Question

1. Consider the salaries of Major League Baseball players from 1988 to 2011 (you can find that data at http://www.mathcs.org/statistics/datasets/MLBPlayerSalaries.xlsx). Do you think that this data is normally distributed, using common sense? Confirm your suspicion by drawing a frequency histogram of the salary, using 6 bins. Based on that histogram, do you think the median is greater or less than the mean? Note that your answer must include that histogram, properly constructed with 6 bins.

Answer 1

Since few people draw a very high salary hence it is very likely that the distribution of salaries would be skewed

The frequency distribution and the histogram is obtained in excel by following these steps,

Step 1: Write the salary data value in excel. The screenshot is shown below,

Step 2: The minimum and the maximum salary values are obtained using the function =MIN() and =MAX() respectively and the class width is obtained using the following formula,

The screenshot is shown below,

Step 3: Make a column bin with the upper-class limit (taking a width of 5500000. The screenshot is shown below,

Step 4: DATA > Data Analysis > Histogram > OK. The screenshot is shown below,

Step 4: Insert Input Range: Salary column, Bin Range: bin column, right tick on Chart output then OK. The screenshot is shown below,

The frequency table and the histogram is obtained.

Bin	Frequency
5562500	17698
11062500	1338
16562500	410
22062500	81
27562500	12
33062500	4

Conclusion: We can see that the distribution is highly skewed to the right (i.e. longer tail in the right side)

Hence the mean value will be larger than the median value.