Question

Dan records the number of students in a variety of classes at his school. The results are shown below in order from least to greatest.
21, 22, 26, 30, 31, 31
Suppose that the class with 30 students changes to 26 students. Answer the following.

What happens to the range?
* A. The range (choose one. increases, decreases) by ___ points.
* B. The range stays the same.
*
* What happens to the interquartile range (IQR)?
* A. The IQR (choose one. increases, decreases) by ___ points.
* B. The IQR stays the same.

Answer 1

To determine how the changes affect the range and interquartile range (IQR), let’s first find the original range and IQR.

**Original Data**: 21, 22, 26, 30, 31, 31

1. **Calculate the Original Range**:
- Range = Maximum - Minimum
- Range = 31 - 21 = 10

2. **Calculate the Original IQR**:
- First quartile (Q1) is the median of the first half (21, 22, 26), which is 22.
- Third quartile (Q3) is the median of the second half (30, 31, 31), which is 31.
- IQR = Q3 - Q1 = 31 - 22 = 9

Now let's consider the new data set after changing the class with 30 students to 26 students:

**New Data**: 21, 22, 26, 26, 31, 31

3. **Calculate the New Range**:
- New Range = Maximum - Minimum
- New Range = 31 - 21 = 10

The range remains the same.

4. **Calculate the New IQR**:
- New Q1 is still 22.
- New Q3 is still 31.
- Therefore, New IQR = Q3 - Q1 = 31 - 22 = 9.

The IQR also remains the same.

### Summary:
* **Range**:
- The range stays the same (Option B).

* **Interquartile Range (IQR)**:
- The IQR stays the same (Option B).

So the final answers are:
- **A. The range stays the same.**
- **A. The IQR stays the same.**