Carol asked a random sample of 10 seventh grade student athletes and 10 seventh grade students who are not athletes how much time, in minutes, they spend studying each weeknight. She recorded her results in the table.
Student Athletes Not Student Athletes
103 62 21 100 140
65 124 45 86 114
101 135 122 43 110
62 31 80 67 126
Calculate the mean and median data values for the student athletes sample.
Calculate the mean and median data values for the not student athletes sample.
When comparing the two samples, what conclusions can you draw about which group spends more time studying each weeknight?
To calculate the mean for the student athletes sample, we add up all the values and divide by the number of values:
(103 + 62 + 21 + 100 + 140 + 65 + 124 + 45 + 86 + 114) / 10 = 89.6
To calculate the median for the student athletes sample, we need to find the middle value. We first need to list the values in order:
21, 45, 62, 65, 86, 100, 103, 114, 124, 140
Since there are an even number of values, we take the average of the two middle values:
Median = (86 + 100) / 2 = 93
To calculate the mean for the not student athletes sample, we add up all the values and divide by the number of values:
(101 + 135 + 122 + 43 + 110 + 62 + 31 + 80 + 67 + 126) / 10 = 87.7
To calculate the median for the not student athletes sample, we need to find the middle value. We first need to list the values in order:
31, 43, 62, 67, 80, 101, 110, 122, 126, 135
Since there are an even number of values, we take the average of the two middle values:
Median = (101 + 110) / 2 = 105.5
Comparing the means, we see that the student athletes sample has a mean of 89.6 while the not student athletes sample has a mean of 87.7. This suggests that student athletes spend slightly more time studying each weeknight on average.
Comparing the medians, we see that the student athletes sample has a median of 93 while the not student athletes sample has a median of 105.5. This suggests that the not student athletes spend more time studying each weeknight on average.
Overall, we can conclude that while there may be some individual student athletes who spend more time studying than individual not student athletes, the not student athletes sample as a whole tends to spend more time studying each weeknight.
To calculate the mean for the student athletes sample, we need to sum up all the values and divide by the total number of values.
Mean for student athletes:
(103 + 62 + 21 + 100 + 140 + 65 + 124 + 45 + 86 + 114) / 10 = 960 / 10 = 96
To calculate the mean for the not student athletes sample, we follow the same process.
Mean for not student athletes:
(101 + 135 + 122 + 43 + 110 + 62 + 31 + 80 + 67 + 126) / 10 = 957 / 10 = 95.7
The median is the middle value when the data values are arranged in ascending order.
Median for student athletes: 100
Arranging the values in ascending order: 21, 31, 45, 62, 65, 86, 100, 103, 114, 140.
The middle value is 100.
Median for not student athletes: 96
Arranging the values in ascending order: 31, 43, 62, 67, 80, 101, 110, 122, 126, 135.
The two middle values are 101 and 110, so the median is the average of these two values: (101 + 110) / 2 = 211 / 2 = 105.5.
Comparing the mean values:
The mean for student athletes is 96, while the mean for not student athletes is 95.7. This suggests that student athletes spend slightly more time studying on average each weeknight compared to not student athletes.
Comparing the median values:
The median for student athletes is 100, while the median for not student athletes is 105.5. This suggests that student athletes have a lower middle value for their study time compared to not student athletes.
Based on both the mean and median comparisons, it can be concluded that student athletes, on average, spend more time studying each weeknight compared to not student athletes.
To calculate the mean and median data values for each sample, follow these steps:
For the student athletes:
1. Add up all the values in the student athletes' sample: 103 + 62 + 21 + 100 + 140 + 65 + 124 + 45 + 86 + 114 = 950.
2. Divide the sum by the number of values in the sample (10): 950 / 10 = 95.
So, the mean for the student athletes' sample is 95.
3. Arrange the values in ascending order: 21, 31, 45, 62, 65, 86, 100, 103, 114, 140.
4. Since there are an even number of values, find the average of the two middle values: (65 + 86) / 2 = 75.5.
So, the median for the student athletes' sample is 75.5.
For the not student athletes:
1. Add up all the values in the not student athletes' sample: 101 + 135 + 122 + 43 + 110 + 62 + 31 + 80 + 67 + 126 = 897.
2. Divide the sum by the number of values in the sample (10): 897 / 10 = 89.7.
So, the mean for the not student athletes' sample is 89.7.
3. Arrange the values in ascending order: 31, 43, 62, 67, 80, 101, 110, 122, 126, 135.
4. Since there are an even number of values, find the average of the two middle values: (80 + 101) / 2 = 90.5.
So, the median for the not student athletes' sample is 90.5.
Now, to compare the two samples:
- The mean for the student athletes is 95, while the mean for the not student athletes is 89.7. Thus, the student athletes spend more time studying on average.
- The median for the student athletes is 75.5, while the median for the not student athletes is 90.5. Again, the student athletes have a lower median, indicating they spend less time studying compared to the not student athletes.
Therefore, based on the mean and the median values, it can be concluded that the not student athletes spend more time studying each weeknight compared to the student athletes.