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.
1 answer:
Answer:
The mean decreases, while the median stays unchanged.
Step-by-step explanation:
A box plot is constructed from the quartiles of the data distribution, incorporating the maximum and minimum values. From this, one can determine the range, median, and interquartile range.
In this scenario, the median maintains its value at $9.5 per hour. The median is represented by the middle line in the box, which remains constant.
Conversely, the range of this data set shrinks from 7 to 3.
Moreover, the mean must decrease because values greater than $11 are no longer represented in the second box plot. The mean is a measure sensitive to such alterations.
Conclusively, the correct finding is The mean decreases, while the median remains unchanged.
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