A college strength coach tested incoming freshman football players on the number of bench press repetitions they could perform at a load of 225 pounds. The scores were arranged into a simple frequency distribution: Number of repetitions f Cum. f 20 1 37 19 0 36 18 1 36 17 2 35 16 3 33 15 4 30 14 2 26 13 3 24 12 6 21 11 4 15 10 3 11 9 4 8 8 2 4 7 1 2 6 1 1 1 What is the percentile of a person who scored (a) 10 repetitions; (b) 16 repetitions?
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 college strength coach tested incoming freshman football players on the number of bench press repetitions they could perform at a load of 225 pounds. The scores were arranged into a simple frequency distribution:
|
Number of repetitions |
f |
Cum. f |
|
20 |
1 |
37 |
|
19 |
0 |
36 |
|
18 |
1 |
36 |
|
17 |
2 |
35 |
|
16 |
3 |
33 |
|
15 |
4 |
30 |
|
14 |
2 |
26 |
|
13 |
3 |
24 |
|
12 |
6 |
21 |
|
11 |
4 |
15 |
|
10 |
3 |
11 |
|
9 |
4 |
8 |
|
8 |
2 |
4 |
|
7 |
1 |
2 |
|
6 |
1 |
1 |
1
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What is the percentile of a person who scored (a) 10 repetitions; (b) 16 repetitions?
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