Question

question 18 of 25
these box plots show the basketball scores for two teams.
wolverines
35 55 80 85 96
panthers
33 50 70 90 107
30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110
basketball scores
compare the shapes of the box plots.
a. the wolverines distribution is negatively skewed, but
the panthers distribution is symmetric.
b. both distributions are symmetric.
c. both distributions are negatively skewed.
d. the wolverines distribution is positively skewed, but
the panthers distribution is symmetric.

Explanation:

Step1: Recall Box Plot Skewness

For a box plot, skewness is determined by the position of the median (line inside the box) and the lengths of the whiskers. If the median is closer to one end of the box, or if one whisker is longer, it indicates skewness. A symmetric distribution has the median in the middle of the box and whiskers of similar length.

Step2: Analyze Wolverines' Box Plot

Wolverines' box plot: The median (line in box) is closer to the right end of the box. The left whisker (from 35 to 55) is shorter than the right whisker (from 85 to 96)? Wait, no—wait, the box is from 55 to 85? Wait, the data points: minimum 35, Q1 55, median (line) around, say, 80 - 85? Wait, no, the box plot for Wolverines: the left whisker is from 35 to 55 (Q1), the box is from 55 to 85 (Q3?), wait, no, box plot components: minimum, Q1, median, Q3, maximum. So Wolverines: min=35, Q1=55, median (line) is between 80 - 85? Wait, the box is from 55 to 85? Then Q1=55, median (line) is closer to Q3 (85), so the left part (from min to median) is longer? Wait, no—if the median is closer to Q3, then the left whisker and left half of the box (from min to median) is longer than the right half (median to max). Wait, min=35, Q1=55, median (let's say at 80), Q3=85, max=96. So from min (35) to median (80): length is 80 - 35 = 45. From median (80) to max (96): length is 16. So the left side (min to median) is longer than the right side (median to max), which means negative skewness? Wait, no—wait, skewness: positive skewness is when the tail is on the right (longer right tail), negative skewness is tail on the left (longer left tail). Wait, no, actually: in a box plot, if the median is closer to Q1 (left of the box), or the left whisker is shorter, right whisker longer: positive skewness. If median is closer to Q3 (right of the box), or left whisker longer, right whisker shorter: negative skewness? Wait, I think I mixed up. Let's correct: Positive skewness (right-skewed): median is closer to Q1, right whisker longer. Negative skewness (left-skewed): median is closer to Q3, left whisker longer. Wait, no, the tail is where the skewness is. So if the left tail (whisker) is longer, it's left-skewed (negative skewness). If right tail is longer, right-skewed (positive skewness). Wait, Wolverines: min=35, Q1=55, median (line) is in the box. Let's check the lengths: from min (35) to Q1 (55): length 20. Q1 (55) to median: let's say median is at 80. Then median to Q3 (85): length 5. Q3 (85) to max (96): length 11. Wait, no, maybe I misread. Wait, the Wolverines' box plot: the left whisker (from 35 to 55) is shorter than the right? No, wait, the minimum is 35, Q1 is 55 (so left whisker length: 55 - 35 = 20). Then the box is from 55 to 85 (Q3=85), so the box length is 30. The median (line) is inside the box, closer to the right (Q3). Then from median to Q3: shorter than from Q1 to median. Then the right whisker: from Q3 (85) to max (96): length 11. So the left side (min to median) is 80 - 35 = 45 (if median is 80), and right side (median to max) is 16. So left tail (whisker + left half of box) is longer? Wait, no, maybe I got it wrong. Alternatively, look at the Panthers' box plot.

Step3: Analyze Panthers' Box Plot

Panthers: min=33, Q1=50, median (line) in the middle of the box (the box is from 50 to 90? Wait, the box is split into two equal parts (since the median line is in the middle of the box). So Q1=50, median=70, Q3=90? Wait, the box is from 50 to 90, median at 70 (middle of 50 and 90). Then min=33, max=107. The left whisker: 33 to 50 (length 17), right whisker: 90 to 107 (length 17). So whiskers are of similar length, median in the middle of the box. So Panthers' distribution is symmetric.

Step4: Re-analyze Wolverines' Skewness

Wolverines: min=35, Q1=55, median (line) is closer to Q3 (85). The left whisker (35 to 55) is shorter than the right? Wait, no—wait, the left side (from min to median) is longer than the right side (median to max)? Wait, no, if the median is closer to Q3, that means the data is skewed left (negative skewness), because the tail is on the left? Wait, no, positive skewness is tail on the right (longer right tail), negative is tail on the left (longer left tail). Wait, let's use the rule: in a box plot, if the median is closer to Q1 (left of the box), or the right whisker is longer, it's positive skewness. If median is closer to Q3 (right of the box), or left whisker is longer, it's negative skewness. Wait, Wolverines: median is closer to Q3 (right of the box), so the left whisker (from min to Q1) is shorter than the right? No, wait, min=35, Q1=55 (left whisker length: 55-35=20), Q3=85, max=96 (right whisker length: 96-85=11). So left whisker is longer than right? Wait, 20 > 11. So left whisker is longer, median closer to Q3: that indicates negative skewness (tail on the left).

So Wolverines: negative skewed (tail on left), Panthers: symmetric. So option A: "The Wolverines’ distribution is negatively skewed, but the Panthers’ distribution is symmetric." matches.

Answer:

A. The Wolverines’ distribution is negatively skewed, but the Panthers’ distribution is symmetric.