Question

the heights of students (in inches) in a class are 59, 60, 61, 62, 63, 64, 65, 67, with an additional student who is 75 inches tall. two boxplots are created for the data: one with and one without the outlier. how does this outlier affect the boxplot? four multiple - choice options are present but not fully transcribed here

Explanation:

1. First, recall the components of a boxplot: minimum, first quartile (Q1), median (Q2), third quartile (Q3), maximum, and range (maximum - minimum), interquartile range (IQR = Q3 - Q1).
2. Without the outlier (75), the data is 59, 60, 61, 62, 63, 64, 65, 67. The minimum is 59, maximum is 67, so range is \(67 - 59 = 8\).
3. With the outlier (75), the data includes 75. Now the maximum is 75, so the new range is \(75 - 59 = 16\), which is a significant increase. The IQR depends on Q1 and Q3. The middle 50% of the data (between Q1 and Q3) is less affected by the outlier since the outlier is an extreme value, so the IQR is slightly affected or remains relatively stable.
4. Analyzing the options:

• Option 1: Incorrect, as 75 is an outlier (much larger than other values) and will affect the boxplot (especially the maximum and range).
• Option 2: Incorrect, the median is the middle value. Without outlier: 8 data points, median is average of 4th and 5th values (\(\frac{62 + 63}{2}=62.5\)). With outlier: 9 data points, median is the 5th value (63). The median changes slightly but not "lowers" in a way that's the main effect; the main effect is on range.
• Option 3: Correct, as shown, the range increases significantly (from 8 to 16) and the IQR (middle 50% spread) is slightly affected since the outlier is outside the middle 50% of the data.
• Option 4: Incorrect, an outlier increases the spread (range) of the data, not decrease it.

Answer:

C. It significantly increases the range and slightly affects the interquartile range (IQR)