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 mi2
B) 5043.6 mi2
C) 15.8 mi2
D) 107.0 mi2

Question

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 mi2
B) 5043.6 mi2
C) 15.8 mi2
D) 107.0 mi2

Quizplus · Accepted Answer

To find the variance, first calculate the mean of the distances: (26 + 32 + 29 + 16 + 45 + 19) / 6 = 27.83. Then, find the squared differences from the mean for each value, sum them, and divide by the number of values minus one: [(26-27.83)² + (32-27.83)² + (29-27.83)² + (16-27.83)² + (45-27.83)² + (19-27.83)²] / 5 = 107.0 mi².

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