Calculate the arithmetic mean of the following frequency distribution:
Class Interval: $0 - 40$ $40 - 80$ $80 - 120$ $120 - 160$ $160 - 200$
Frequency: $12$ $20$ $25$ $30$ $23$

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Solution

Make the required frequency distribution table.
First, we have to prepare a table to find the value of $\sum f_{i} x_{i}$
Class Interval:
Frequency ( $f_{i}$ ):
Mid value $(x_{i})$
$f_{i} x_{i}$
$0 - 40$
$12$
$20$
$240$
$40 - 80$
$20$
$60$
$1200$
$80 - 120$
$25$
$100$
$2500$
$120 - 160$
$30$
$140$
$4200$
$160 - 200$
$23$
$180$
$4140$

$\sum f_{i} = 110$

$\sum f_{i} x_{i} = 12280$
Calculate the Mean.
Mean $= \frac{\sum f_{i} x_{i}}{\sum f_{i}}$
Mean $= \frac{12280}{110}$
Mean $= 111.64$ .
Hence, the arithmetic mean of the following data is $= 111.64$ .

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Class	0-40	40-80	80-120	120-160	160-200
Frequency	12	20	35	30	23

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

Find the arithmetic mean of the following frequency distribution:

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

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

The arithmetic mean of the following frequency distribution is $50$ . Determine the value of $p$ .

Class-interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$16$	$p$	$30$	$32$	$14$

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Class Interval:	$0 - 40$	$40 - 80$	$80 - 120$	$120 - 160$	$160 - 200$
Frequency:	$12$	$20$	$25$	$30$	$23$