Calculate the Arithmetic mean of the following data by direct method.
x $5$ $10$ $15$ $20$ $25$ $30$
f $4$ $5$ $7$ $4$ $3$ $2$

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Solution

x f fx
$5$ $4$ $20$
$10$ $5$ $50$
$15$ $7$ $105$
$20$ $4$ $80$
$25$ $3$ $75$
$30$ $2$ $60$
Total $N = 25$ $\sum f x = 390$
Arithmetic Mean, $¯ x = \frac{\sum f x}{N}$
$= \frac{390}{25} = 15.6$

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$x$ :	$5$	$10$	$15$	$20$	$25$
$f$ :	$7$	$k$	$8$	$4$	$5$

$x$	$5$	$10$	$15$	$20$	$25$
$f$	$3$	$10$	$25$	$7$	$5$

Class	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$
Frequency	$4$	$5$	$7$	$12$	$7$	$5$

Class	:	0-5	5-10	10-15	15-20	20-25	25-30	30-35	35-40
Frequency	:	2	5	7	13	21	16	8	3

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
No. of students	$5$	$10$	$25$	$30$	$20$	$10$

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