3. Manipulating Numbers to Solve the Mean

In some cases, it is possible to simplify the computation. Take the following numbers as an example: 20, 40, 30, 50. It is possible to add all the numbers together and divide by 4 (the number of values present). However, it is also possible to use common sense to lower the amount of computation needed. It is easy to figure out the average of 20 and 40 (A):

A. (20 +40) / 2 = 60/2 = 30

And then figure out the average between 30 and 50 (B):

B. (30 +50) / 2 = 80/2 = 40

Then we figure out the average between these two answers, A and B:

(30 + 40) / 2 = 70/2 = 35.

Therefore, the average of the four numbers provided is 35. Following the formula will garner the same answer, but students may need a calculator:

(20+30+40+50) /4 = 140/4 = 35


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