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The random sample of scores on a recent test were selected and recorded below68, 71, 77, 82, 85, 88, 89, 90, 92, 93, 96, 99Calculate the mean and standard deviation for the data set. Round your answers to 3 decimal places

User Toerktumlare
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1 Answer

21 votes
21 votes

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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The random sample of scores on a recent test were selected and recorded below68, 71, 77, 82, 85, 88, 89, 90, 92, 93, 96, 99Calculate-example-1
User Dfr
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