Question

students, they have to commute too far to school, and so university officials should build more housing near campus. in response, the officials studied the commute distance (in miles) of 72 students at the university and published the following frequency distribution in the school paper. commute distance (in miles) frequency 1 to 5 22 6 to 10 21 11 to 15 15 16 to 20 7 21 to 25 4 26 to 30 3 based on the frequency distribution, using the midpoint of each data class, estimate the mean commute distance for the students. for your intermediate computations, use four or more decimal places, and round your answer to one decimal place.

Explanation:

Step1: Find the mid - points of each class

For 1 - 5: $\frac{1 + 5}{2}=3$; for 6 - 10: $\frac{6+10}{2}=8$; for 11 - 15: $\frac{11 + 15}{2}=13$; for 16 - 20: $\frac{16+20}{2}=18$; for 21 - 25: $\frac{21+25}{2}=23$; for 26 - 30: $\frac{26 + 30}{2}=28$.

Step2: Calculate the product of mid - point and frequency for each class

For 1 - 5: $3\times22 = 66$; for 6 - 10: $8\times21=168$; for 11 - 15: $13\times15 = 195$; for 16 - 20: $18\times7=126$; for 21 - 25: $23\times4 = 92$; for 26 - 30: $28\times3=84$.

Step3: Sum up the products

$66+168 + 195+126+92+84=731$.

Step4: Sum up the frequencies

$22 + 21+15+7+4+3=72$.

Step5: Calculate the mean

The mean $\bar{x}=\frac{731}{72}\approx10.2$.

Answer:

$10.2$