Combined Mean
The combined mean is the overall average of two or more separate groups of data pooled together into one data set. It is found by adding the totals of every group and dividing by the total number of values, not by averaging the group means directly. It appears in GCSE Statistics questions on summarising combined samples.
Before you start
Make sure you're comfortable with these topics first:
Method
- Find the total for each group by multiplying its mean by the number of items in that group.
- Add the totals from all the groups together to get the grand total.
- Add the number of items in each group together to get the grand total count.
- Divide the grand total by the grand total count to get the combined mean.
- Check your answer lies between the smallest and largest of the individual group means.
Worked example
Class A has 12 students with a mean test score of 68. Class B has 18 students with a mean test score of 74. Find the combined mean score of both classes.
- Total for Class A = 12 x 68 = 816.
- Total for Class B = 18 x 74 = 1332.
- Grand total = 816 + 1332 = 2148.
- Grand count = 12 + 18 = 30.
- Combined mean = 2148 / 30 = 71.6.
Practice questions
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Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A survey records the mean number of pets owned by 12 families in Street A as 2.5, and by 8 families in Street B as 1.75. Calculate the combined mean number of pets owned by all 20 families.
Two groups of data have 10 items each, with means 18 and 30. Work out the combined mean of all 20 items.
A factory tests light bulbs. In batch 1, 40 bulbs have a mean lifetime of 850 hours. In batch 2, 60 bulbs have a mean lifetime of x hours. The combined mean lifetime of all 100 bulbs is 910 hours. Find x.
Free printable worksheet
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