The test scores of five students are 70, 80, 90, 100, and 110. What is the standard deviation of these scores?
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Correct answer
B. 14.14
Principle or equation
Standard deviation is the square root of the variance. Variance = sum of squared deviations from the mean divided by the number of data points (population variance).
Why this answer is correct
Mean = (70+80+90+100+110)/5 = 90. Deviations: -20, -10, 0, 10, 20. Squared deviations: 400, 100, 0, 100, 400. Sum = 1000. Variance = 1000/5 = 200. Standard deviation = sqrt(200) ≈ 14.14.
Example
For data 2,4,6, mean=4, variance=((4+0+4)/3)=8/3, sd≈1.63.
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