Linda keeps track of the time it takes her to drive to work. Over 4 days, she takes 45 minutes, 47 minutes, 41 minutes, and 69 minutes. Which of the four times is most likely an outlier? Select one: 69 minutes 45 minutes 47 minutes 41 minutes Clear my choice

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UpStudy AI · Accepted Answer

To determine which of the four times is most likely an outlier, we can use the interquartile range (IQR) method. Here are the steps to identify the outlier:

1. **List the times in ascending order**: 
   - 41 minutes, 45 minutes, 47 minutes, 69 minutes

2. **Calculate the median (Q2)**:
   - Since there are 4 values, the median will be the average of the two middle values (45 and 47).
   $$
   Q2 = \frac{45 + 47}{2} = 46
   $$

3. **Calculate the first quartile (Q1)**:
   - Q1 is the median of the first half of the data (41 and 45).
   $$
   Q1 = \frac{41 + 45}{2} = 43
   $$

4. **Calculate the third quartile (Q3)**:
   - Q3 is the median of the second half of the data (47 and 69).
   $$
   Q3 = \frac{47 + 69}{2} = 58
   $$

5. **Calculate the interquartile range (IQR)**:
   $$
   IQR = Q3 - Q1 = 58 - 43 = 15
   $$

6. **Determine the lower and upper bounds for outliers**:
   - Lower bound: $$ Q1 - 1.5 \times IQR = 43 - 1.5 \times 15 = 43 - 22.5 = 20.5 $$
   - Upper bound: $$ Q3 + 1.5 \times IQR = 58 + 1.5 \times 15 = 58 + 22.5 = 80.5 $$

7. **Identify outliers**:
   - Any value below 20.5 or above 80.5 is considered an outlier.

Now, let's analyze the times:
- 41 minutes: Not an outlier
- 45 minutes: Not an outlier
- 47 minutes: Not an outlier
- 69 minutes: Not an outlier

Since all times fall within the bounds, we can look for the value that is significantly higher than the others. The time of 69 minutes is noticeably higher than the other three times.

Thus, the most likely outlier is **69 minutes**.
69 minutes is the most likely outlier.

Linda keeps track of the time it takes her to drive to work. Over 4 days, she takes 45 minutes, 47 minutes, 41 minutes, and 69 minutes. Which of the four times is most likely an outlier? Select one: 69 minutes 45 minutes 47 minutes 41 minutes Clear my choice

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