Question: It seems these days that college graduates who are employed full-time work more than 40-hour weeks…

It seems these days that college graduates who are employed full-time work more than 40-hour weeks. In a survey for a recent year, there were 76 respondents who were college graduates employed full-time. The reported number of hours each worked per week is summarized in the following histogram, which was displayed in a government publication.

[Histogram image]

Based on the histogram, using the midpoint of each data class, estimate the mean number of hours worked per week by these respondents. Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.

[Input field for hours per week]

Solution

To find the mean number of hours worked per week using the histogram, we can follow these steps: First, identify the midpoint of each class: - \(26-30\) midpoint = \( \frac{26+30}{2} = 28 \) - \(31-35\) midpoint = \( \frac{31+35}{2} = 33 \) - \(36-40\) midpoint = \( \frac{36+40}{2} = 38 \) - \(41-45\) midpoint = \( \frac{41+45}{2} = 43 \) - \(46-50\) midpoint = \( \frac{46+50}{2} = 48 \) - \(51-55\) midpoint = \( \frac{51+55}{2} = 53 \) Next, multiply each midpoint by the frequency for that class: \[ \begin{align*} 28 \times 9 & = 252 \\ 33 \times 24 & = 792 \\ 38 \times 19 & = 722 \\ 43 \times 14 & = 602 \\ 48 \times 7 & = 336 \\ 53 \times 3 & = 159 \\ \end{align*} \] Now, sum up these products: \[ 252 + 792 + 722 + 602 + 336 + 159 = 2863 \] Sum up the frequencies to find the total number of respondents: \[ 9 + 24 + 19 + 14 + 7 + 3 = 76 \] Calculate the mean by dividing the sum of the products by the total number of respondents: \[ \frac{2863}{76} \approx 37.6711 \] Round to one decimal place: The mean number of hours worked per week is approximately \(37.7\) hours.