Math worksheet for practicing box and whisker plots with three data sets.

To solve the problem, we need to determine the five-number summary for each data set and then create a box-and-whisker plot. The five-number summary consists of:

1. Minimum: The smallest value in the data set.
2. Maximum: The largest value in the data set.
3. Median (Q₂): The middle value when the data is ordered. If there is an even number of data points, the median is the average of the two middle values.
4. First Quartile (Q₁): The median of the lower half of the data (not including the median if the data set has an odd number of values).
5. Third Quartile (Q₃): The median of the upper half of the data (not including the median if the data set has an odd number of values).

Let's solve each part step by step.

---

Data Set 1: \( 7, 25, 18, 1, 24, 3, 11, 9, 15, 22, 23, 5, 12 \)

#### Step 1: Order the data
\[ 1, 3, 5, 7, 9, 11, 12, 15, 18, 22, 23, 24, 25 \]

#### Step 2: Find the Minimum and Maximum
- Minimum: \( 1 \)
- Maximum: \( 25 \)

#### Step 3: Find the Median (Q₂)
The data set has 13 values (odd number), so the median is the 7th value:
\[ Q₂ = 12 \]

#### Step 4: Find the First Quartile (Q₁)
The lower half of the data (excluding the median) is:
\[ 1, 3, 5, 7, 9, 11 \]
The median of this subset is the average of the 3rd and 4th values:
\[ Q₁ = \frac{5 + 7}{2} = 6 \]

#### Step 5: Find the Third Quartile (Q₃)
The upper half of the data (excluding the median) is:
\[ 15, 18, 22, 23, 24, 25 \]
The median of this subset is the average of the 3rd and 4th values:
\[ Q₃ = \frac{22 + 23}{2} = 22.5 \]

#### Five-Number Summary:
- Minimum: \( 1 \)
- Q₁: \( 6 \)
- Median (Q₂): \( 12 \)
- Q₃: \( 22.5 \)
- Maximum: \( 25 \)

---

Data Set 2: \( 1, 24, 13, 4, 11, 7, 22, 15, 19 \)

#### Step 1: Order the data
\[ 1, 4, 7, 11, 13, 15, 19, 22, 24 \]

#### Step 2: Find the Minimum and Maximum
- Minimum: \( 1 \)
- Maximum: \( 24 \)

#### Step 3: Find the Median (Q₂)
The data set has 9 values (odd number), so the median is the 5th value:
\[ Q₂ = 13 \]

#### Step 4: Find the First Quartile (Q₁)
The lower half of the data (excluding the median) is:
\[ 1, 4, 7, 11 \]
The median of this subset is the average of the 2nd and 3rd values:
\[ Q₁ = \frac{4 + 7}{2} = 5.5 \]

#### Step 5: Find the Third Quartile (Q₃)
The upper half of the data (excluding the median) is:
\[ 15, 19, 22, 24 \]
The median of this subset is the average of the 2nd and 3rd values:
\[ Q₃ = \frac{19 + 22}{2} = 20.5 \]

#### Five-Number Summary:
- Minimum: \( 1 \)
- Q₁: \( 5.5 \)
- Median (Q₂): \( 13 \)
- Q₃: \( 20.5 \)
- Maximum: \( 24 \)

---

Data Set 3: \( 6, 9, 7, 13, 10, 12, 8, 15, 19, 2, 11 \)

#### Step 1: Order the data
\[ 2, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19 \]

#### Step 2: Find the Minimum and Maximum
- Minimum: \( 2 \)
- Maximum: \( 19 \)

#### Step 3: Find the Median (Q₂)
The data set has 11 values (odd number), so the median is the 6th value:
\[ Q₂ = 10 \]

#### Step 4: Find the First Quartile (Q₁)
The lower half of the data (excluding the median) is:
\[ 2, 6, 7, 8, 9 \]
The median of this subset is the 3rd value:
\[ Q₁ = 7 \]

#### Step 5: Find the Third Quartile (Q₃)
The upper half of the data (excluding the median) is:
\[ 11, 12, 13, 15, 19 \]
The median of this subset is the 3rd value:
\[ Q₃ = 13 \]

#### Five-Number Summary:
- Minimum: \( 2 \)
- Q₁: \( 7 \)
- Median (Q₂): \( 10 \)
- Q₃: \( 13 \)
- Maximum: \( 19 \)

---

Final Answers

1. Data Set 1:
- Minimum: \( 1 \)
- Q₁: \( 6 \)
- Median (Q₂): \( 12 \)
- Q₃: \( 22.5 \)
- Maximum: \( 25 \)

2. Data Set 2:
- Minimum: \( 1 \)
- Q₁: \( 5.5 \)
- Median (Q₂): \( 13 \)
- Q₃: \( 20.5 \)
- Maximum: \( 24 \)

3. Data Set 3:
- Minimum: \( 2 \)
- Q₁: \( 7 \)
- Median (Q₂): \( 10 \)
- Q₃: \( 13 \)
- Maximum: \( 19 \)

Box-and-Whisker Plots

Using the five-number summaries, you can draw the box-and-whisker plots on the provided number lines. Each plot will have:
- A box from Q₁ to Q₃.
- A line inside the box at the median (Q₂).
- Whiskers extending to the minimum and maximum values.

Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Data Set 1: } \{1, 6, 12, 22.5, 25\} \\
\text{Data Set 2: } \{1, 5.5, 13, 20.5, 24\} \\
\text{Data Set 3: } \{2, 7, 10, 13, 19\}
\end{array}
}
\]