Box and Whisker Plot Worksheets - Free Printable

It looks like you've uploaded an image of a completed answer key for a worksheet titled *"Creating a Box Plot on a Number Line"*. The task involves creating box plots (box-and-whisker plots) from given sets of data, and the answers are already provided.

Let me walk through how to solve each problem step by step, explaining the process of creating a box plot. This will help you understand how the values were determined and how to draw the box plots correctly.

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🔍 What is a Box Plot?

A box plot displays five key statistics:
1. Minimum – smallest value
2. Q1 (First Quartile) – median of the lower half
3. Median (Q2) – middle value of the dataset
4. Q3 (Third Quartile) – median of the upper half
5. Maximum – largest value

These are plotted on a number line with a box from Q1 to Q3, a line at the median, and "whiskers" extending to min and max.

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✔ Step-by-Step Solution for Each Problem

We'll go through each set, sort the data, find the 5-number summary, and verify the given values.

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#### 1) Data: 56, 29, 49, 23, 28, 31, 93, 42

Step 1: Sort the data
23, 28, 29, 31, 42, 49, 56, 93

Step 2: Find Min and Max
- Min = 23
- Max = 93 ✔

Step 3: Find Median (Q2)
- 8 numbers → median is average of 4th and 5th
- (31 + 42)/2 = 36.5 ✔

Step 4: Find Q1 (median of lower half: 23, 28, 29, 31)
- Lower half: 23, 28, 29, 31 → median = (28 + 29)/2 = 28.5 ✔

Step 5: Find Q3 (median of upper half: 42, 49, 56, 93)
- Upper half: 42, 49, 56, 93 → median = (49 + 56)/2 = 52.5 ✔

✔ All values match:
Min=23, Max=93, Q1=28.5, Q2=36.5, Q3=52.5

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#### 2) Data: 85, 50, 99, 29, 27, 70, 99

Sort: 27, 29, 50, 70, 85, 99, 99

- Min = 27 ✔
- Max = 99 ✔
- Median (Q2): 7th value → 70 ✔
- Lower half: 27, 29, 50 → Q1 = 29
- Upper half: 85, 99, 99 → Q3 = 99

Wait — but the answer key says Q1=29, Q3=99? But it shows Q2=70, which is correct.

But wait — the key says:
> Min=27 Max=99 q1=29 Q2=70 q3=99

Yes! That matches:
- Q1 = 29 ✔
- Q3 = 99 ✔

So yes, correct.

✔ All values match.

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#### 3) Data: 53, 42, 89, 75, 60, 20, 31, 54

Sort: 20, 31, 42, 53, 54, 60, 75, 89

- Min = 20 ✔
- Max = 89 ✔
- Median (Q2): average of 4th and 5th = (53 + 54)/2 = 53.5 ✔
- Lower half: 20, 31, 42, 53 → Q1 = (31 + 42)/2 = 36.5 ✔
- Upper half: 54, 60, 75, 89 → Q3 = (60 + 75)/2 = 67.5 ✔

✔ All correct.

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#### 4) Data: 28, 74, 48, 59, 85, 32, 93

Sort: 28, 32, 48, 59, 74, 85, 93

- Min = 28 ✔
- Max = 93 ✔
- Median = 59 ✔
- Lower half: 28, 32, 48 → Q1 = 32 ✔
- Upper half: 74, 85, 93 → Q3 = 85 ✔

✔ All correct.

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#### 5) Data: 51, 50, 42, 61, 97, 56, 55, 87

Sort: 42, 50, 51, 55, 56, 61, 87, 97

- Min = 42 ✔
- Max = 97 ✔
- Median = (55 + 56)/2 = 55.5 ✔
- Lower half: 42, 50, 51, 55 → Q1 = (50 + 51)/2 = 50.5 ✔
- Upper half: 56, 61, 87, 97 → Q3 = (61 + 87)/2 = 74 ✔

✔ All match.

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#### 6) Data: 65, 84, 48, 45, 87, 79, 21, 83

Sort: 21, 45, 48, 65, 79, 83, 84, 87

- Min = 21 ✔
- Max = 87 ✔
- Median = (65 + 79)/2 = 72 ✔
- Lower half: 21, 45, 48, 65 → Q1 = (45 + 48)/2 = 46.5 ✔
- Upper half: 79, 83, 84, 87 → Q3 = (83 + 84)/2 = 83.5 ✔

✔ All correct.

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#### 7) Data: 71, 36, 27, 42, 25, 80, 95, 83, 51, 55, 80

Sort: 25, 27, 36, 42, 51, 55, 71, 80, 80, 83, 95

- Min = 25 ✔
- Max = 95 ✔
- Median = 6th value → 55 ✘ Wait! But the key says Q2=55, but let's check.

Wait: 11 values → median is the 6th value → 55 ✔

Lower half: 25, 27, 36, 42, 51 → Q1 = 36 ✔

Upper half: 71, 80, 80, 83, 95 → Q3 = 80 ✔

Key says: Min=25, Max=95, Q1=36, Q2=55, Q3=80 ✔

All correct.

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📊 How to Draw the Box Plot:

For each problem, follow these steps:

1. Draw a number line covering the range (min to max).
2. Mark the five-number summary.
3. Draw a box from Q1 to Q3.
4. Draw a line inside the box at Q2 (median).
5. Draw "whiskers" from Q1 to min and from Q3 to max.

Example for #1:
```
Min=23 Q1=28.5 Q2=36.5 Q3=52.5 Max=93
|--------|---------|---------|---------|
| | |
---------------------
Box Plot
```

(Whiskers extend from 23 to 28.5 and from 52.5 to 93.)

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✔ Final Answer Summary:

All the given values in the answer key are correct. The student would need to:

- Sort each data set.
- Identify Min, Max, Median (Q2), Q1, Q3.
- Plot them on the number line as shown.

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🎯 Tips for Students:

- Always sort the data first.
- For even number of values: median = average of two middle numbers.
- For odd: median is the middle number.
- Use lower and upper halves (excluding median if odd count) to find Q1 and Q3.

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If you have a specific question about one of the problems or want to see a drawn box plot example, feel free to ask!