The variance of following:
Age $20 - 25$ $25 - 30$ $30 - 35$ $35 - 40$ $40 - 45$ $45 - 50$
Number of persons $170$ $110$ $80$ $45$ $40$ $35$

62.62

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56.56

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7.93

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9.24

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Solution

The correct option is D $9.24$
$¯ x = \frac{\sum F x}{\sum F} = \frac{14500}{480} = 30.2$ .
$σ^{2} = \frac{\sum F (x - ¯ x)^{2}}{\sum F} = \frac{40983.25}{480} = 85.38$
$σ = 9.24$

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Age (in Years)	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
Frequency	$110$	$x$	$75$	$55$	$y$	$30$

(x - y)

Size of item	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
No. of items	$4$	$8$	$18$	$30$	$20$	$10$	$5$	$2$

280

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