Question

1. coach fuller logged the number of points scored in his team’s 52 basketball games. his results are shown in the box plot below.

a. what percentage of games did the team score over 40 points? ______
b. what percentage of games did the team score between 22 and 40 points? ______
c. each quartile contains how many games? ______
d. how many games did the team score under 30 points? ______
e. what is the interquartile range (iqr) of the data? ______

Explanation:

Part a

Step1: Identify upper whisker limit

The upper whisker ends at 40, so games over 40: from box plot, the upper whisker is at 40, but the maximum (whisker end) is 40? Wait, no, the box plot: the upper whisker is from Q3 to max. Wait, the total games are 52. Wait, first, in a box plot, the data is divided into quartiles. Each quartile is 25% of the data (since 4 quartiles, 100%/4 = 25% each). Wait, the upper whisker: the maximum value (the end of the upper whisker) is 40? Wait, the plot shows the upper whisker ends at 40? Wait, no, the vertical line (whisker) at the top: the left side of the box is Q1, middle is median, right side is Q3. The whiskers go from Q1 to min, and Q3 to max. Wait, the min is 22 (left whisker end), Q1 is 26? Wait, no, the number line: 20,24,28,32,36,40,44. The box starts at 26? Wait, no, the box is from, let's see, the left edge of the box is at 26? Wait, no, the first quartile (Q1) is the left side of the box, median is the line inside the box, Q3 is the right side of the box. Wait, the total number of games is 52. So each quartile has 52/4 = 13 games? Wait, 52 divided by 4 is 13. So Q1 is the 13th percentile? No, quartiles: Q1 is 25th percentile, Q2 (median) 50th, Q3 75th. So number of games in each quartile: 25% of 52. So 0.25*52 = 13. So each quartile has 13 games. Now, part a: games over 40. The upper whisker: the max is 40? Wait, the upper whisker ends at 40? So games over 40: from the box plot, the upper whisker is from Q3 to max. If max is 40, then games over 40: 0? Wait, no, maybe the upper whisker is from Q3 (right side of box) to max. Wait, the box's right side is at 40? No, the box is between, say, Q1=26, median=30, Q3=40? Wait, no, the number line: 20,24,28,32,36,40,44. The box is from, let's see, the left whisker is at 22 (min), box starts at 26 (Q1), median at 30, box ends at 40 (Q3), and upper whisker to 40? No, that can't be. Wait, maybe the upper whisker is from Q3 (40) to max (40)? No, that would mean max is 40. So games over 40: 0. But that seems odd. Wait, maybe I misread. Wait, the total games are 52. Let's re-express:

In a box plot, the five-number summary is min, Q1, median, Q3, max.

From the plot:

• Min: 22 (left whisker end)
• Q1: 26 (left side of box)
• Median: 30 (line inside box)
• Q3: 40 (right side of box)
• Max: 40 (upper whisker end)

Wait, so max is 40. So games over 40: 0. But that seems wrong. Wait, maybe the upper whisker is from Q3 (40) to max (40), so no games over 40. So percentage: (0/52)*100 = 0%. But that seems odd. Wait, maybe the Q3 is 36? Wait, the number line: 20,24,28,32,36,40,44. The box is from 26 to 40? No, the box is between, say, 26 (Q1) and 40 (Q3), median at 30. Then max is 40. So games over 40: 0. So percentage is 0. But maybe I made a mistake. Wait, let's check part b: between 22 and 40. Min is 22, max is 40, so all games? But 52 games. Wait, no, the whiskers are from Q1 to min, and Q3 to max. Wait, no: the left whisker is from min to Q1, and right whisker from Q3 to max. So min is 22, Q1 is 26, so games between 22 and 26: 25%? No, Q1 is 25th percentile, so games ≤ Q1: 25%, between Q1 and median: 25%, median and Q3: 25%, Q3 and max: 25%. Wait, total games 52. So:

• Games ≤ Q1 (26): 0.25*52 = 13
• Games between Q1 (26) and median (30): 13
• Games between median (30) and Q3 (40): 13
• Games between Q3 (40) and max (40): 13? No, max is 40, so Q3 to max is 13 games (25% of 52). Wait, that would mean max is 40, so games over 40: 0. So part a: games over 40: 0. Percentage: (0/52)*100 ≈ 0%.

But maybe the upper whisker is beyond 40? Wait, the plot shows the…

Step1: Identify range

Min is 22, max is 40. So games between 22 and 40: all games except those below 22 or above 40. But min is 22, max is 40, so all 52 games? Wait, no, the whiskers: left whisker is from min (22) to Q1 (26), so games between 22 and 26: 13 (25%), Q1 to median (30):13, median to Q3 (40):13, Q3 to max (40):13. So between 22 and 40: all 52 games? Wait, min is 22, max is 40, so the range is 22 to 40, which includes all games. So percentage: (52/52)*100 = 100%. But that seems odd. Wait, maybe the max is above 40? Wait, the plot shows the upper whisker ends at 40, so max is 40. So between 22 and 40: all games. So 100%.

Part c

Step1: Total games and quartiles

Total games: 52. Quartiles divide data into 4 equal parts. So each quartile has 52 / 4 = 13 games.

Part d

Answer:

0% (assuming max is 40, so no games over 40)

b.