Combined Mean | Formula and Examples

What is Combined Mean?

When two or more series having different arithmetic means and number of items are combined together, the combined mean of all the series can be calculated using,

Combined Mean i.e.

Combined Mean i.e.

Where,

Combined Mean

Mean of the first series

N₁ = Number of items in the first series

Mean of the second series

N₂ = Number of items in the second series

Mean of the third series

N₃ = Number of items on the third series

Examples of Combined Mean

Example 1:

Find out the combined mean when , N₁ = 6, , N₂ = 9.

Solution:

Combined Mean

Combined Mean

Combined Mean

Example 2:

Find out the combined mean when

	Series 1	Series 2
Mean	6	7
No. of Items	12	14

Solution:

Combined Mean

Combined Mean

Combined Mean

Example 3:

Class A has 15 students with mean marks of 60, and Class B has 12 students with mean marks of 48. Calculate the combined mean.

Solution:

For Class A, , N₁ = 15

For Class B, , N₂ = 12

The required combined mean

Combined Mean

Example 4:

Assume that group 1 has 25 employees with an average salary of ₹82, group 2 has 32 employees with an average salary of ₹45, and group 3 has 77 employees. If the combined salary of the three groups is 70.86, find out the average salary of group 3.

Solution:

For Group 1, , N₁ = 25

For Group 2, , N₂ = 32

For Group 3, Assume average salary be and it is given that N₃ = 77

So, Combined Mean

9,495.24 = 3,490 + 77m

77m = 6005.24

m = ₹77.99 or ₹78

Hence, the average salary of group 3 is ₹78.