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 \(x_3\) = 505
\(\bar{x}\) = \(n_1\bar{x_1} + n_2\bar{x_2} + n_3\bar{x_3}\over {n_1 + n_2 + n_3}\)
= \((25\times 70) + (40\times 65) + (35\times 50)\over 25 + 40 + 35\)
= \(1750 + 2600 + 1750\over 100\) = \(6100\over 100\) = 61%