Question

A box-and-whisker plot. The number line goes from 0 to 9. The whiskers range from 0 to 7, indicated by A and E. The box ranges from 2 to 6, indicated by B and D. The line divides the box at 4, indicated by C.
Choose the set of letters that represents each situation.

The range of the data =
.
The top 25% of the data =
.
The interquartile range =
.

Answer 1

To analyze the provided box-and-whisker plot description, we can assign values to the letters as follows:

1. **The range of the data**: The range is calculated as the difference between the maximum and minimum values. Here, the minimum value (whisker) is 0 (A) and the maximum value (whisker) is 7 (E).

\[
\text{Range} = \text{Maximum} - \text{Minimum} = 7 - 0 = 7
\]

Therefore, the range of the data is **A, E** (0 to 7).

2. **The top 25% of the data**: The top 25% corresponds to the upper quartile (Q3) and above, which is represented by values greater than D (the upper edge of the box). From the description, the upper edge of the box is at 6.

Therefore, the top 25% of the data consists of values from 6 to 7, which corresponds to **D, E**.

3. **The interquartile range (IQR)**: The interquartile range is calculated as the difference between the upper quartile (Q3, represented by D) and the lower quartile (Q1, represented by B).

From the description, Q1 is at 2 (B) and Q3 is at 6 (D).

\[
\text{IQR} = Q3 - Q1 = 6 - 2 = 4
\]

Therefore, the interquartile range is represented by **B, D** (2 to 6).

Summarizing:
- The range of the data = **A, E**
- The top 25% of the data = **D, E**
- The interquartile range = **B, D**