set (n=117n=117)
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.
Here is a data set (n=117n=117) that has been sorted.
| 12.2 | 13.2 | 13.3 | 13.4 | 14.3 | 15.3 | 15.9 | 16.4 | 16.8 |
| 17.6 | 17.7 | 18.5 | 19.5 | 19.5 | 19.6 | 20.7 | 21 | 21.4 |
| 21.6 | 21.9 | 22.4 | 22.5 | 22.8 | 23 | 23.3 | 23.8 | 23.9 |
| 24 | 24.5 | 24.9 | 24.9 | 24.9 | 25.1 | 25.1 | 25.6 | 25.7 |
| 25.9 | 26.4 | 26.7 | 26.8 | 26.9 | 27 | 27.1 | 27.3 | 27.4 |
| 27.7 | 28 | 28 | 28 | 28.2 | 28.3 | 28.5 | 28.7 | 28.9 |
| 28.9 | 29 | 29.2 | 29.3 | 29.6 | 30 | 30.1 | 30.3 | 30.4 |
| 30.5 | 30.7 | 30.7 | 30.8 | 31.8 | 32 | 32.1 | 32.5 | 33 |
| 33.1 | 33.3 | 33.4 | 33.4 | 33.5 | 33.6 | 33.8 | 33.9 | 34.5 |
| 35.1 | 35.4 | 35.6 | 35.7 | 35.8 | 36 | 36.2 | 36.3 | 36.4 |
| 36.4 | 36.6 | 36.6 | 36.6 | 36.9 | 37.3 | 37.7 | 37.9 | 38.1 |
| 38.2 | 38.3 | 38.6 | 39.8 | 40.3 | 40.4 | 40.9 | 41.2 | 41.7 |
| 41.8 | 42.1 | 42.3 | 42.4 | 43.2 | 43.3 | 43.4 | 43.5 | 50.2 |
Find the 63rd-Percentile:
P63 =
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