Calculate 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 $12$ $18$ $15$ $25$ $26$ $15$ $9$

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Solution

Step 1: Creating the table
The given table is completed as below,
Class-interval Frequency $(f_{i})$ Mid values $(x_{i})$ $(f_{i} x_{i})$
$0 - 20$ $12$ $10$ $120$
$20 - 40$ $18$ $30$ $540$
$40 - 60$ $15$ $50$ $750$
$60 - 80$ $25$ $70$ $1750$
$80 - 100$ $26$ $90$ $2340$
$100 - 120$ $15$ $110$ $1650$
$120 - 140$ $9$ $130$ $1170$
Total $\sum_{} f_{i} = 120$ $\sum_{} (f_{i} x_{i}) = 8320$

Step 2: Finding the arithmetic mean
The formula for the arithmetic mean is given by,
$A r i t h m e t i c M e a n = \frac{\sum_{} (f_{i} x_{i})}{\sum_{} f_{i}}$
where $\sum_{} f_{i}$ is the total frequency and $x_{i}$ is the mid-value of the class intervals.
$\Rightarrow A r i t h m e t i c M e a n = \frac{8320}{120} ∴ A r i t h m e t i c M e a n = 69.33$
Therefore, the value of the arithmetic mean is $69.33$ .

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Similar questions

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

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

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	$12$	$18$	$15$	$25$	$26$	$15$	$9$

Find the mean for each of the following frequency distribution

Class interval

Frequency

$0 - 20$

$20 - 40$

$40 - 60$

$60 - 80$

$80 - 100$

$100 - 120$

$120 - 140$

$12$

$18$

$15$

$5$

$26$

$15$

$9$

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

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