Question

date
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interpreting box plots sheet 3

1. this box plot show the annual rainfall in inches across different states in the us.

(box plot image with axis labels 15, 20, 25, 30, 35, 40, 45, 50, 55, 60)

a) the median rainfall across the us is ______ inches.
b) the state with the highest rainfall recorded ______ inches
c) the data is \t skewed to the left \t skewed to the right \t symmetric
d) the range in the rainfall data is ______ inches.
e) about 25% of states have rainfall that is less than ______ inches
f) about 25% of states have rainfall that is more than ______ inches.
g) the interquartile range of rainfall is ______ inches

1. this box plot shows the number of points scored in a basketball tournament by a group of players.

(box plot image with axis labels 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90 and a basketball image)

a) the median number of points scored was __________.
b) the highest scoring player scored __________ points.
c) the range of points scored was __________
d) most of the players scored more than 65 points. \t true \t false \t cant tell
e) the data is \t skewed to the left \t skewed to the right \t symmetric
f) the interquartile range is ______________ points.
g) about 75% of the players scored more than 71 points. \t true \t false \t cant tell

Explanation:

Step1: Analyze the first box plot (rainfall)

a) Median

In a box plot, the median is the line inside the box. From the plot, the box's middle line is at 30? Wait, no, the x - axis labels: 15,20,25,30,35,40,45,50,55,60. Wait, the box is between 25 - 40? Wait, no, the left whisker starts at 15, the box starts at 25, the median line (inside the box) is at 30? Wait, no, maybe I misread. Wait, the box plot for rainfall: the box has two parts, maybe the median is at 30? Wait, no, let's check again. Wait, the x - axis: 15,20,25,30,35,40,45,50,55,60. The box is from 25 to 40, and the median line (the middle of the box) is at 30? Wait, no, maybe the box is from 25 to 40, and the median is at 30? Wait, no, perhaps the box is divided into two parts, with the median at 30. Wait, maybe I made a mistake. Let's take the first sub - question (a) of the first problem:

a) Median rainfall

In a box - and - whisker plot, the median is the vertical line inside the box. Looking at the rainfall box plot, the box is positioned such that the median line is at 30? Wait, no, the x - axis labels: 15,20,25,30,35,40,45,50,55,60. The box starts at 25, ends at 40, and the median (the middle line of the box) is at 30? Wait, maybe. So the median is 30 inches.

b) Highest rainfall

The right whisker ends at 60, so the highest rainfall is 60 inches.

c) Skewness

The left whisker is longer (from 15 to 25) and the right whisker is from 40 to 60. Wait, no, the box is from 25 to 40, left whisker 15 - 25, right whisker 40 - 60. The left tail (whisker) is longer? Wait, no, skewness: if the right whisker is longer, it's skewed right. Wait, the right whisker goes from 40 to 60 (length 20), left whisker from 15 to 25 (length 10). So the data is skewed to the right.

d) Range

Range = maximum - minimum. Minimum is 15, maximum is 60. So range = 60 - 15 = 45.

e) 25% less than

In a box - plot, the first quartile (Q1) is the left end of the box. The box starts at 25, so Q1 is 25. So about 25% of states have rainfall less than 25 inches.

f) 25% more than

The third quartile (Q3) is the right end of the box. The box ends at 40, so Q3 is 40. So about 25% of states have rainfall more than 40 inches.

g) Interquartile range (IQR)

IQR = Q3 - Q1. Q3 = 40, Q1 = 25. So IQR = 40 - 25 = 15.

Now for the second box plot (basketball points):

a) Median points

The box plot for basketball: x - axis 40,45,50,55,60,65,70,75,80,85,90. The box is from 55 to 70, and the median line inside the box is at 65? Wait, the box is divided into two parts, with the median at 65? So median is 65.

b) Highest scoring

The right whisker ends at 90, so highest score is 90.

c) Range

Range = maximum - minimum. Minimum is 40, maximum is 90. So range = 90 - 40 = 50.

d) Most players scored more than 65?

The median is 65, which means 50% of the data is above and 50% below. So "most" (more than 50%)? No, 50% is above 65. So the statement "Most of the players scored more than 65 points" is false? Wait, no, median is 65, so 50% are above, 50% below. So "most" (more than 50%) is false.

e) Skewness

Left whisker: 40 - 55, right whisker:70 - 90. The left whisker is longer (15 units: 55 - 40 = 15) and the right whisker is 20 units (90 - 70 = 20)? Wait, no, the box is from 55 to 70. Left whisker 40 - 55 (length 15), right whisker 70 - 90 (length 20). Wait, but the left tail (whisker) is longer? Wait, no, skewness: if the left whisker is longer, it's skewed left? Wait, no, skewness is determined by the tail. If the left tail is longer, skewed left; right tail longer, skewed right. Wait, the left whisker (from 40 to 55) is length 15, right whisker (70 to 90) is length 20. Wait, maybe I made a mistake. Wait, the box is from 55 to 70, median at 65. The left whisker is from 40 to 55 (15 units), right whisker from 70 to 90 (20 units). So the right tail is longer? Wait, no, 90 - 70 = 20, 55 - 40 = 15. So right tail is longer, so skewed to the right? Wait, no, skewness: the direction of the longer tail. If right tail is longer, skewed right; left tail longer, skewed left. So here, right tail (from 70 to 90) is longer (20) than left tail (40 to 55, 15), so skewed to the right? Wait, but the median is in the middle of the box (65 is the middle of 55 and 70). Wait, maybe the data is symmetric? Wait, 70 - 65 = 5, 65 - 55 = 10? No, 70 - 65 = 5, 65 - 55 = 10. Wait, no, the box is from 55 to 70, so the length of the box is 15 (70 - 55 = 15). The median is at 65, which is 10 units from 55 and 5 units from 70. So the left part of the box (55 - 65) is 10, right part (65 - 70) is 5. So the box is not symmetric, and the right whisker is longer. So skewed to the right?

f) Interquartile range (IQR)

Q1 = 55, Q3 = 70. IQR = 70 - 55 = 15.

g) About 75% of players scored more than 71?

Q3 is 70, so 25% of the data is above Q3 (70). 71 is above 70, so less than 25% of players scored more than 71. So the statement "About 75% of the players scored more than 71 points" is false.

But let's answer the first sub - question (a) of the first problem properly:

1a) Median rainfall

In a box - and - whisker plot, the median is the vertical line inside the box. From the rainfall box plot, the box's middle line (median) is at 30 (looking at the x - axis labels: 15,20,25,30,35,40,45,50,55,60. The box is between 25 and 40, and the median line is at 30). So the median rainfall is 30 inches.

Step2: (1b) Highest rainfall

The right whisker of the rainfall box plot ends at 60, so the maximum (highest rainfall) is 60 inches.

Step3: (1c) Skewness

The left whisker (from 15 to 25) is shorter than the right whisker (from 40 to 60)? Wait, no, 25 - 15 = 10, 60 - 40 = 20. So the right whisker is longer, which means the data is skewed to the right (because the right tail is longer).

Step4: (1d) Range of rainfall

Range = maximum - minimum. Minimum is 15 (left whisker start), maximum is 60. So range = 60 - 15 = 45.

Step5: (1e) 25% less than

In a box - plot, the first quartile (Q1) is the left end of the box. The box for rainfall starts at 25, so Q1 = 25. So about 25% of states have rainfall less than 25 inches.

Step6: (1f) 25% more than

The third quartile (Q3) is the right end of the box. The box for rainfall ends at 40, so Q3 = 40. So about 25% of states have rainfall more than 40 inches.

Step7: (1g) Interquartile range of rainfall

IQR = Q3 - Q1 = 40 - 25 = 15.

Now for the basketball part (2a):

Step8: (2a) Median points

The box for basketball points has the median line at 65 (x - axis: 40,45,50,55,60,65,70,75,80,85,90. The box is from 55 to 70, and the median line is at 65). So median is 65.

Step9: (2b) Highest scoring player

The right whisker ends at 90, so highest score is 90.

Step10: (2c) Range of points

Range = 90 - 40 = 50.

Step11: (2d) Most players scored more than 65?

Median is 65, so 50% of players scored above 65 and 50% below. So "most" (more than 50%) is false.

Step12: (2e) Skewness

The left part of the box (55 - 65) is longer than the right part (65 - 70), and the left whisker (40 - 55) is shorter than the right whisker (70 - 90)? Wait, no, 55 - 40 = 15, 90 - 70 = 20. The right whisker is longer, and the right part of the box is shorter. So the data is skewed to the right? Wait, no, skewness is determined by the tail. If the right tail is longer, skewed right.

Step13: (2f) Interquartile range of points

Q1 = 55, Q3 = 70. IQR = 70 - 55 = 15.

Step14: (2g) About 75% scored more than 71?

Q3 is 70, so 25% of data is above 70. 71 is above 70, so less than 25% scored more than 71. So the statement is false.

Answer:

1a) 30

1b) 60

1c) skewed to the right

1d) 45

1e) 25

1f) 40

1g) 15

2a) 65

2b) 90

2c) 50

2d) false

2e) skewed to the right

2f) 15

2g) false