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 $8 per hour. The graph of the resulting salaries is shown in plot 2. A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 15, and the box ranges from 8.8 to 10.2. A line divides the box at 9.5. Plot 1 A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 11, and the box ranges from 8.7 to 10. A line divides the box at 9.6. Plot 2 How does the mean and median change from plot 1 to plot 2? The mean and median remain the same. The mean decreases, and the median remains the same. The mean remains the same, and the median decreases. The mean and median decrease.
Answers
(The diagram has been attached with the answer below.)
MEAN
We can find out the mean of the salaries via the following formula:
As per the above formula, both of the given parameters will affect the resulting mean.
Now, focusing on the two parameters:-
(i) Number of Employees
According to the question, one employee is substituted by another.
∴ the total number of employees remains the same
(ii) Total Salaries
It is stated in the question that a person earning $15/hr had quit, and the new person in his place earns $8/hr
∴ New sum of salaries = (Old sum of salaries) - 15 + 8
⇒ New sum of salaries = (Old sum of salaries) - 7
∴ The new sum of salaries has decreased by 7
Now, since the numerator decreased while the denominator remained unchanged,
∴ the mean will decrease
MEDIAN
The vertical candles is present over each of the whiskers plot signify, within which the middlemost line signifies the median between two successive figures on the plot.
In the first plot, the middle line of the vertical candle is situated almost in between 9 and 10.
∴ In the first plot, the median is 9.5 (approx.)
As far as the second plot is concerned, the position of the middle line is the same; i.e. it is located between 9 and 10.
∴ In the second plot, the median given is 9.5 (approx.)
Hence, the median will remain the same in both cases.
A similar solution can be found here -
https://brainly.com/question/8020805
Given : The hourly wages earned by 20 employees are shown in plot 1
The person earning $15 per hour quits and is replaced with a person earning $8 per hour
The graph of the resulting salaries is shown in plot 2
To Find : How does the mean and median change from plot 1 to plot 2
Solution:
Plot 1
The whiskers range from 8 to 15, and the box ranges from 8.8 to 10.2. A line divides the box at 9.5
Q₁ = 8.8
Q₂ = Median = 9.5
Q₃ = 10.2
The person earning $15 per hour quits and is replaced with a person earning $8 per hour.
The whiskers range from 8 to 11, and the box ranges from 8.7 to 10. A line divides the box at 9.6.
Q₁ = 8.7
Q₂ = Median = 9.6
Q₃ = 10
There is mistake in Data as $15 per hour quits and $8 per hour joins
Join person is less than Q₂ and Quit person is more than Q₂
Hence either median Q₂ remains same or median will decrease
Hence Q₂ = Median = 9.6 in Plot 2 is impossible.
There is no chance of median increasing
Also as there is $7 decrease in total wages Hence Mean will decrease
The mean and median decrease.
or
The mean decreases, and the median remains the same are two possible solutions
But as data of median is not correct hence nothing can be concluded about median
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