Answer:
1. A marathon race was completed by 5 participants. 3.7 hours, 6.3 hours 2.9 hours, 4.1 hours, and 7.3 hours are the recorded
time of the participants. The organizer wants to know the difference between the first and the last to finish.
To find the difference, we use the range. It is the difference between the highest and lowest value in a data set. In
this example, the range is 4.4 hours. The winner of the race is faster by 4.4 hours from the last to finish.
2. Jeff and James measured the height of the dogs (in millimeters). The height is: 600 mm, 470 mm, 170 mm, 430 mm, and 300
mm. If they want to know the average dog’s height from the mean, they can use average deviation, because average
deviation is telling us how far, on average, all values are from the middle. The average deviation is 127.2 mm.
This average deviation indicates that the heights of the dogs are 127.2 mm far from the mean which is 394 mm. You
can also infer that the heights of the dogs are scattered because the average deviation is too high.
3. Two groups of students competed for the championship. The First Group scored 70, 95, 60, 80 and 100 while the Second
Group scored 82, 80, 83, 81 and 79. Which group performed better together?
We can use the variance. From the given, the variance of the first group is 280 square units while the second group is
2.5 square units. Using the variance as a measure of variability for the sets of scores, the first group showed more variability
in performance. Note that the higher the variance, the more variable or far apart the values are from each other. So that
means, the second group has closer scores than the first. Thus, they performed better together.
4. Chris wants to know how consistent his bowling scores have been during the past seasons. What measures of variability would
provide the most appropriate answer to his questions?
Step-by-step explanation:
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Answers & Comments
Answer:
1. A marathon race was completed by 5 participants. 3.7 hours, 6.3 hours 2.9 hours, 4.1 hours, and 7.3 hours are the recorded
time of the participants. The organizer wants to know the difference between the first and the last to finish.
To find the difference, we use the range. It is the difference between the highest and lowest value in a data set. In
this example, the range is 4.4 hours. The winner of the race is faster by 4.4 hours from the last to finish.
2. Jeff and James measured the height of the dogs (in millimeters). The height is: 600 mm, 470 mm, 170 mm, 430 mm, and 300
mm. If they want to know the average dog’s height from the mean, they can use average deviation, because average
deviation is telling us how far, on average, all values are from the middle. The average deviation is 127.2 mm.
This average deviation indicates that the heights of the dogs are 127.2 mm far from the mean which is 394 mm. You
can also infer that the heights of the dogs are scattered because the average deviation is too high.
3. Two groups of students competed for the championship. The First Group scored 70, 95, 60, 80 and 100 while the Second
Group scored 82, 80, 83, 81 and 79. Which group performed better together?
We can use the variance. From the given, the variance of the first group is 280 square units while the second group is
2.5 square units. Using the variance as a measure of variability for the sets of scores, the first group showed more variability
in performance. Note that the higher the variance, the more variable or far apart the values are from each other. So that
means, the second group has closer scores than the first. Thus, they performed better together.
4. Chris wants to know how consistent his bowling scores have been during the past seasons. What measures of variability would
provide the most appropriate answer to his questions?
Step-by-step explanation: