Question

analyzing box-and-whisker plots
directions: use the box-and-whisker plot graphs below to answer the questions that follow
1.) robinson’s points scored per game
a.) what was the highest total points scored?
b.) what was the lowest total points scored?
c.) what was the median number of points scored?
d.) what percent of games did robinson score 19 or more points?
e.) what percent of games did robinson score 13 points or fewer?
f.) how many points do you think robinson will score in his next game and why?
2.) science test scores (as percents)
a.) what was the highest grade on the test?
b.) what was the lowest total grade on the test?
c.) what was the median test score?
d.) what percent of test scores were greater than 96%?
e.) what percent of test scores were less than 96%?
f.) do you think that students performed well on this test overall? why or why not?

Explanation:

Step1: Analyze box - and - whisker plot for Robinson's Points

• For part A: The right - most point of the whisker is the highest value. In the "Robinson's Points Scored Per Game" plot, the right - most value is \(36\).
• For part B: The left - most point of the whisker is the lowest value. In the "Robinson's Points Scored Per Game" plot, the left - most value is \(8\).
• For part C: The line inside the box is the median. In the "Robinson's Points Scored Per Game" plot, the median line is at \(19\).
• For part D: The box - and - whisker plot divides the data into four equal parts (quartiles). The value \(19\) is the median. The data to the right of the median (including the median) represents \(50\%\) of the data. So, \(50\%\) of the games Robinson scored \(19\) or more points.
• For part E: The value \(13\) is the first quartile (\(Q1\)). The first quartile represents \(25\%\) of the data. So, \(25\%\) of the games Robinson scored \(13\) or fewer points.

Step2: Analyze box - and - whisker plot for Science Test Scores

• For part A: The right - most point of the whisker is the highest value. In the "Science Test Scores" plot, the right - most value is \(100\).
• For part B: The left - most point of the whisker is the lowest value. In the "Science Test Scores" plot, the left - most value is \(53\).
• For part C: The line inside the box is the median. In the "Science Test Scores" plot, the median line is at \(84\).
• For part D: The value \(96\) is the third quartile (\(Q3\)). The data to the right of \(Q3\) (excluding \(Q3\)) represents \(25\%\) of the data. But since \(96\) is a single point (not part of the quartile division in the strict sense here, but considering the whisker - end), if we assume the data is evenly distributed, the percentage of data greater than \(96\) is \(0\%\) (because \(96\) is the end of the whisker and there is no data beyond it in the plot shown).
• For part E: The value \(96\) is the end of the whisker. The data to the left of \(96\) (including \(96\)) represents \(100\%\) of the data (since there is no data beyond \(96\) in the plot shown).

Answer:

1.
A. \(36\)
B. \(8\)
C. \(19\)
D. \(50\%\)
E. \(25\%\)
F. (Answers may vary. For example) Maybe around \(19\) (the median) because the median represents the middle value of the data set and is a measure of central tendency.
2.
A. \(100\)
B. \(53\)
C. \(84\)
D. \(0\%\)
E. \(100\%\)
F. (Answers may vary. For example) Yes, because the median score is \(84\) (a relatively high score) and the lower whisker starts at \(53\) but most of the data (as indicated by the box and the upper whisker) is in the higher range.