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A bowler's scores for a sample of six games were:

172, 168, 188, 190, 172, 182, 174

The sample standard deviation is closest to:

A. 64.0
B. 8.64
C. 74.67
D. 8.00

Answer :

Final answer:

To find the sample standard deviation, calculate the mean, find the deviation of each score from the mean, square each deviation, sum up the squared deviations, and take the square root. The closest sample standard deviation is approximately 9.30.

Explanation:

To find the sample standard deviation, we need to first find the mean of the sample scores. The mean is obtained by summing up all the scores and dividing by the number of scores:

Mean = (172 + 168 + 188 + 190 + 172 + 182 + 174) / 7 = 1246 / 7 = 178

Next, we calculate the deviation of each score from the mean:

Deviation = Score - Mean

Then, we square each deviation:

Squared Deviation = Deviation^2

After that, we sum up all the squared deviations:

Sum of Squared Deviations = (172-178)^2 + (168-178)^2 + (188-178)^2 + (190-178)^2 + (172-178)^2 + (182-178)^2 + (174-178)^2 = 520

Finally, we divide the sum of squared deviations by the number of scores minus one, and take the square root of the result:

Sample Standard Deviation = √(Sum of Squared Deviations / (Number of scores - 1)) = √(520 / 6) = √86.66 ≈ 9.30

Therefore, the closest sample standard deviation to the given scores is 9.30.

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