A combined mean is **a mean of two or more separate groups**, and is found by :

- Calculating the mean of each group,
- Combining the results.

## Combined Mean Formula

More formally, a combined mean for two sets can be calculated by the formula

:

Where:

- x
_{a}= the mean of the first set, - m = the number of items in the first set,
- x
_{b}= the mean of the second set, - n = the number of items in the second set,
- x
_{c}the combined mean.

A combined mean is simply a weighted mean, where the weights are the size of each group.

For more than two groups:

- Add the means of each group—each weighted by the number of individuals or data points,
- Divide the sum from Step 1 by the sum total of all individuals (or data points).

## Calculating a Combined Mean: Examples

Suppose you are running a survey on math proficiency (as measured by an achievement test) in kindergarten, and you have results from two different schools.

- In school 1, 57 kindergarteners were tested and their mean score was 82.
- In school 2, 23 kindergartners were tested and their mean score was 63.

The combined mean can be calculated by plugging in our numbers into the formula given above:

[(57*82)+(23*63)]/(57+23) = 76.5.

Now suppose you were running a survey on reading speed, as measured by how long it took 1st graders to read a given block of text. Your results come in for five schools:

To calculate the combined mean:

- Multiply column 2 and column 3 for each row,
- Add up the results from Step 1,
- Divide the sum from Step 2 by the sum of column 2.

(189*83+46*121 +89*82 +40*147+12*60)/(189+46+89+50+12)

Plug that in your calculator, and the answer you get—91.06—is the combined mean for all five schools; the average reading time for all students.

This same method may be used to combine any number of means.

## References

The Mean of a Combined Batch. Retrieved from

http://www.open.edu/openlearn/science-maths-technology/prices-location-and-spread/content-section-2.1 on June 10, 2018.

Mandal, Satya. Math 365 Class Notes, Lesson 2. Measures of Central Tendency and Measures of Dispersion Retrieved from http://www.math.ku.edu/~mandal/math365/newMath365/les2.html on June 10, 2018.

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