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Summary

When combining sets of data, it is important to consider the size of the sample when calculating an average position or conversion rate. To calculate a weighted average (average of averages), one can add a column calculating the average position by combining the two sets of data, summing the numbers in matching rows, and calculating a new average position = (sum of positions)/(sum of impressions).
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This approach can also be used to combine calculated metrics such as average, rate, percentage, and conversion rate, as well as to generate a generic approach by breaking down the data into their base metrics, combining duplicate rows, summing the numbers in every column, and recalculating the calculated metrics from the (summed) base metrics.
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Alternatively, an average can be defined as the sum of the numbers divided by how many numbers are in the list (the arithmetic mean).
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According to

Summary
When merging sets of data, it is important to consider the size of the sample when calculating an average position or conversion rate. To simplify the problem, one can add a column calculating the average position by combining the two sets of data, summing the numbers in matching rows, and calculating a new average position = (sum of positions)/(sum of impressions). This approach can be used to combine calculated metrics such as average, rate, percentage, and conversion rate, as well as to generate a generic approach by breaking down the data into their base metrics, combining duplicate rows, summing the numbers in every column, and recalculating the calculated metrics from the (summed) base metrics.

Calculating a Weighted Average (Average of Averages) | Analytics Edge Help
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Summary
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean ). For example, the average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5

Average - Wikipedia
wikipedia.org

Illustrated definition of Average: A calculated central value of a set of numbers. To ... Example: what is the average of 2, 7 and 9? Add the numbers: 2 + 7 + ...

Definition of Average
mathsisfun.com

The average calculator calculates the average of a set of up to 30 numbers. ... The average calculator will calculate the mean of up to thirty numbers . An ...

Average Calculator
omnicalculator.com

Name: RJ Who is asking: Student Level: Secondary Question: in a class with 22 students, the average garde on an exam was 68%, in another class with 32 ...

The average of two averages
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