# Calculating Combined Arithmetic Mean

Combined arithmetic means involves the series as a whole. Calculating combined arithmetic mean is generally used when 2 or more series are involved. Let’s take a look.

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## The formula for Combined Arithmetic Mean

**In case only 2 series are involved then the following formula is applied;**

**In case only 3 series are involved then the following formula is applied;**

## Solved Questions

- 60 students of section A of Class XI, obtained 40 mean marks in statistics, 40 students of section B obtained 35 mean marks in statistics. Find out mean marks in Statistics for class XI as a whole.

Solution:

N1 = 60, Arithmetic Mean 1 = 40

N2 = 40, Arithmetic Mean 2 = 35

Combined Mean = 40 x 60 + 35 x 40 / (60+40)

Combined Mean = 2400 + 1400 / 100

Combined Mean = 3800/100 = 38

2. The mean monthly salary paid to all employees in a certain company was Rs 600. The mean monthly salaries paid to male and female employees were Rs 620 and Rs 520 respectively. Find the percentage of male to female employees in the company.

Solution.

Combined Mean = 600

Arithmetic Mean 1 = 620

Arithmetic Mean 2 = 520

N1 = Male Employees and N2 = Female Employees

Using the formula;

600 = 620 N1 + 520 N2/ (N1+N2)

600N1 + 600N2 = 620 N1 + 520 N2

80N2 = 20 N1

N1/N2 = 80/20 = 4/1

N1 : N2 = 4 : 1

**Percentage of male employees = 4 / (4+1) x 100 = 80%**

**Percentage of female employees = 1 / (4+1) x 100 = 20%**

## Practice Yourself

- The mean monthly salary paid to 77 employees in a company was Rs78. The mean salary of 32 of them was Rs 45 and of the other 25 was Rs 82. What was the mean salary of the remaining?

**(Answer – 125.8)**

I hope it was helpful, you can refer to more posts related to the statistics.

- Individual Series Arithmetic Mean
- Discrete Series Arithmetic Mean
- Continuous Series Arithmetic Mean
- Inclusive and Exclusive Series – Arithmetic mean
- Introduction to the statistics.
- Functions and importance of statistics.
- Calculating Correct Arithmetic mean

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