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.
Liam has the higher average because his median is to the right of Vicki's median. The median is visually shown as the vertical line inside the box. For Liam, his median is 15. Vicki's median is some value between 10 and 15 (closer to 10).
Liam is also more consistent. How can we tell? Note how Liam's box and whisker plot has a shorter/smaller box. Also the min and max are closer together as well. The range is smaller for Liam. The interquartile range (IQR) is also smaller for Liam. Liam's scores are closer together. Vicki's scores are more spread out due to a larger range and IQR.
Notes 1) The IQR is defined as the horizontal distance from the left edge to the box to the right edge
2) IQR = Q3 - Q1 where Q1 and Q3 are the first and third quartiles respectively
3) Q1 is the left edge of the box; Q3 is the right edge of the box