Question

The first quartile of a data set is 52, and the third quartile is 72. Which of these values in the data set is an outlier?
A. 41 B. 101 C. 21 D. 81

Answer 1

To determine if a value is an outlier in a data set, we can use the interquartile range (IQR) method.

1. **Find the IQR**:
- IQR = Q3 - Q1
- Here, Q1 = 52 and Q3 = 72.
- IQR = 72 - 52 = 20.

2. **Determine the outlier boundaries**:
- Lower Boundary = Q1 - 1.5 * IQR = 52 - 1.5 * 20 = 52 - 30 = 22.
- Upper Boundary = Q3 + 1.5 * IQR = 72 + 1.5 * 20 = 72 + 30 = 102.

3. **Check the given values against these boundaries**:
- A. 41: Not an outlier (41 > 22).
- B. 101: Not an outlier (101 < 102).
- C. 21: Outlier (21 < 22).
- D. 81: Not an outlier (81 < 102).

The value that is an outlier in the data set is **C. 21**.