The table shows the number of hours that a group of friends spent in their first week training to run a marathon. In the second week, they each add 4 hours to their training times. What are the mean, median, mode, and range of times for the second week?
Runner Hours
Jeff
Mark
Karen
Costas
Brett
Nikki
Jack
5
10
5
9
7
5
7
To find the mean, median, mode, and range for the second week of training times, we first need to add 4 hours to each runner's time:
Jeff: 5 + 4 = 9 hours
Mark: 10 + 4 = 14 hours
Karen: 5 + 4 = 9 hours
Costas: 9 + 4 = 13 hours
Brett: 7 + 4 = 11 hours
Nikki: 5 + 4 = 9 hours
Jack: 7 + 4 = 11 hours
Now we have the following times for the second week:
9, 14, 9, 13, 11, 9, 11
Mean: To find the mean, add all the times together and divide by the number of runners (7):
(9 + 14 + 9 + 13 + 11 + 9 + 11) / 7 = 76 / 7 ≈ 10.86 hours
Median: The median is the middle number when the times are arranged in order:
9, 9, 9, 11, 11, 13, 14
The median is 11 hours.
Mode: The mode is the number that appears most frequently. In this case, the mode is 9 hours.
Range: To find the range, subtract the smallest time from the largest time:
14 - 9 = 5 hours
Therefore, for the second week of training times, the mean is approximately 10.86 hours, the median is 11 hours, the mode is 9 hours, and the range is 5 hours.