A group of five friends are long-distance runners who will be running in an upcoming marathon. To prepare for the marathon, each of the friends recorded the number of miles they ran each week for 12 weeks. The results of the friends' training are shown in the data set provided below. Which of the friends was the most consistent with the number of miles run each week during the training? Hint: You should not need to compute the standard deviation for each friend. Ashton Caleb Jordan Kyle Noah 24 35 22 15 13 34 36 39 26 29 25 34 26 24 18 31 35 41 25 31 19 37 38 27 15 33 35 37 24 19 27 34 40 25 27 29 36 27 26 32 36 35 21 32 15 16 33 42 24 17 18 36 33 21 28 26 35 35 27 21
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A group of five friends are long-distance runners who will be running in an upcoming marathon. To prepare for the marathon, each of the friends recorded the number of miles they ran each week for 12 weeks. The results of the friends' training are shown in the data set provided below. Which of the friends was the most consistent with the number of miles run each week during the training? Hint: You should not need to compute the standard deviation for each friend.
|
Ashton |
Caleb |
Jordan |
Kyle |
Noah |
|
24 |
35 |
22 |
15 |
13 |
|
34 |
36 |
39 |
26 |
29 |
|
25 |
34 |
26 |
24 |
18 |
|
31 |
35 |
41 |
25 |
31 |
|
19 |
37 |
38 |
27 |
15 |
|
33 |
35 |
37 |
24 |
19 |
|
27 |
34 |
40 |
25 |
27 |
|
29 |
36 |
27 |
26 |
32 |
|
36 |
35 |
21 |
32 |
15 |
|
16 |
33 |
42 |
24 |
17 |
|
18 |
36 |
33 |
21 |
28 |
|
26 |
35 |
35 |
27 |
21 |
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