Question

the finishing times for a school marathon are all between 125 to 150 minutes, except for one elite athlete who finished in 94 minutes. how will this outlier affect the boxplot? options: a) the outlier does not change the boxplot because it is an measurement error. b) the outlier creates a longer lower whisker, indicating a wider spread of data. c) the outlier shortens the boxplot since the elite athlete finished much quicker. d) the presence of the outlier increases the median finish...

Explanation:

1. Recall the components of a boxplot: minimum, Q1, median, Q3, maximum. The whiskers extend to the minimum and maximum non - outlier values, and outliers are plotted as individual points.
2. In this case, most finishing times are between 125 - 150 minutes. The elite athlete's time of 94 minutes is much lower (an outlier).
3. For option A: The outlier is a minimum value candidate, but since it's an outlier, the lower whisker will be from Q1 to the minimum non - outlier value (around 125), and the outlier (94) is plotted separately. So the outlier does not change the box (Q1, median, Q3) but creates a longer lower whisker (from the minimum non - outlier to the outlier's position), indicating a wider spread of data (since there's a value far from the main cluster).
4. For option C: The boxplot's length (interquartile range) is based on Q1 and Q3, which are not affected by the outlier. The outlier is a separate point, so it doesn't shorten the boxplot.
5. For the median - related option (not fully visible, but median is the middle value, and one outlier at the low end won't increase the median as the median depends on the middle of the ordered data. Most data is in 125 - 150, so the median is still determined by that cluster).

Answer:

B. The outlier creates a longer lower whisker, indicating a wider spread of data.