Box and Whisker Plot worksheet for students to practice creating plots from given data sets.

Absolutely! Let’s solve each problem step by step. For each data set, we need to find the five-number summary:

> Five-Number Summary = [Minimum, Q₁ (First Quartile), Q₂ (Median), Q₃ (Third Quartile), Maximum]

Then, we’ll describe how to draw the box-and-whisker plot on the number line provided.

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## ✔ Problem 1:
Data Set: 7, 25, 18, 1, 24, 3, 11, 9, 15, 22, 23, 5, 12

Step 1: Sort the data in ascending order

→ 1, 3, 5, 7, 9, 11, 12, 15, 18, 22, 23, 24, 25

There are 13 numbers → odd count.

Step 2: Find Minimum and Maximum

- Minimum = 1
- Maximum = 25

Step 3: Find Median (Q₂)

Since n=13 (odd), median is the 7th value.
→ Sorted: 1, 3, 5, 7, 9, 11, 12, 15, 18, 22, 23, 24, 25
→ Q₂ = 12

Step 4: Find Q₁ (First Quartile)

Q₁ is the median of the lower half (not including the overall median).

Lower half: first 6 numbers → 1, 3, 5, 7, 9, 11
→ n=6 (even) → average of 3rd and 4th values: (5 + 7)/2 = 6

→ Q₁ = 6

Step 5: Find Q₃ (Third Quartile)

Q₃ is the median of the upper half (not including the overall median).

Upper half: last 6 numbers → 15, 18, 22, 23, 24, 25
→ n=6 (even) → average of 3rd and 4th values: (22 + 23)/2 = 22.5

→ Q₃ = 22.5

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✔ Five-Number Summary for Problem 1:
- Minimum: 1
- Q₁: 6
- Q₂: 12
- Q₃: 22.5
- Maximum: 25

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## ✔ Problem 2:
Data Set: 1, 24, 13, 4, 11, 7, 22, 15, 19

Step 1: Sort the data

→ 1, 4, 7, 11, 13, 15, 19, 22, 24

There are 9 numbers → odd count.

Step 2: Min and Max

- Minimum = 1
- Maximum = 24

Step 3: Median (Q₂)

n=9 → 5th value → 13

→ Q₂ = 13

Step 4: Q₁

Lower half (first 4 numbers): 1, 4, 7, 11
→ n=4 (even) → average of 2nd and 3rd: (4 + 7)/2 = 5.5

→ Q₁ = 5.5

Step 5: Q₃

Upper half (last 4 numbers): 15, 19, 22, 24
→ average of 2nd and 3rd: (19 + 22)/2 = 20.5

→ Q₃ = 20.5

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✔ Five-Number Summary for Problem 2:
- Minimum: 1
- Q₁: 5.5
- Q₂: 13
- Q₃: 20.5
- Maximum: 24

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## ✔ Problem 3:
Data Set: 6, 9, 7, 13, 10, 12, 8, 15, 19, 2, 11

Step 1: Sort the data

→ 2, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19

There are 11 numbers → odd count.

Step 2: Min and Max

- Minimum = 2
- Maximum = 19

Step 3: Median (Q₂)

n=11 → 6th value → 10

→ Q₂ = 10

Step 4: Q₁

Lower half (first 5 numbers): 2, 6, 7, 8, 9
→ n=5 → median = 3rd value → 7

→ Q₁ = 7

Step 5: Q₃

Upper half (last 5 numbers): 11, 12, 13, 15, 19
→ median = 3rd value → 13

→ Q₃ = 13

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✔ Five-Number Summary for Problem 3:
- Minimum: 2
- Q₁: 7
- Q₂: 10
- Q₃: 13
- Maximum: 19

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## 📊 How to Draw the Box-and-Whisker Plot:

For each problem, on the given number line (from 1 to 25):

1. Mark the five points: Min, Q₁, Q₂, Q₃, Max.
2. Draw a box from Q₁ to Q₃.
3. Draw a vertical line inside the box at Q₂ (median).
4. Draw “whiskers”:
- Left whisker from Q₁ to Min.
- Right whisker from Q₃ to Max.

You can sketch this directly on the worksheet using the labeled number line.

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## 📝 Final Answers to Fill In:

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Problem 1:

- Minimum: 1
- Q₁: 6
- Q₂: 12
- Q₃: 22.5
- Maximum: 25

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Problem 2:

- Minimum: 1
- Q₁: 5.5
- Q₂: 13
- Q₃: 20.5
- Maximum: 24

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Problem 3:

- Minimum: 2
- Q₁: 7
- Q₂: 10
- Q₃: 13
- Maximum: 19

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Let me know if you’d like me to generate an actual image of the plots or explain any part further! 😊