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How can you average averages?

Updated: 9/19/2023
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13y ago

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-- Multiply the first averages by the number of observation for each set of these.

-- Add up the sets of averages.

-- Divide the sum by the total number of observations (Add cardinaility of each set).

-- The result is the average of the averages.

If you say have 4 "average" value and just add these, and divide by 4, the result is "unfair" because average may be of 3 observations, while another of 1000. So, to "compensate" and make every observation just as valuable, you re-generate the "sum of sums" and then divide by the total number of observations.

If all sets are the same you can divide by number of observations.

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13y ago
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13y ago

adding up all the data and then dividing the sum by the number of data you had (for example, the average of the numbers 1, 2, and 3 is 1+2+3=6/3=2)

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