Answer:
- mean: 85.833
- standard deviation: 9.263
Explanation:
You want the mean and standard deviation for the given data set of 12 test scores.
Mean
The sum of scores is 1030, so the mean of the 12 scores is ...
µ = 1030/12 ≈ 85.833
Standard deviation
The sum of the squares of the scores is 89438, so the mean square is ...
89438/12 ≈ 7453.167
Then the variance is ...
σ² = 7453.167 -(85.833)² ≈ 85.806
And the standard deviation is ...
σ ≈ √85.806 ≈ 9.263
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Additional comment
It is not clear what "data set" is being referenced by the problem statement. If an estimate of the standard deviation of the population of all test scores is needed, that will be √(12/11) times the value shown here:
S = σ√(12/11) ≈ 9.675
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