Compute the Standard Deviation of a Variable from Raw Data
-The top speeds (in mph) for a sample of five new automobile brands are listed below. Calculate the standard deviation of the speeds.
$145,135,195,180,105$
A) $36.0 \mathrm { mph }$
B) $27,360.00 \mathrm { mph }$
C) $152.00 \mathrm { mph }$
D) $90 \mathrm { mph }$

Question

Quizplus · Accepted Answer

To calculate the standard deviation, first find the mean (average) speed: $(145 + 135 + 195 + 180 + 105) / 5 = 760 / 5 = 152$ mph. Then, calculate the variance by finding the squared differences from the mean, summing them, and dividing by the number of observations minus one (for a sample standard deviation): $[(145-152)^2 + (135-152)^2 + (195-152)^2 + (180-152)^2 + (105-152)^2] / (5-1) = 5180 / 4 = 1295$. The standard deviation is the square root of the variance: $\sqrt{1295} \approx 36.0$ mph.

Compute the Standard Deviation of a Variable from Raw Data 145,135,195,180,105145,135,195,180,105145,135,195,180,105

Compute the Standard Deviation of a Variable from Raw Data $145,135,195,180,105$