Math worksheet for creating box and whisker plots with three data sets and number lines.

To solve the problem, we need to create a box and whisker plot for each data set. This involves finding the five-number summary (Minimum, Q₁, Q₂, Q₃, Maximum) for each data set. Let's go through each step for all three data sets.

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Step 1: Organize the Data

For each data set, first arrange the numbers in ascending order.

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

#### Step 1.1: Arrange in Ascending Order
\[ 1, 3, 5, 7, 9, 11, 12, 15, 18, 22, 23, 24, 25 \]

#### Step 1.2: Find the Minimum and Maximum
- Minimum: The smallest value is \( 1 \).
- Maximum: The largest value is \( 25 \).

#### Step 1.3: Find the Median (Q₂)
The median is the middle value. Since there are 13 values (odd number), the median is the 7th value.
\[ Q_2 = 12 \]

#### Step 1.4: Find Q₁ (First Quartile)
Q₁ is the median of the lower half of the data (excluding the median if the total number of values is odd). The lower half is:
\[ 1, 3, 5, 7, 9, 11 \]
The median of this subset is the average of the 3rd and 4th values:
\[ Q_1 = \frac{5 + 7}{2} = 6 \]

#### Step 1.5: Find Q₃ (Third Quartile)
Q₃ is the median of the upper half of the data (excluding the median if the total number of values is odd). The upper half is:
\[ 15, 18, 22, 23, 24, 25 \]
The median of this subset is the average of the 3rd and 4th values:
\[ Q_3 = \frac{22 + 23}{2} = 22.5 \]

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

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

#### Step 2.1: Arrange in Ascending Order
\[ 1, 4, 7, 11, 13, 15, 19, 22, 24 \]

#### Step 2.2: Find the Minimum and Maximum
- Minimum: The smallest value is \( 1 \).
- Maximum: The largest value is \( 24 \).

#### Step 2.3: Find the Median (Q₂)
The median is the middle value. Since there are 9 values (odd number), the median is the 5th value.
\[ Q_2 = 13 \]

#### Step 2.4: Find Q₁ (First Quartile)
Q₁ is the median of the lower half of the data (excluding the median if the total number of values is odd). The lower half is:
\[ 1, 4, 7, 11 \]
The median of this subset is the average of the 2nd and 3rd values:
\[ Q_1 = \frac{4 + 7}{2} = 5.5 \]

#### Step 2.5: Find Q₃ (Third Quartile)
Q₃ is the median of the upper half of the data (excluding the median if the total number of values is odd). The upper half is:
\[ 15, 19, 22, 24 \]
The median of this subset is the average of the 2nd and 3rd values:
\[ Q_3 = \frac{19 + 22}{2} = 20.5 \]

#### Five-Number Summary for Data Set 2:
- Minimum: \( 1 \)
- Q₁: \( 5.5 \)
- Q₂: \( 13 \)
- Q₃: \( 20.5 \)
- Maximum: \( 24 \)

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

#### Step 3.1: Arrange in Ascending Order
\[ 2, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19 \]

#### Step 3.2: Find the Minimum and Maximum
- Minimum: The smallest value is \( 2 \).
- Maximum: The largest value is \( 19 \).

#### Step 3.3: Find the Median (Q₂)
The median is the middle value. Since there are 11 values (odd number), the median is the 6th value.
\[ Q_2 = 10 \]

#### Step 3.4: Find Q₁ (First Quartile)
Q₁ is the median of the lower half of the data (excluding the median if the total number of values is odd). The lower half is:
\[ 2, 6, 7, 8, 9 \]
The median of this subset is the 3rd value:
\[ Q_1 = 7 \]

#### Step 3.5: Find Q₃ (Third Quartile)
Q₃ is the median of the upper half of the data (excluding the median if the total number of values is odd). The upper half is:
\[ 11, 12, 13, 15, 19 \]
The median of this subset is the 3rd value:
\[ Q_3 = 13 \]

#### Five-Number Summary for Data Set 3:
- Minimum: \( 2 \)
- Q₁: \( 7 \)
- Q₂: \( 10 \)
- Q₃: \( 13 \)
- Maximum: \( 19 \)

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Final Answers

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

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

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

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Box and Whisker Plots

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

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Final Answer Box:

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