Question: The 7 students in Mr. Allen's class were asked how many minutes it takes them to get to school in the morning. Here is what they answered.
15, 14, 9, 3, 6, 7, 5
Find the median and mean travel times for these students.
If necessary, round your answers to the nearest tenth.
1. **State the problem:** We have 7 travel times: $15, 14, 9, 3, 6, 7, 5$. We need to find the median and mean travel times.
2. **Find the median:**
- Arrange the numbers in ascending order: $3, 5, 6, 7, 9, 14, 15$
- Since there are 7 numbers (an odd number), the median is the middle number.
- The middle number is the 4th number: $7$
3. **Find the mean:**
- Use the formula for mean: $$\text{mean} = \frac{\text{sum of all values}}{\text{number of values}}$$
- Calculate the sum: $15 + 14 + 9 + 3 + 6 + 7 + 5 = 59$
- Number of values: $7$
- Calculate the mean: $$\text{mean} = \frac{59}{7}$$
- Show intermediate step with cancellation: $$\frac{\cancel{59}}{\cancel{7}}$$ (no common factors to cancel here, so fraction remains as is)
- Calculate decimal value: $$\frac{59}{7} \approx 8.4285714$$
- Round to nearest tenth: $8.4$
4. **Final answers:**
- Median travel time: $7$ minutes
- Mean travel time: $8.4$ minutes