Practice worksheet for creating box-and-whisker plots with given data sets.

To solve the problem involving the box-and-whisker plot, we need to analyze the given data set and determine the key components of the box-and-whisker plot: the minimum, maximum, median (Q2), first quartile (Q1), and third quartile (Q3). Let's go through the steps systematically.

Given Data Set:

The data set is:
\[ 25, 35, 45, 39, 41, 53, 37, 50, 68, 43, 57, 39, 50, 33 \]

Step 1: Arrange the Data in Ascending Order

First, we sort the data in ascending order:
\[ 25, 33, 35, 37, 39, 39, 41, 43, 45, 50, 50, 53, 57, 68 \]

Step 2: Identify the Minimum and Maximum

- Minimum: The smallest value in the sorted data.
\[ \text{Minimum} = 25 \]
- Maximum: The largest value in the sorted data.
\[ \text{Maximum} = 68 \]

Step 3: Find the Median (Q2)

The median is the middle value of the data set. Since there are 14 data points (an even number), the median is the average of the 7th and 8th values in the ordered list.
- The 7th value is \( 41 \).
- The 8th value is \( 43 \).
- Median (Q2):
\[
Q2 = \frac{41 + 43}{2} = \frac{84}{2} = 42
\]

Step 4: Find the First Quartile (Q1)

The first quartile is the median of the lower half of the data (not including the median if the data set has an odd number of values). Here, the lower half consists of the first 7 values:
\[ 25, 33, 35, 37, 39, 39, 41 \]
- The median of these 7 values is the 4th value.
- Q1:
\[
Q1 = 37
\]

Step 5: Find the Third Quartile (Q3)

The third quartile is the median of the upper half of the data (not including the median if the data set has an odd number of values). Here, the upper half consists of the last 7 values:
\[ 43, 45, 50, 50, 53, 57, 68 \]
- The median of these 7 values is the 4th value.
- Q3:
\[
Q3 = 50
\]

Final Answer:

Now, we can fill in the blanks in the box-and-whisker plot:

- Minimum: \( 25 \)
- Q1: \( 37 \)
- Median (Q2): \( 42 \)
- Q3: \( 50 \)
- Maximum: \( 68 \)

Box-and-Whisker Plot Representation:

- The whiskers extend from the minimum (25) to the maximum (68).
- The box spans from Q1 (37) to Q3 (50).
- The median (Q2) is marked at 42 within the box.

Final Answer:

\[
\boxed{
\begin{array}{c}
\text{Minimum: } 25 \\
Q1: 37 \\
Q2: 42 \\
Q3: 50 \\
\text{Maximum: } 68
\end{array}
}
\]