Question

The list shows the temperature, in °F at noon during a 9-day period.



76, 71, 74, 77, 75, 71, 87, 77, 75

Which temperature is an outlier?

Answer 1

To determine if there is an outlier in the given set of temperatures, we can use the IQR (Interquartile Range) method.

1. **Sort the Data**:
The temperatures in sorted order:
- 71, 71, 74, 75, 75, 76, 77, 77, 87

2. **Find the First Quartile (Q1) and Third Quartile (Q3)**:
- **Q1** (the median of the first half) is the average of the 2nd and 3rd numbers:
Q1 = (71 + 74) / 2 = 72.5
- **Q3** (the median of the second half) is the average of the 7th and 8th numbers:
Q3 = (77 + 77) / 2 = 77

3. **Calculate the Interquartile Range (IQR)**:
- IQR = Q3 - Q1 = 77 - 72.5 = 4.5

4. **Determine the Outlier Boundaries**:
- Lower Boundary = Q1 - 1.5 * IQR = 72.5 - 1.5 * 4.5 = 72.5 - 6.75 = 65.75
- Upper Boundary = Q3 + 1.5 * IQR = 77 + 1.5 * 4.5 = 77 + 6.75 = 83.75

5. **Identify Outliers**:
- Any temperature below 65.75 or above 83.75 is considered an outlier.

From the list, 87°F is the only temperature that falls above the upper boundary of 83.75. Thus, **87°F is the outlier**.