Math worksheet with two word problems on box and whisker plots.

Absolutely! Let’s solve both problems step by step, explaining how to find the five-number summary and how to construct a box-and-whisker plot.

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## 🔢 Problem 1: Keith’s Ticket Sales

Data:
11, 1, 22, 25, 13, 10, 20, 6, 24
→ Total = 9 values

✔ Step 1: Sort the data in ascending order

1, 6, 10, 11, 13, 20, 22, 24, 25

✔ Step 2: Find the Five-Number Summary

#### ➤ Minimum:
The smallest value → 1

#### ➤ Maximum:
The largest value → 25

#### ➤ Median (Q₂):
Middle value of the sorted list. Since there are 9 numbers, the median is the 5th value.

Sorted: 1, 6, 10, 11, 13, 20, 22, 24, 25
→ Q₂ = 13

#### ➤ Lower Quartile (Q₁):
Median of the lower half (not including Q₂ if odd number of data points).

Lower half: 1, 6, 10, 11 → 4 numbers → median is average of 2nd and 3rd:
(6 + 10) / 2 = 8

→ Q₁ = 8

#### ➤ Upper Quartile (Q₃):
Median of the upper half (not including Q₂).

Upper half: 20, 22, 24, 25 → 4 numbers → median is average of 2nd and 3rd:
(22 + 24) / 2 = 23

→ Q₃ = 23

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✔ Five-Number Summary for Problem 1:
- Minimum: 1
- Q₁: 8
- Q₂ (Median): 13
- Q₃: 23
- Maximum: 25

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📊 Box-and-Whisker Plot Instructions:

On the number line from 1 to 25:

1. Draw a whisker from 1 to 8.
2. Draw a box from 8 to 23.
3. Inside the box, draw a vertical line at 13 (median).
4. Draw a whisker from 23 to 25.

You now have your box-and-whisker plot!

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## 🔢 Problem 2: First National Bank Transactions

Data:
9, 8, 25, 7, 3, 5, 10, 18, 21
→ Total = 9 values

✔ Step 1: Sort the data in ascending order

3, 5, 7, 8, 9, 10, 18, 21, 25

✔ Step 2: Find the Five-Number Summary

#### ➤ Minimum:
Smallest value → 3

#### ➤ Maximum:
Largest value → 25

#### ➤ Median (Q₂):
Middle value — 5th value in sorted list.

Sorted: 3, 5, 7, 8, 9, 10, 18, 21, 25
→ Q₂ = 9

#### ➤ Lower Quartile (Q₁):
Median of lower half: 3, 5, 7, 8 → 4 numbers → average of 2nd and 3rd:
(5 + 7) / 2 = 6

→ Q₁ = 6

#### ➤ Upper Quartile (Q₃):
Median of upper half: 10, 18, 21, 25 → 4 numbers → average of 2nd and 3rd:
(18 + 21) / 2 = 19.5

→ Q₃ = 19.5

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✔ Five-Number Summary for Problem 2:
- Minimum: 3
- Q₁: 6
- Q₂ (Median): 9
- Q₃: 19.5
- Maximum: 25

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📊 Box-and-Whisker Plot Instructions:

On the number line from 1 to 25:

1. Draw a whisker from 3 to 6.
2. Draw a box from 6 to 19.5.
3. Inside the box, draw a vertical line at 9 (median).
4. Draw a whisker from 19.5 to 25.

> 💡 Note: Since 19.5 is halfway between 19 and 20, you can place it midway on the number line.

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## ✍️ Final Answers to Fill In:

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Problem 1:

- Minimum: 1
- Maximum: 25
- Q₁: 8
- Q₂: 13
- Q₃: 23

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Problem 2:

- Minimum: 3
- Maximum: 25
- Q₁: 6
- Q₂: 9
- Q₃: 19.5

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## 🧠 Key Concepts Recap:

- Five-number summary = Min, Q₁, Median (Q₂), Q₃, Max
- Q₁ = median of lower half (excluding overall median if odd)
- Q₃ = median of upper half (excluding overall median if odd)
- Box-and-whisker plot visually shows spread and center of data using these five numbers.

Let me know if you’d like me to sketch the plots for you too! 😊