Means, Frequency Tables, and Weighted Average

Mean (Arithmetic Average)

When we find the mean of a set of values, we are finding the arithmetic average. We often consider this as "evening out" the various values.

Example: Consider five block-towers with heights of 3, 2, 4, 1, and 5 blocks. Find the mean height of these five block towers by rearranging the blocks to the same height.

A child may work this problem by stacking blocks and then restacking the blocks to towers of the same size.

We see from the picture that, "on the average", the 5 towers are 3 blocks tall.
Notice that this is exactly the same solution as when we find the mean of the heights of the towers numerically:  

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Self Check Problem

Shawn's scores on the six homework assignments were 5, 3, 4, 5, 2,and 4. What was Shawn's mean score on the homework?

Solution

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