MATH SOLVE

2 months ago

Q:
# The hourly wages earned by 20 employees are shown in the first box and whisker plot below. The person earning $15 per hour quits and is replaced with a person earning eight dollars per hour. The graph of the resulting salaries is shown in part two. How does the mean and median change from plot 1 to plot two

Accepted Solution

A:

I added the plots in the attachments.Answer:The mean will decreaseThe median will remain the sameExplanation:1- checking the mean:Mean of the salaries is calculated as follows:[tex]Mean = \frac{sum-of-salaries}{number-of-employees}[/tex]Now, we can note that two parameters affect the mean, let's consider each:a. Number of employees:We are given that one employee is replaced with another. This means that the number of employees did not changeb. Sum of salaries:We are given that a person earning $15 left and the new person earns $7. This means that:New sum of salaries = old sum of salaries - 15 + 7 = old sum of salaries - 8This means that the sum of salaries decreased by 8Now, for the mean:We can conclude that since the numerator decreased while the denominator stayed the same, the mean will decrease2- checking the median:In the whisker plots, the median is represented by the vertical line inside the plot.In the first plot, we can note that the vertical line is nearly half the distance between 9 and 10. This means that, for the first plot, the median is approximately 9.5In the second plot, the place of the median is unchanged. It is still approximately midway between 9 and 10 which means that the median in the second plot is approximately 9.5Therefore, the median of the data remains unchanged.Hope this helps :)