The problem provides a frequency table showing the time each of 40 students takes to travel to school. We are asked to calculate an estimate of the mean travel time. The time intervals are $0 < m \le 10$, $10 < m \le 25$, $25 < m \le 40$, and $40 < m \le 60$, with corresponding frequencies of 3, 18, 15, and 4.

1. Problem Description

The problem provides a frequency table showing the time each of 40 students takes to travel to school. We are asked to calculate an estimate of the mean travel time. The time intervals are $0 < m \le 10$, $10 < m \le 25$, $25 < m \le 40$, and $40 < m \le 60$, with corresponding frequencies of 3, 18, 15, and

4.

2. Solution Steps

To estimate the mean, we first need to find the midpoint of each time interval.

Midpoint of $0 < m \le 10$ is $\frac{0+10}{2} = 5$.

Midpoint of $10 < m \le 25$ is $\frac{10+25}{2} = 17.5$.

Midpoint of $25 < m \le 40$ is $\frac{25+40}{2} = 32.5$.

Midpoint of $40 < m \le 60$ is $\frac{40+60}{2} = 50$.

Now, we multiply each midpoint by its corresponding frequency:

$5 \times 3 = 15$

$17.5 \times 18 = 315$

$32.5 \times 15 = 487.5$

$50 \times 4 = 200$

Then, we sum these products:

$15 + 315 + 487.5 + 200 = 1017.5$

Finally, we divide the sum by the total frequency (number of students), which is 40:

$\text{Estimated Mean} = \frac{1017.5}{40} = 25.4375$

3. Final Answer

The estimated mean travel time is 25.4375 minutes.