To create a box-and-whisker plot (also known as a box plot) from the data in the image, follow these steps:

Step 1: Organize the Data

The first step in creating a box plot is to arrange the data in ascending order. The data from the image seems to be already organized by categories (e.g., "JUNIOR" and "CALIFORNIA").

Step 2: Calculate the Five-Number Summary

The five-number summary consists of:

1. Minimum: The smallest data point.
2. First Quartile (Q1): The median of the lower half of the data (excluding the median if the number of observations is odd).
3. Median (Q2): The middle value of the data set.
4. Third Quartile (Q3): The median of the upper half of the data.
5. Maximum: The largest data point.

Example:

Assume that you are calculating the five-number summary for one category (e.g., "JUNIOR" scores):

1. Order the data points (already in order in the image): $8.1, 8.2, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 9.0$

2. Minimum: 8.1

3. Q1: Calculate the median of the first half: $Q1 = \text{Median of } [8.1, 8.2, 8.4, 8.5, 8.6] = 8.4$

4. Median (Q2): $Q2 = 8.6$

5. Q3: Calculate the median of the second half: $Q3 = \text{Median of } [8.6, 8.7, 8.8, 8.9, 9.0] = 8.8$

6. Maximum: 9.0

Step 3: Calculate the Interquartile Range (IQR)

The IQR is the difference between the third quartile and the first quartile: $\text{IQR} = Q3 - Q1 = 8.8 - 8.4 = 0.4$

Step 4: Create the Box Plot

1. Draw a number line that includes the range of your data.
2. Draw a box from Q1 to Q3.
3. Draw a line inside the box at the median (Q2).
4. Add whiskers: Draw lines from the box to the minimum and maximum data points.

Step 5: Identify Outliers (Optional)

An outlier is any data point outside the range defined by: $\text{Lower bound} = Q1 - 1.5 \times \text{IQR}$ $\text{Upper bound} = Q3 + 1.5 \times \text{IQR}$

Step 6: Repeat for Other Categories

Follow the same process for the other categories (e.g., "CALIFORNIA").

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Additional Questions You Might Explore:

1. How do you interpret the spread of the data using the box plot?
2. What does it mean if the whiskers are uneven in a box plot?
3. How would you identify and mark outliers on the box plot?
4. What insights can be drawn from comparing box plots of different categories?
5. How does the IQR relate to the overall variability of the data?

Tip:

Use software tools like Excel, Python, or Google Sheets to automate the creation of box plots for larger data sets.