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 five hours to their training times. What are the mean, median, mode, and range of times for the second week?
9, 5, 5, 5, 7, 6, 7
In the second week, each friend adds 5 hours to their training times:
14, 10, 10, 10, 12, 11, 12
Mean: To find the mean, you add up all the numbers and divide by the total count:
(14 + 10 + 10 + 10 + 12 + 11 + 12) / 7 = 11
The mean training time in the second week is 11 hours.
Median: To find the median, you put the numbers in order from least to greatest and find the middle number:
10, 10, 10, 11, 12, 12, 14
The median training time in the second week is 11 hours.
Mode: To find the mode, you look for the number that appears most frequently:
The mode of the second week training times is 10 hours.
Range: To find the range, you subtract the smallest value from the largest value:
14 - 10 = 4
The range of the second week training times is 4 hours.
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To find the mean, median, mode, and range of the training times for the second week, follow these steps:
Mean:
1. Add 5 hours to each training time from the first week: 9 + 5 = 14, 5 + 5 = 10, 5 + 5 = 10, 5 + 5 = 10, 7 + 5 = 12, 6 + 5 = 11, 7 + 5 = 12.
2. Add up all the training times from the second week: 14 + 10 + 10 + 10 + 12 + 11 + 12 = 79.
3. Divide the sum by the total number of training times (7): 79 / 7 = 11.29 (rounded to two decimal places).
So, the mean of the training times for the second week is approximately 11.29 hours.
Median:
1. Arrange the training times from the second week in ascending order: 10, 10, 10, 11, 12, 12, 14.
2. Since there is an odd number of training times (7), the median is the middle value.
Therefore, the median of the training times for the second week is 11.
Mode:
1. Identify the value that appears most frequently in the training times from the second week.
In this case, 10 appears three times, which is more frequent than any other value.
Therefore, the mode of the training times for the second week is 10.
Range:
1. Subtract the smallest value from the largest value in the training times from the second week: 14 - 10 = 4.
So, the range of the training times for the second week is 4 hours.