Find the 54th percentile, P54, from the following data
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.
![**Question 7**
**Find the 54th percentile, \(P_{54}\), from the following data:**
| | | | | |
|-----|-----|-----|-----|-----|
| 10.8 | 10.9 | 12.8 | 13.6 | 14.8 |
| 14.9 | 15.2 | 15.4 | 17.3 | 17.6 |
| 19.1 | 21.1 | 22.7 | 23.2 | 24.6 |
| 26.5 | 28.6 | 28.8 | 30.2 | 30.5 |
| 31.6 | 31.9 | 32.6 | 33.5 | 34.7 |
| 35.9 | 38.1 | 38.3 | 39.1 | 39.5 |
| 39.9 | 40.8 | 41.4 | 41.9 | 43.7 |
| 45.4 | 46.8 | 47.7 | 49.5 | |
**\(P_{54}\) =** [_______]
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_Instructions: Calculate the 54th percentile from the given data set. Input your answer in the space provided and click "Submit Question" to confirm your answer._
(Note: The data is organized into a table with eight rows and five columns, showing various numerical values.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce002935-0cb2-4ae4-99f4-aff8adef33c2%2F542bd072-0e9c-40fe-8dd2-c655b92bf09f%2F9wzb1gj.jpeg&w=3840&q=75)
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