# Combined Mean – Formula and Examples

Here you will learn what is combined mean formula and how to find combined mean with examples.

Let’s begin –

## Combined Mean Formula

If $$\bar{x_1}$$ and $$\bar{x_2}$$ be the means of two groups having $$n_1$$ and $$n_2$$ terms respectively then the mean(combined mean) of their composite group is given by

Combined mean = $$n_1\bar{x_1} + n_2\bar{x_2}\over {n_1 + n_2}$$

If there are more than two groups then, combined mean = $$n_1\bar{x_1} + n_2\bar{x_2} + n_3\bar{x_3} + …..\over {n_1 + n_2 + n_3 + ….}$$

Example : There are three sections A, B and C in class X with 25, 40 and 35 students respectively. The average marks obtained by section A, B and C are 70%, 65% and 50% respectively. Find the average marks of the entire class X.

Solution : $$n_1$$ = 25            $$x_1$$ = 70%

$$n_2$$ = 40                $$x_2$$ = 65%

$$n_3$$ = 35               $$x_3$$ = 50%

$$\bar{x}$$ = $$n_1\bar{x_1} + n_2\bar{x_2} + n_3\bar{x_3}\over {n_1 + n_2 + n_3}$$

= $$(25\times 70) + (40\times 65) + (35\times 50)\over 25 + 40 + 35$$

= $$1750 + 2600 + 1750\over 100$$ = $$6100\over 100$$ = 61%