FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.3Example 2 : If 5, 8, 6 and 2 occur with frequency 3, 2, 4 and 1 respectively, find the Arithmetic mean.
Arithmetic mean ( ) ( ) ( ) ( )
3 5 2 8 4 6 1 2
3 2 4 1
× + × + × + ×
= + + + =15 16 24 2+ 10 + + =^5710 = 5.7 ∴ (^) x = 5.7
Calculation of Arithmetic Mean (or simply Mean) from a grouped frequency distribution –– Continuous
Series.
(i) Ordinary method (or Direct Method)
In this method the mid-values of the class-intervals are multiplied by the corresponding class-frequencies.
The sum of products thus obtained is divided by the total frequency to get the Mean. The mean x is given
by
x ( fx)
= N
(^) , where x = mid-value of a class and N = total frequency
Example 3 : Calculate the mean of daily-wages of the following table :
Wages () No. of workers 4–6 6 6–8 12 8–10 17 10–12 10 12–14 5 Solution: Table : Calculation of Mean Daily Wages Class Mid values Frequency fx Interval () x f
4–6 5 6 30
6–8 7 12 84
8–10 9 17 153
10–12 11 10 110
12–14 13 5 65
Total –– N = 50 fx = 442
∴ Mean Daily Wages
fx 442
N 50
=^ = = ` 8.84