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Find the standard deviation of a series of ACT scores listed below.
24, 21, 15, 27, 23

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Answer: population standard deviation is 4

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Step-by-step explanation:

Add up the scores

24 + 21 + 15 + 27 + 23 = 110

Then divide by the sample size n = 5

110/n = 110/5 = 22

The sample mean is 22.

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Subtract the sample mean from each item

24 - 22 = 2

21 - 22 = -1

15 - 22 = -7

27 - 22 = 5

23 - 22 = 1

The results we got were: 2, -1, -7, 5, 1

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Square each result

2^2 = 4

(-1)^2 = 1

(-7)^2 = 49

5^2 = 25

1^2 = 1

Then add up the squares

4 + 1 + 49 + 25 + 1 = 80

Divide this over n = 5 to get the population variance

80/n = 80/5 = 16

The population variance is 16. The variance and standard deviation measure how spread out a data set is. The larger the value, the more spread out the set will be.

The square root of the variance is the population standard deviation

sqrt(16) = 4

The population standard deviation is 4

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