Box and Whisker Plots Notes and Worksheets - Lindsay Bowden - Free Printable

Let’s work through each problem step by step.

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Problem 1: Find the range, Q1, Q2, Q3, and the IQR using the box and whisker plot.

Looking at the number line:

- The minimum (min) is at 25
- Q1 (first quartile) is at 40
- Q2 (median) is at 65
- Q3 (third quartile) is at 80
- The maximum (max) is at 90

Now calculate:

→ Range = max – min = 90 – 25 = 65

→ IQR (Interquartile Range) = Q3 – Q1 = 80 – 40 = 40

So for Problem 1:
- Range = 65
- Q1 = 40
- Q2 = 65
- Q3 = 80
- IQR = 40

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Problem 2: Temperatures: 71°, 80°, 73°, 75°, 72°, 84°, 78°, 79°, 81°

First, sort the data in order:

71, 72, 73, 75, 78, 79, 80, 81, 84

There are 9 numbers → odd count → median is the middle one (5th value).

→ Q2 (median) = 78

Now split into lower half and upper half (exclude median when splitting for odd counts):

Lower half: 71, 72, 73, 75 → 4 numbers → median of this is average of 2nd and 3rd → (72 + 73)/2 = 72.5

→ Q1 = 72.5

Upper half: 79, 80, 81, 84 → median = (80 + 81)/2 = 80.5

→ Q3 = 80.5

Min = 71, Max = 84

→ Range = 84 – 71 = 13

→ IQR = Q3 – Q1 = 80.5 – 72.5 = 8

To draw the box and whisker plot:

- Draw a number line from 70 to 86 (as given)
- Mark min (71), Q1 (72.5), Q2 (78), Q3 (80.5), max (84)
- Draw box from Q1 to Q3, with line at Q2
- Draw whiskers from min to Q1 and from Q3 to max

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Problem 3: Test scores: 90, 63, 75, 88, 96, 34, 76, 82, 94, 73, 80, 85, 71, 68, 79, 82, 64

Step 1: Sort the data:

34, 63, 64, 68, 71, 73, 75, 76, 79, 80, 82, 82, 85, 88, 90, 94, 96

Count: 17 numbers → odd → median is 9th value → Q2 = 79

Split into lower and upper halves (exclude median):

Lower half (first 8): 34, 63, 64, 68, 71, 73, 75, 76
→ Median of lower half = average of 4th and 5th = (68 + 71)/2 = 69.5 → Q1

Upper half (last 8): 80, 82, 82, 85, 88, 90, 94, 96
→ Median of upper half = average of 4th and 5th = (85 + 88)/2 = 86.5 → Q3

Min = 34, Max = 96

→ Range = 96 – 34 = 62

→ IQR = 86.5 – 69.5 = 17

To draw:

- Make a number line that includes 34 to 96 (maybe start at 30, go to 100)
- Mark min (34), Q1 (69.5), Q2 (79), Q3 (86.5), max (96)
- Draw box from Q1 to Q3, line at Q2
- Whiskers from min to Q1 and Q3 to max

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Final Answer:

Problem 1:
Range = 65, Q1 = 40, Q2 = 65, Q3 = 80, IQR = 40

Problem 2:
Sorted data: 71, 72, 73, 75, 78, 79, 80, 81, 84
Min = 71, Q1 = 72.5, Q2 = 78, Q3 = 80.5, Max = 84
Range = 13, IQR = 8
(Box plot drawn on given number line with these values)

Problem 3:
Sorted data: 34, 63, 64, 68, 71, 73, 75, 76, 79, 80, 82, 82, 85, 88, 90, 94, 96
Min = 34, Q1 = 69.5, Q2 = 79, Q3 = 86.5, Max = 96
Range = 62, IQR = 17
(Number line and box plot drawn with these values)