Combined Mean — CA Foundation Maths Statistics Formula & Questions

What Is the Combined Mean?

In statistics, the arithmetic mean is the average of a set of values. Sometimes you have two or more separate groups, each with its own mean and its own number of items, and you need a single average for all the groups taken together. This single average is called the combined mean (or composite mean).

It is a regularly tested idea in CA Foundation Paper 3 (Quantitative Aptitude), in the Measures of Central Tendency chapter, because it shows whether you truly understand what a mean represents.

Combined Mean Formula

For two groups, if group 1 has n1 items with mean x1, and group 2 has n2 items with mean x2, then the combined mean is:

Combined Mean = (n1 × x1 + n2 × x2) / (n1 + n2)

The logic is simple: the mean of a group multiplied by its number of items gives the total of that group (n × mean = sum). So you add the totals of both groups and divide by the total number of items.

For three or more groups, just extend it:

Combined Mean = (n1x1 + n2x2 + n3x3 + ...) / (n1 + n2 + n3 + ...)

Solved Example 1

The mean salary of 20 male employees is Rs. 26,000 and of 30 female employees is Rs. 21,000. Find the combined mean salary.

Solved Example 2 (Finding a Missing Group)

The combined mean of two groups of 10 and 15 students is 48. If the mean of the first group is 45, find the mean of the second group.

This "work backwards" type is a favourite in MCQ papers.

Common Mistakes to Avoid

ICAI Exam Questions on Combined Mean

CA Foundation MCQs on combined mean typically:

Remember there is negative marking (0.25) in Paper 3, so be sure of the formula before you attempt.

Quick Revision

Practise combined-mean MCQs on CA Saarthi to build speed for the statistics section.