Foundation · Explanatory preview
Adding and averaging
Add the values, then divide by how many there are. An average does not preserve the individual values.
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What does an average keep, and what does it lose?
Imagine four equally sized containers holding 3, 1, 1 and 3 units. Combining them gives 8 units. Sharing the total equally between the four containers gives 2 in each. Two is the average; the original containers were not all equal.
The number of observations and the sum of their values are different quantities. Doubling the number of repeated observations doubles the sum but leaves the average unchanged.
One worked example
- Add 3 + 1 + 1 + 3 to obtain 8.
- Count four values.
- Divide 8 by 4 to obtain 2.
- Repeating the list gives 16 divided by 8, still 2.
A stopping point: An average is a total shared equally among the number of observations.
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