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