The arithmetic mean for the following distribution is $53$ . Find the value of $p$ .
$C l a s s$ $0 - 20$ $20 - 40$ $40 - 60$ $60 - 80$ $80 - 100$
$F r e q u e n c y$ $15$ $18$ $21$ $p$ $17$

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Solution

Class

Mid values $(x_{i})$

Frequency $(f_{i})$

$f_{i} x_{i}$

0-20

10

17

170

20-40

30

P

30p

40-60

50

32

1600

60-80

70

24

1680

80-100

90

19

1710

Total=92+p

$M e a n (¯ ¯ ¯ x) = \frac{\sum f_{i} x_{i}}{\sum f_{i}}$
$50 = \frac{5160 + 30 p}{92 + p}$
Therfore,
$p = 28$

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Class:	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency:	$7$	$p$	$10$	$9$	$13$

Classes	0−20	20−40	40−60	60−80	80−100
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Class :	0−20	20−40	40−60	60−80	80−100
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$C l a s s$	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
$F r e q u e n c y$	$15$	$18$	$21$	$p$	$17$