How to calculate the mean from grouped data

Written by bill brown
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How to calculate the mean from grouped data
You can get an estimate of a mean from grouped data. (calculator image by jedphoto from

If you are working from grouped data--data that have been already averaged by groups, and for which you do not have the raw figures--it's possible to get a very good estimate of the mean or average for the entire data group. The process involves multiplying each group's mean by the number of members of each group, summing the total and calculating the mean from that sum. To make this calculation, you must know the number of items in each group of data, along with the mean for each group.

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  1. 1

    Multiply the total number of items in each data group by the group's mean. For instance, if you have 10 items in a group of persons that earn between £6,500 and £12,999 annually, and the mean income for the group is £9,750, the total is £97,500.

  2. 2

    Repeat this step for each group of data.

  3. 3

    Add the total for all groups. For example, if your group sums are £97,500 for the first group, £195,000 for the second and £292,500 for the third, that comes to £585,000.

  4. 4

    Add the total number of items in each group of data. For example, if there are 10 persons in the first group, 10 in the second and five in the third, the total is 25 items.

  5. 5

    Divide the total in Step 3 by the sum of the number of total items in Step 4 to determine an estimate for the mean for all grouped data. In this example, £585,000 divided by 25 yields a mean of £23,400.

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