Arithmetic Mean Examples

In this class, We discuss Arithmetic Mean Examples.

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The reader should have prior knowledge of arithmetic mean properties. Click Here.

1) The average salary of the male employees in a firm was 5200, and that of females was 4200.

The mean salary of all the employees was 5000. What is the percentage of male and female employees?

Given: X1′ Mean of male employees.

X2′ Mean of female employees.

X’ Mean of all the employees.

N1 is the number of male employees

N2 is the number of female employees.

From the properties, we know X’ = (N1X1′ + N2X2′)/ (N1 + N2)

5000 = (N1* 5200 + N2 * 4200)/(N1 + N2)

5000N1 + 5000N2 = 5200N1 + 4200N2

200N1 = 800 N2

N1/N2 = 800/200

N1 : N2 = 4 : 1

N1 = (4/5)*100 = 80%

N2 = (1/5) * 100 = 20%

2) The average marks of 25 students were found to be 78.4. Later it was found that a score of 96 was misread as 69.

Find the correct mean?

Given:

n = 25

X’ = 78.4 = mean

From the properties ΣXi = X’n

ΣXi = 78.4 * 25 = 1960 = Sum of all the data values.

Correct ΣXi = 1960 – 69 + 96

ΣXi = 1987

X’ = 1987/25

X’ = 79.48