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 = \(n_1\bar{x_1} + n_2\bar{x_2} + n_3\bar{x_3} + …..\over {n_1 + n_2 + n_3 + ….}\)

Also Read : What is the Formula for Mean Median and Mode

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%

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