Find the mean of the following frequency distribution.
Class interval $0 - 20$ $20 - 40$ $40 - 60$ $60 - 80$ $80 - 100$ $100 - 120$ $120 - 140$
Frequency $4$ $15$ $23$ $12$ $16$ $8$ $2$

335.45

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234.65

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63.25

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328.67

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Solution

The correct option is C 63.25
$C I$ $F r e q u e n c y$
$f_{i}$ $M i d - v a l u e$
$x_{i}$ $f_{i} x_{i}$
$0 - 20$ $4$ $10$ $40$
$20 - 40$ $15$ $30$ $450$
$40 - 60$ $23$ $50$ $1150$
$60 - 80$ $12$ $70$ $840$
$80 - 100$ $16$ $90$ $1440$
$100 - 120$ $8$ $110$ $880$
$120 - 140$ $2$ $130$ $260$
$\sum f_{i} = 80$ $\sum f_{i} x_{i} = 5060$
$\Rightarrow$ $¯ ¯ ¯ x = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{5060}{80} = 63.25$

Suggest Corrections

Class	0 − 20	20 − 40	40 − 60	60 − 80	80 − 100	100 – 120	120 – 140
Frequency	6	8	10	12	6	5	3

Class	0-20	20-40	40-60	60-80	80-100	100-120	120-140
Frequency	12	18	15	25	26	15	9

Class-interval	20−40	40−60	60−80	80−100	100−120	120−140	140−160
Frequency	3	7	11	15	13	6	2

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency	$4$	$15$	$23$	$12$	$16$	$8$	$2$

Classes:	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency:	$6$	$8$	$10$	$12$	$6$	$5$	$3$