Q. 3.178 - Elementary Statistics

Question

Starting Salaries. The National Association of Colleges and Employers (NACE) conducts surveys of salary offers to new college graduates and publishes the results in Salary Survey. The following diagram provides boxplots for the starting annual salaries in thousands of dollars, obtained from samples of $35$ business graduates (top boxplot) and $32$ education graduates (bottom boxplot). Use the boxplots to compare the starting salaries of the sampled business graduates and education graduates. paying special attention to center and variation.

Step-by-Step Solution

Answer

The variation of education graduates is greater than business graduates.

Step 1: Given Information

We are given two boxplots one is of education graduates i.e., bottom plot and other one is of business graduates i.e., top plot and we have to compare them.

Step 2: Explanation

According to the boxplots,

The bottom boxplots have the mean starting salary around $33k$ while from the top box plots have the mean starting salary around $40k$ which indicates that the education graduates have high variance because range from lowest to highest in boxplot is greater than business graduates and in bottom boxplots center line is near $33k$ and top boxplots $40k$. As from the box plot the mid line i.e., $Q_2$ will give the mean starting salary on the basis of that find the mean salary and then observe till how much range it is spread. More will be the boxplot spread, More will be the variance and that is why bottom boxplot has more variation that top boxplots.

Hence this is the comparison between bottom boxplots and top boxplots.