A set of exam scores is 80, 75, 85, 90, 100, 70, 60. The standard deviation equals
A) 7
B) $\sqrt { 10 }$
C) $\sqrt { 50 }$
D) $\sqrt { 20 }$
E) none of these

Question

Quizplus · Accepted Answer

The standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. Given the scores, the mean is $\frac{80 + 75 + 85 + 90 + 100 + 70 + 60}{7} = \frac{560}{7} = 80$. The squared deviations from the mean are: $0^2, 5^2, 5^2, 10^2, 20^2, 10^2, 20^2$, which sum to $0 + 25 + 25 + 100 + 400 + 100 + 400 = 1050$. The average of these squared deviations is $\frac{1050}{7} = 150$. The square root of 150 is not listed among the options, hence the correct answer is E, none of these.

A Set of Exam Scores Is 80, 75, 85, 90 10\sqrt { 10 }10​

A Set of Exam Scores Is 80, 75, 85, 90 $\sqrt { 10 }$