The table shows the number of hours that a group of students been studying for the SAT during their first week of preparation the students each add 4 hours to their study times in the second week what are the mean medium and mode and range of these times for the second week
First Week Study Times:
7, 6, 5, 4, 5, 4, 6, 5, 7, 6
Mean:
(7 + 6 + 5 + 4 + 5 + 4 + 6 + 5 + 7 + 6) / 10 = 55 / 10 = 5.5 hours
Median:
Arrange the study times in ascending order: 4, 4, 5, 5, 5, 6, 6, 6, 7, 7
Since there are an even number of data points, the median will be the average of the two middle values: (5 + 6) / 2 = 5.5 hours
Mode:
The mode is the value that appears most frequently. In this case, both 5 and 6 appear three times, so both 5 and 6 are modes.
Range:
Range = Maximum Study Time - Minimum Study Time
Range = 7 - 4 = 3 hours
Second Week Study Times (after adding 4 hours each):
11, 10, 9, 8, 9, 8, 10, 9, 11, 10
Mean:
(11 + 10 + 9 + 8 + 9 + 8 + 10 + 9 + 11 + 10) / 10 = 95 / 10 = 9.5 hours
Median:
Arrange the study times in ascending order: 8, 8, 9, 9, 9, 10, 10, 10, 11, 11
Since there are an even number of data points, the median will be the average of the two middle values: (9 + 10) / 2 = 9.5 hours
Mode:
The mode is the value that appears most frequently. In this case, both 9 and 10 appear three times, so both 9 and 10 are modes.
Range:
Range = Maximum Study Time - Minimum Study Time
Range = 11 - 8 = 3 hours
Therefore, the mean, median, mode (bimodal), and range of the study times for the second week are:
Mean: 9.5 hours
Median: 9.5 hours
Mode: 9 hours, 10 hours
Range: 3 hours