To estimate the mean commute distance for the students using the midpoint of each data class and frequency distribution, we will follow these steps:

Steps:

1. Find the midpoint of each class interval. The midpoint is calculated by averaging the lower and upper bounds of each interval.
2. Multiply the midpoint by the corresponding frequency for each class.
3. Add up all the products from step 2.
4. Divide by the total number of students (sum of frequencies) to get the mean commute distance.

Table:

Total Computations:

• Total midpoint × frequency = 66 + 168 + 182 + 144 + 115 + 84 = 759
• Total frequency = 22 + 21 + 14 + 8 + 5 + 3 = 73

Mean Commute Distance:

$\text{Mean} = \frac{759}{73} \approx 10.3973$

Rounding to one decimal place: $\text{Mean commute distance} \approx 10.4 \text{ miles}$

Let me know if you want further clarification, or if you'd like to dive into any specific step!

Related Questions:

1. How do you calculate the variance from a frequency distribution?
2. What is the significance of using midpoints in grouped data?
3. How does frequency distribution relate to the mode?
4. What are other methods to estimate the average commute distance?
5. How would outliers affect the mean commute distance?

Tip: When working with grouped data, always ensure that midpoints accurately represent the class intervals before proceeding with further calculations!