MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Complete the final two columns in the following frequency distribution and then find percentiles and percentile ranks requested:
Transcribed Image Text:**Title: Understanding Frequency Distributions and Percentile Ranks**
**Objective:** Learn how to complete a frequency distribution table and calculate percentile ranks.
**Instructions:**
Complete the final two columns in the following frequency distribution table and then find the percentiles and percentile ranks requested.
| X | f | cf | c% |
|---|---|----|----|
| 5 | 2 | | |
| 4 | 5 | | |
| 3 | 3 | | |
**Tasks:**
a. What is the percentile rank for X = 1.5?
b. What is the percentile rank for X = 4.5?
**Explanation:**
- **X:** Represents the data points or scores.
- **f (Frequency):** Number of times the data point occurs.
- **cf (Cumulative Frequency):** Total number of data points that are less than or equal to a given data point.
- **c% (Cumulative Percentage):** Percentage of data points that are less than or equal to a given data point.
**Steps to Complete:**
1. Calculate the cumulative frequency (cf) by adding the frequencies from the top row downward.
2. Calculate the cumulative percentage (c%) using the formula: \( c\% = \left(\frac{\text{cf}}{\text{Total Frequency}}\right) \times 100 \).
**Challenge:**
- After filling out the table, use the cumulative percentages to calculate the requested percentile ranks for given values of X.
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