Question

For which one set of data below would the mean perform best as a measure of the center?

1. Hourly Wages: $15, $35, $200, $12, $17, $22, $19, $19, $21

2. Number of Employees Injured Each Month (Jan - Dec): 19, 31, 28, 35, 32, 27, 29, 38, 37, 30, 26, 0

3. Heights of Male Business Majors (inches): 68.5, 71.0, 73.5, 76.5, 69.5, 69.0, 67.5, 69.0, 74.0, 73.5, 74.5

4. Property Value (thousands of dollars): $265, $255, $149, $176, $208, $165, $1,900

Answer 1

Mean perform best as a measure of the center when there are no outliers in the data.

Outliers being the extreme values either at the lower side of observations or the upper side of the observations.

Firstly, look at the Hourly Wages: $15, $35, $200, $12, $17, $22, $19, $19, $21

Here, $200 is an outlier at the upper side. Hence, mean can not play the best measure.

Now, look at the number of Employees Injured Each Month (Jan - Dec): 19, 31, 28, 35, 32, 27, 29, 38, 37, 30, 26, 0

Here, 0 is an outlier at the lower side. Hence, mean can not play the best measure.

Now, look at the Heights of Male Business Majors (inches): 68.5, 71.0, 73.5, 76.5, 69.5, 69.0, 67.5, 69.0, 74.0, 73.5, 74.5

Here, we can not see any extreme outlier value in the data. In this data set mean can be the best measure of center.

Looking at Property Value (thousands of dollars): $265, $255, $149, $176, $208, $165, $1,900

Here, $1900 is an outlier at the upper side. Hence, mean can not play the best measure.