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
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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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Q1Group A has 4 items with mean 12. Group B has 4 items with mean 20. Find the combined mean.Show answer
Answer: 16 (total 128 divided by 8)
Q2Group A has 10 items with mean 50. Group B has 5 items with mean 80. Find the combined mean.Show answer
Answer: 60 (total 900 divided by 15)
Q3Group A has 6 items with mean 15. Group B has 9 items with mean 25. Find the combined mean.Show answer
Answer: 21 (total 315 divided by 15)
Q4Three groups have 8 items with mean 10, 12 items with mean 15, and 5 items with mean 20. Find the combined mean.Show answer
Answer: 14.4 (total 360 divided by 25)
Q5Group A has 18 items with mean 62. Group B has 22 items with mean 70. Find the combined mean.Show answer
Answer: 66.4 (total 2656 divided by 40)
Q6A class of 15 students has a mean score of 30. When combined with another class of 25 students, the combined mean of all 40 students is 40. Find the mean score of the second class.Show answer
Answer: 46 (combined total 1600, minus 450 for the first class, divided by 25)
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.
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Two groups of data have 10 items each, with means 18 and 30. Work out the combined mean of all 20 items.
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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.
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Free printable worksheet
Want more practice on paper? Download the combined mean worksheet pack - 12 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 7 of GCSE Statistics Foundation Workbook 2 and chapter 11 of GCSE Statistics Higher Workbook 2, the whole course as one free printable PDF.
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