Math worksheet on box plots with exercises for analyzing and creating box plots.

Here are the solutions to the problems on the worksheet, broken down by section.

Section A

Problem 1 (Left Plot: Distance)
To find the values, we look at where the lines fall on the number line.
* Median: This is the vertical line inside the box. It lines up with 16.
* Interquartile Range (IQR): This is the width of the box ($Q3 - Q1$).
* Right side of box ($Q3$) = 17
* Left side of box ($Q1$) = 13
* $17 - 13 =$ 4
* Range: This is the total length from the end of the left whisker to the end of the right whisker ($Max - Min$).
* End of right whisker = 19
* End of left whisker = 9
* $19 - 9 =$ 10

Problem 2 (Right Plot: Time)
* Median: The line inside the box is at 18.
* Interquartile Range (IQR):
* Right side of box ($Q3$) = 32
* Left side of box ($Q1$) = 11
* $32 - 11 =$ 21
* Range:
* End of right whisker = 48
* End of left whisker = 5
* $48 - 5 =$ 43

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Section B

Problem 1 (Draw a box plot)
You need to draw a plot using these numbers: Low=3, High=17, Median=9.5, Lower Quartile=5, Upper Quartile=12.
* Draw a vertical line at 3.
* Draw a vertical line at 5.
* Draw a vertical line at 9.5 (halfway between 9 and 10).
* Draw a vertical line at 12.
* Draw a vertical line at 17.
* Connect 5 to 12 with a box.
* Connect 3 to 5 with a line (whisker).
* Connect 12 to 17 with a line (whisker).

Problem 2 (Draw two box plots)
You will draw Class A and Class B on the same grid.

* Class A:
* Whiskers: 14 to 66
* Box: 31 to 59
* Median line: 42
* Class B:
* Whiskers: 24 to 59
* Box: 34 to 40
* Median line: 36

*(Tip: You might want to draw Class A slightly higher up on the grid and Class B slightly lower so they don't overlap).*

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Section C

Problem (Yoan's Class Test)
First, we must organize the data to find the "Five Number Summary."

1. Order the data from smallest to largest:
4, 9, 17, 21, 24, 24, 25, 27, 28, 29, 30, 32
(There are 12 numbers total).

2. Find the Five Numbers:
* Lowest Value: 4
* Highest Value: 32
* Median: Since there are 12 numbers (an even amount), the median is the average of the two middle numbers (the 6th and 7th numbers).
* 6th number: 24
* 7th number: 25
* Average: $(24 + 25) / 2 =$ 24.5
* Lower Quartile (Q1): This is the median of the bottom half (first 6 numbers: 4, 9, 17, 21, 24, 24).
* Middle two are 17 and 21.
* Average: $(17 + 21) / 2 =$ 19
* Upper Quartile (Q3): This is the median of the top half (last 6 numbers: 25, 27, 28, 29, 30, 32).
* Middle two are 28 and 29.
* Average: $(28 + 29) / 2 =$ 28.5

3. Draw the Plot:
* Draw vertical lines at 4, 19, 24.5, 28.5, and 32.
* Make a box from 19 to 28.5.
* Put a line inside the box at 24.5.
* Draw whiskers connecting the ends of the box to 4 and 32.

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Final Answer:

Section A
* Distance Plot: Median: 16, IQR: 4, Range: 10
* Time Plot: Median: 18, IQR: 21, Range: 43

Section B
* Plot 1 Values: Min: 3, Q1: 5, Med: 9.5, Q3: 12, Max: 17
* Plot 2 Class A Values: Min: 14, Q1: 31, Med: 42, Q3: 59, Max: 66
* Plot 2 Class B Values: Min: 24, Q1: 34, Med