45 . 7

45-55. 4

55-65. 4

65-75. 2

75-85 . 1

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Class-interval	$10 - 25$	$25 - 40$	$40 - 55$	$55 - 70$	$70 - 85$	$85 - 100$
Frequency	$2$	$3$	$7$	$5$	$6$	$7$