Box and Whisker Plot Worksheets - Free Printable

Since I can't view or access images directly, I can't see the specific data or image you've uploaded. However, if you describe the content of the image (such as the data sets for the box-and-whisker plots or any other details), I can help you solve the problems and explain the solutions step by step.

For now, let me provide a general guide on how to solve Box-and-Whisker Plot problems like the ones in your worksheet:

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🔷 What is a Box-and-Whisker Plot?

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

The "box" spans from Q₁ to Q₃, with a line at the median. The "whiskers" extend to the min and max values (unless there are outliers).

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✔ Problem 1: Make a box-and-whisker plot

Data: 90, 70, 82, 65, 90, 88, 70, 78, 85, 91

#### Step 1: Order the data
65, 70, 70, 78, 82, 85, 88, 90, 90, 91

#### Step 2: Find the five-number summary
- Min: 65
- Max: 91
- Median (Q₂): Middle of 10 numbers → average of 5th and 6th: (82 + 85)/2 = 83.5
- Q₁: Median of first half (65, 70, 70, 78, 82) → 70
- Q₃: Median of second half (85, 88, 90, 90, 91) → 90

So:
- Min = 65
- Q₁ = 70
- Median = 83.5
- Q₃ = 90
- Max = 91

Now draw the box plot using these values.

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✔ Problem 2: Use the plot to answer questions

Suppose the plot shows:
- Min = 42
- Q₁ = 50
- Median = 58
- Q₃ = 64
- Max = 72

Then:
- Range = Max − Min = 72 − 42 = 30
- Interquartile Range (IQR) = Q₃ − Q₁ = 64 − 50 = 14
- Outliers? Check if any values are below Q₁ − 1.5×IQR or above Q₃ + 1.5×IQR
- Lower bound: 50 − 1.5×14 = 50 − 21 = 29
- Upper bound: 64 + 21 = 85
So no outliers unless data includes values outside [29, 85].

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✔ Problem 3: Compare two data sets

If given two box plots (e.g., Class A and Class B), compare:
- Median → which class has higher central tendency?
- IQR → which class has more spread in the middle 50%?
- Range → overall spread
- Outliers → any extreme values?

Example:
- If Class A has higher median than Class B → Class A generally scored higher.
- If Class A has smaller IQR → scores are more consistent.

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Please provide the specific data or descriptions from your image (like the numbers in each problem), and I’ll give you exact answers and explanations tailored to your worksheet!