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Commute Time

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Commute Time


1. **Problem statement:** We have commute times over 7 days: 30, 28, 35, 40, 32, 100, 31 minutes. 2. **Calculate the mean commute time:** Mean is the sum of all times divided by the number of days. $$\text{Mean} = \frac{30 + 28 + 35 + 40 + 32 + 100 + 31}{7} = \frac{296}{7} \approx 42.29 \text{ minutes}$$ 3. **Calculate the median commute time:** First, order the data from smallest to largest: 28, 30, 31, 32, 35, 40, 100 Since there are 7 data points (an odd number), the median is the middle value, which is the 4th value. $$\text{Median} = 32 \text{ minutes}$$ 4. **Determine which measure better reflects usual travel time and why:** The mean is approximately 42.29 minutes but is heavily influenced by the outlier 100 minutes, which is much larger than the other values. The median is 32 minutes, which represents the middle of the data and is not affected significantly by the outlier. Therefore, **the median better reflects the usual travel time** because it is resistant to the very high commute time that is unusual relative to the other days.