A 17. Complete the final two columns in the following frequency distribution table and then find the percentiles and percentile ranks requested: X cf c% 4. 6. 4 1 3 Sampe a. What is the percentile rank for X=1.5? b. What is the percentile rank for X=4.5?

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Complete the final two columns in the following frequency distribution and then find percentiles and percentile ranks requested:
**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.
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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