Question

a class has test scores of 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 and one student scoring 140. two boxplots were created for the data: one without the outlier, and one with it included. how does the outlier affect the second boxplot compared to the first? the outlier makes the boxplot longer and shifts the median slightly towards the higher scores; the outlier causes the median to decrease; the outlier increases the spread of the data, making the boxplot wider but does not affect the median; the outlier does not change the boxplot because it is outside the range of the rest of the data.

Explanation:

1. Recall the components of a boxplot: The box represents the interquartile range (IQR, from Q1 to Q3), the median is the line inside the box, and whiskers extend to the minimum and maximum non - outlier values (or to outliers with special markings). When an outlier is present:

• The median is the middle value of the data set. For the original data without the outlier (10 values: 55, 60, 65, 70, 75, 80, 85, 90, 95, 100), the median is the average of the 5th and 6th values, which is $\frac{75 + 80}{2}=77.5$. When we add the outlier 140 (now 11 values), the median is the 6th value, which is 80. The change in median is small and not a major effect of an outlier on a boxplot.
• The outlier (140) is a very large value compared to the rest of the data. The whisker on the upper end (or the position of the maximum value) will be affected. The spread of the data (measured by the range or the distance from the minimum to the maximum) will increase because the maximum value is now much larger (140 instead of 100). The box (IQR) is based on the middle 50% of the data and is not affected by the outlier, but the overall spread (from min to max, including the outlier) makes the boxplot wider. The median is relatively resistant to outliers, so the outlier increases the spread of the data, making the boxplot wider but does not affect the median significantly.
• The first option is incorrect because the box (IQR) is not made longer by the outlier (the IQR depends on Q1 and Q3, which are not affected by the outlier). The second option is incorrect because the median does not decrease (it either stays relatively the same or increases a bit, but not decrease). The fourth option is incorrect because the outlier is outside the range of the rest of the data, so it will affect the whisker or the maximum value, thus changing the spread.

Answer:

The outlier increases the spread of the data, making the boxplot wider but does not affect the median.