## Exploring Standard Deviation Answer Keys

### Answer Key for * Why We Need It *

A : { 3, 3, 4, 4, 4, 5, 5 } Range = __2__ Mean = __4__

B : { 3, 3, 3, 4, 5, 5, 5 } Range = __2__ Mean = __4__

C : { 1, 2, 3, 4, 5, 6, 7 } Range = __6__ Mean = __4__

D : { 1, 1, 3, 4, 5, 7, 7 } Range = __6__ Mean = __4__

E : { 1, 1, 3, 3, 6, 7, 7 } Range = __6__ Mean = __4__

The sum of the numbers was always 28 and the divisor was always 7.

In sets A and B the maximum and minimum were 5 and 3, so the range was 2 for both sets. Similarly, the maximum and minimum of sets C through F were 7 and 1, so the range was always 6.

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#### ``` X X X X X X X A : ---- | ---- | ---- | ---- | ---- | ---- | --- | ---- 1 2 3 4 5 6 7 X X X X X X X B : ---- | ---- | ---- | ---- | ---- | ---- | --- | ---- 1 2 3 4 5 6 7 X X X X X X X C : ---- | ---- | ---- | ---- | ---- | ---- | --- | ---- 1 2 3 4 5 6 7 X X X X X X X D : ---- | ---- | ---- | ---- | ---- | ---- | --- | ---- 1 2 3 4 5 6 7 X X X X X X X E : ---- | ---- | ---- | ---- | ---- | ---- | --- | ---- 1 2 3 4 5 6 7 X X X X X X X F : ---- | ---- | ---- | ---- | ---- | ---- | --- | ---- 1 2 3 4 5 6 7```

** Study the line plots and the pattern of their distributions. How do the patterns help to explain why all the sets had a mean of 4?

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