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Find the percentile rank of 50,55 and 75 of both subject

To find the percentile rank of the scores 50, 55, and 75 in both subjects (Math and English), we can use the following formula for the percentile rank (P):

\[ P = \left( \frac{L + 0.5S}{N} \right) \times 100 \]

where:
- \( L \) is the number of scores below the given score
- \( S \) is the number of scores equal to the given score
- \( N \) is the total number of scores

Given the total number of students is 16, we can calculate the percentile ranks for each score.

### Math Scores

#### Percentile rank of 50
- Scores below 50: 5 (25, 35, 40, 45, 48)
- Scores equal to 50: 1

\[ P_{50, \text{Math}} = \left( \frac{5 + 0.5 \times 1}{16} \right) \times 100 = \left( \frac{5.5}{16} \right) \times 100 = 34.375 \]

#### Percentile rank of 55
- Scores below 55: 6 (25, 35, 40, 45, 48, 50)
- Scores equal to 55: 1

\[ P_{55, \text{Math}} = \left( \frac{6 + 0.5 \times 1}{16} \right) \times 100 = \left( \frac{6.5}{16} \right) \times 100 = 40.625 \]

#### Percentile rank of 75
- Scores below 75: 11 (25, 35, 40, 45, 48, 50, 55, 62, 65, 68, 70)
- Scores equal to 75: 1

\[ P_{75, \text{Math}} = \left( \frac{11 + 0.5 \times 1}{16} \right) \times 100 = \left( \frac{11.5}{16} \right) \times 100 = 71.875 \]

### English Scores

#### Percentile rank of 50
- Scores below 50: 3 (20, 35, 40)
- Scores equal to 50: 1

\[ P_{50, \text{English}} = \left( \frac{3 + 0.5 \times 1}{16} \right) \times 100 = \left( \frac{3.5}{16} \right) \times 100 = 21.875 \]

#### Percentile rank of 55
- Scores below 55: 4 (20, 35, 40, 50)
- Scores equal to 55: 1

\[ P_{55, \text{English}} = \left( \frac{4 + 0.5 \times 1}{16} \right) \times 100 = \left( \frac{4.5}{16} \right) \times 100 = 28.125 \]

#### Percentile rank of 75
- Scores below 75: 8 (20, 35, 40, 45, 50, 55, 60, 65)
- Scores equal to 75: 1

\[ P_{75, \text{English}} = \left( \frac{8 + 0.5 \times 1}{16} \right) \times 100 = \left( \frac{8.5}{16} \right) \times 100 = 53.125 \]

### Summary of Percentile Ranks
- Percentile rank of 50 in Math: **34.375**
- Percentile rank of 55 in Math: **40.625**
- Percentile rank of 75 in Math: **71.875**

- Percentile rank of 50 in English: **21.875**
- Percentile rank of 55 in English: **28.125**
- Percentile rank of 75 in English: **53.125**

Would you like more details or have any questions? 

Here are some related questions:
1. How do you calculate percentile ranks for other scores?
2. What is the formula for finding percentile rank?
3. How is the rank determined in a set of scores?
4. Can percentile ranks be used to compare scores across different subjects?
5. What is the significance of percentile ranks in statistics?
6. How can we interpret the percentile rank of a score?
7. What is the difference between percentile rank and percentage?
8. How does the number of students affect the percentile rank calculation?

**Tip:** Always double-check the values you use for your calculations to ensure accuracy.

Learn how to calculate percentile ranks for scores 50, 55, and 75 in both Math and English. Understand the percentile rank formula and its application with detailed step-by-step examples. Suitable for high school students and anyone interested in statistics.

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