Let's analyze the box-and-whisker plot shown in the image.

The diagram displays the results from two math classes (Class A and Class B) based on test scores. The plot provides information such as the minimum, maximum, median, and quartiles of the data sets.

Question 2.3.1: What is the median point of both classes (tests)?

• Class A Median: The median line inside the box for Class A is at 60.
• Class B Median: The median line for Class B is at 70.

Question 2.3.2: Comment on the minimum point of both classes (tests) and how it affects the box-and-whisker diagram.

• Class A Minimum: The minimum point for Class A is 40.
• Class B Minimum: The minimum point for Class B is 60.

This affects the length of the "whiskers" on the left side. Since Class A has a lower minimum, its whisker on the left side is longer compared to Class B, where the minimum is higher, and thus, the whisker is shorter.

Question 2.3.3: Discuss the distribution of data of Class B.

• The median is 70, meaning half of the scores are above 70, and half are below.
• The interquartile range (IQR) (difference between the third quartile and first quartile) shows that the middle 50% of the data lies between approximately 65 and 75, indicating that most of the data is tightly clustered.
• The whiskers indicate the data range, with the minimum at 60 and the maximum at 80, which suggests that the overall distribution is compact with no outliers, and the data is skewed slightly to the left (since the left whisker is slightly longer).

Would you like more details or explanations? Here are some follow-up questions to expand this:

1. How is the interquartile range for both classes different?
2. What does the whisker length indicate about the variability of the data?
3. How can outliers be identified using box-and-whisker plots?
4. What would the plot look like if Class A had a maximum value of 100?
5. How do box plots help in comparing two data sets effectively?

Tip: The length of the box in a box-and-whisker plot indicates the interquartile range, a key measure of statistical spread.