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.

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.

Quizplus · Accepted Answer

To find the variance, first calculate the mean (average) distance: $(26 + 32 + 29 + 16 + 45 + 19) / 6 = 167 / 6 = 27.833$ miles. Then, calculate the squared differences from the mean for each data point, sum them, and divide by the number of data points to get the variance: $((26 - 27.833)^2 + (32 - 27.833)^2 + (29 - 27.833)^2 + (16 - 27.833)^2 + (45 - 27.833)^2 + (19 - 27.833)^2) / 6 = 642 / 6 = 107.0$ square miles.

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