We are asked to compare the data distribution by using their shapes and appropriate measures of center and variation. To do so, let's first find the distribution of each histogram and the measures that best represent each data set. Then we will compare the center and variation of the data sets.
Distribution and Measures
Professional Football Players Histogram
We can see that most of the data are on the left of the distribution and the tail of the graph extends to the right. Then the distribution is skewed right. Therefore, the median and the five-number summary best represent the data.
Company Employees Histogram
We can see that the data on the right of the distribution is approximately a mirror image of the data on the left of the distribution. The distribution is symmetric. Therefore, the mean and the standard deviation best represent the data.
Comparison
Center
The median of the football players' data set is probably in the 3-5 or 6-8 interval, while the mean of the employees' data set is probably in the 9-11 or 12-14 interval. This means that a typical company employee is much more likely to have more years of experience than a typical professional football player.
Variation
The data for the company employees is more variable than the data for the professional football players. This means that the number of years of experience tends to differ more from one company employee to the next.
