Find the 14th percentile, P14, from the following data 10 10.2 11.9 15.4 15.8 16.7 17.7 18.6 19.7 20.6 22.2 22.7 24 24.5 24.9 26.9 27.3 27.7 29.6 30.5 30.8 30.9 31.1 31.7 33.8 34.4 44.4 45.3 46.8 46.9 P14 %3D
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.
![**Find the 14th Percentile (P₁₄) from the Following Data**
The table below presents a series of numerical data points:
| 10.0 | 10.2 | 11.9 | 15.4 | 15.8 |
|------|------|------|------|------|
| 16.7 | 17.7 | 18.6 | 19.7 | 20.6 |
| 22.2 | 22.7 | 24.4 | 24.5 | 24.9 |
| 26.9 | 27.3 | 27.7 | 29.6 | 30.5 |
| 30.8 | 30.9 | 31.1 | 31.7 | 33.8 |
| 34.4 | 44.4 | 45.3 | 46.8 | 46.9 |
To find the 14th percentile, P₁₄, one would need to determine the value below which 14% of the data falls.
**Calculation:**
Locate the position of P₁₄ using:
\[ \text{Position} = \frac{14}{100} \times \text{Total Number of Data Points} \]
Enter the calculated value in the provided space and click "Submit Question" to check the result.
**Graph/Diagram Explanation:**
The table is a simple grid of numerical values with 25 entries spread across five rows. The numbers are raw data points meant for the calculation of the percentile. There is no additional graph or diagram included.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65f900eb-b634-4182-a839-b2016fefdf6d%2F13eeb047-e2d1-450a-a28d-e85c9538022e%2Fm64z9ds_processed.jpeg&w=3840&q=75)
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