05 / 12 · Read a set of numbers
Same average, different experience
Compare how spread out the values are, not just their center.
Builds on Does the average describe most people?
Go to practice ↓A question to keep in mind
One route takes 4 minutes every time. Another takes 0, 2, 4, 6, 8. Are they the same?
Both lists average 4 minutes, but one never changes and the other varies a lot. Spread describes how far apart the values are.
A simple measure is the range: largest minus smallest. It is easy to calculate, but uses only the two endpoints. Different lists can share both the same mean and the same range.
Work through an example
| Route | Times | Mean |
|---|---|---|
| A | 4, 4, 4, 4, 4 | 4 |
| B | 0, 2, 4, 6, 8 | 4 |
- A: largest 4 minus smallest 4 gives a range of 0.
- B: largest 8 minus smallest 0 gives a range of 8.
- Both means are 4, but B varies more in these observations.
Your turn
0 / 3Which route has more consistent times in the recorded data?
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A
A is more consistent in these five observations. That is a statement about the data, not a guarantee about every future trip.
Calculate the range for A and B.
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- Range of A: 0 min
- Range of B: 8 min
A has range 0; B has range 8. Both still have mean 4.
Two lists have the same mean and range. Must all their values be the same?
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No. The values in between can differ.
0,2,4,6,8 and 0,4,4,4,8 have matching means and ranges but different shapes.
Bring it back to your own work
Find a situation where predictability matters as much as the average. Write which extra data you would want to see.
Statistical literacy: directory, audit and transfer assessment
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