                 Between 9 and 11 hours per week, depending on your approach to your problem.

Complete Solution:

There are many ways to do this problem. The answer can only be approximated because of the way the data are reported.

If you assume that the table shows data for 100 students, then the 7% who worked from one to five hours would correspond to seven students who worked one to five hours. To find an average (mean), you need to estimate the total number of hours worked. Consider the seven students who worked from one to five hours. Taken together, the least time they could have worked is seven hours. The greatest they could have worked is 35 hours. (The actual number is probably somewhere in between these values.) The first chart shows the least number of hours the 100 students could have worked, while the second chart shows the greatest number of hours they could have worked.

 Least Number of Hours Number of Students1 Least Number of Total Hours 0 36 0 1 7 7 6 9 54 11 11 121 16 17 272 21 21 441 Total 100 895

 Greatest Number of Hours Number of Students1 Least Number of Total Hours 0 36 0 5 7 35 10 9 90 15 11 165 20 17 340 251 21 525 Total 100 1155

1estimated

To find the lower value for the average number of hours worked per week, divide the total number of hours by the number of students: 895 ÷ 100 = 8.95. The larger value for the average workweek can be foud in the same way: 1155 ÷ 100 = 11.55. Using this approach, an estimate for the average for a high school senior is between 8.5 and 12.5 hours.

Another way to estimate the average uses an average for the hours worked in each category.

 Smallest Number of Hours Largest Number of Hours Average Number of Hours Number of Students1 Total Hours Worked 0 0 0 36 0 1 5 3 7 21 6 10 8 9 72 11 15 13 11 143 16 20 18 17 306 21 251 23 21 483 Total 100 1025

1estimated

To find a value for the average, divide the total number of hours by the number of students: 1025 ÷ 100 = 10.25. This method results in an average of about 10 and 1/4 hours.     Home · Back to the Challenge · Try These · Think About This  ·  Did You Know? · Resources Try Another Challenge · Challenge Index · Math Index · Printing the Challenges · En Español Family Corner · Teacher Corner · About Figure This! · Purchase the CD  ©2004 National Council of Teachers of Mathematics Web site and CD-ROM design/production © 1999-2004 KnowNet Construction, Inc.    