Different Perspectives on Achieving the Mean of a Distribution

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Using a small dataset , we can determine the mean value corresponding to five different perspectives on an equitable distribution. Within each perspective, use the slider to accomplish the desired goal.

Contributed by: Alexander White, Matthew Straughn, and Layla Guyot (July 2016)
Open content licensed under CC BY-NC-SA



For each perspective, the choice of achieves a particular goal. By sliding the control for , you can explore different properties of the mean.

Snapshot 1: Colored bars represent data values. Choose to divide the total into equal parts to show that the mean represents a "fair share."

Snapshot 2: Towers represent data values. By varying , remove area from the taller bars and add it to the shorter bars. Choose so that all the bars are leveled off at the same height.

Snapshot 3: Circles on the number line represent data values. Each square represents the squared distance from an observation to . Choose to minimize the sum of the areas of the squares.

Snapshot 4: Circles with unit mass on the "teeter-totter" number line represent data values. The position of the fulcrum is given by . Choose to achieve balance.

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