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Chapter 3: Problem 132

In a study of distances traveled to a college by commuting students, data from 100 commuters yielded a mean of \(8.73\) miles. After the mean was calculated, data came in late from three students, with respective distances of \(11.5,7.6\), and \(10.0\) miles. Calculate the mean distance for all 103 students.

Short Answer

Expert verified
The mean distance traveled to college by all 103 students is approximately \(8.76\) miles.

Step by step solution

01

Understand the Initial Mean

In this exercise, it is given that the mean distance (denoted by \(\mu\)) using 100 students' data is \(8.73\) miles.
02

Calculate the Total Distance for 100 students

To find the total distance traveled by the first 100 students, we multiply their mean distance by their number, i.e., \(\mu \times n\) where \(\mu=8.73\) and \(n=100\). This yields a total distance of \(873\) miles.
03

Include Extra Data

The data from the 3 late students is also given (distances of \(11.5, 7.6\) and \(10.0\) miles). We add these to the total distance so far, which gives us \(873 + 11.5 + 7.6 + 10.0 = 902.1\) miles in total.
04

Recalculate the Mean

Finally, to find the mean distance with all 103 students' data, we divide the total distance by the total number of students. That is, \(\mu = Total Distance / Total Number = 902.1 / 103\).

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