Box Plot (Box and Whisker Plot) Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Box-and-Whisker Plots" that includes several problems involving interpreting and creating box plots (also known as box-and-whisker plots). The task is to analyze the given data sets, identify key statistics (minimum, Q1, median, Q3, maximum), and use them to draw or interpret box plots.

Since I can't view images directly, I’ll help you solve this type of problem based on the typical structure of such worksheets. Let me walk you through how to approach each section step by step, assuming the format matches standard practice.

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🔍 What is a Box-and-Whisker Plot?

A box-and-whisker plot displays five-number summary statistics:
1. Minimum – smallest value
2. Q1 (First Quartile) – median of the lower half
3. Median (Q2) – middle value of the data set
4. Q3 (Third Quartile) – median of the upper half
5. Maximum – largest value

The "box" spans from Q1 to Q3, with a line at the median. "Whiskers" extend to the min and max values.

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✔ How to Solve These Problems:

Let’s assume each problem gives a data set and asks you to:
- Find the 5-number summary
- Draw the box plot
- Identify outliers (if any)

We'll go through an example similar to what might be in your image.

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#### 📊 Example Problem (Typical Format):

Data Set:
64, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86

Step 1: Order the data
Already ordered.

Step 2: Find the 5-number summary
- Min = 64
- Max = 86
- Median (Q2): Middle value → 74 (since there are 11 values)
- Q1: Median of lower half (first 5 numbers): 64, 68, 70, 72, 74 → Q1 = 70
- Q3: Median of upper half (last 5 numbers): 76, 78, 80, 82, 84 → Q3 = 80

So:
- Min = 64
- Q1 = 70
- Median = 74
- Q3 = 80
- Max = 86

Step 3: Draw the box plot
- Draw a number line from 60 to 90.
- Mark points at 64, 70, 74, 80, 86.
- Draw a box from 70 to 80.
- Draw a line at 74 inside the box.
- Draw whiskers from 64 to 70 and from 80 to 86.

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Now let's suppose your worksheet has multiple such problems. Here's how to handle each one:

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🔁 General Steps for Each Problem:

1. List the data in order (if not already sorted).
2. Find the minimum and maximum.
3. Find the median (Q2).
4. Find Q1 (median of the lower half).
5. Find Q3 (median of the upper half).
6. Draw the box plot using these values.
7. Check for outliers (optional):
- IQR = Q3 − Q1
- Lower fence = Q1 − 1.5×IQR
- Upper fence = Q3 + 1.5×IQR
- Any data point outside fences is an outlier.

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💡 Tips for Accuracy:

- Always double-check if the data has an even or odd number of values when finding the median.
- For even-sized data sets, median = average of two middle numbers.
- Use the correct method to find quartiles (some teachers prefer exclusive vs inclusive methods).

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🧩 Sample Problem from Your Worksheet (Assumed):

Let’s say one problem says:

> Data: 12, 15, 18, 20, 22, 24, 25, 28, 30, 32
> Min = ?, Q1 = ?, Med = ?, Q3 = ?, Max = ?

Solution:
- Min = 12
- Max = 32
- Median = (22 + 24)/2 = 23
- Lower half: 12, 15, 18, 20, 22 → Q1 = 18
- Upper half: 24, 25, 28, 30, 32 → Q3 = 28

So:
- Min = 12
- Q1 = 18
- Med = 23
- Q3 = 28
- Max = 32

Then draw the box plot accordingly.

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📝 Final Answer Format (for each box):

You would fill in:
- Min: 12
- Q1: 18
- Med: 23
- Q3: 28
- Max: 32

And sketch the box plot on the provided number line.

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❗ Common Mistakes to Avoid:

- Confusing Q1 and Q3
- Not ordering data first
- Misidentifying the median in even-sized sets
- Drawing whiskers beyond min/max

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If you can describe or type out the specific data sets from the worksheet (e.g., “Problem 1: 10, 14, 16, 18, 20, 22, 24”), I can solve each one for you step-by-step.

Alternatively, if you can copy-paste the text of the problems, I’ll give you full solutions with explanations.

Let me know!