The owner of a manufacturing plant employs eighty people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The distances for a random sample of six employees are listed below: $\begin{array} { l l l l l l } 26 & 32 & 29 & 16 & 45 & 19 \end{array}$
Find the variance for the given data.
A) $18.9 \mathrm { mi } ^ { 2 }$
B) $5043.6 \mathrm { mi } ^ { 2 }$
C) $15.8 \mathrm { mi } ^ { 2 }$
D) $107.0 \mathrm { mi } ^ { 2 }$

Question

Quizplus · Accepted Answer

The variance of a data set is calculated by finding the mean (average) distance, then finding the squared differences from the mean for each data point, summing those squared differences, and finally dividing by the number of data points minus one (for a sample variance). For the given distances: mean = (26 + 32 + 29 + 16 + 45 + 19) / 6 = 167 / 6 = 27.8333. Squared differences from the mean are: (26 - 27.8333)^2, (32 - 27.8333)^2, (29 - 27.8333)^2, (16 - 27.8333)^2, (45 - 27.8333)^2, (19 - 27.8333)^2. Summing these and dividing by (6 - 1) gives a variance of 107.0 mi^2.

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The Owner of a Manufacturing Plant Employs Eighty People $\begin{array} { l l l l l l } 26 & 32 & 29 & 16 & 45 & 19 \end{array}$