Find the 24th percentile, P24,  from the following data
1000	1600	1700	1800	2100
2300	2400	2500	2700	3300
4000	4600	4800	5200	5400
5600	6500	6700	6800	6900
7100	7200	7500	7800	7900
8400	8700			

P24  = 


To find the 24th percentile (P24) from the given data, we need to follow these steps:

1. **Arrange the data**: The data is already arranged in ascending order.
   \[
   1000, 1600, 1700, 1800, 2100, 2300, 2400, 2500, 2700, 3300, 4000, 4600, 4800, 5200, 5400, 5600, 6500, 6700, 6800, 6900, 7100, 7200, 7500, 7800, 7900, 8400, 8700
   \]
   There are \( n = 27 \) data points in total.

2. **Calculate the position for the 24th percentile (P24)**:  
   The formula for the percentile rank position is:
   \[
   P_k = \left( \frac{k}{100} \right) \times (n + 1)
   \]
   For the 24th percentile, \( k = 24 \) and \( n = 27 \).
   \[
   P_{24} = \left( \frac{24}{100} \right) \times (27 + 1) = 0.24 \times 28 = 6.72
   \]

   The position is 6.72, which means the 24th percentile lies between the 6th and 7th data points.

3. **Find the value between the 6th and 7th data points**:  
   The 6th data point is 2300, and the 7th data point is 2400.

   Now, we interpolate between these two values:
   \[
   P_{24} = 2300 + (0.72) \times (2400 - 2300) = 2300 + (0.72) \times 100 = 2300 + 72 = 2372
   \]

Thus, the 24th percentile (P24) is **2372**.

Would you like further details or clarifications?

Here are 5 related questions to expand your understanding:

1. How do you find percentiles for data that is not already sorted?
2. How does the formula for the percentile rank change when using a different dataset size?
3. What is the difference between percentiles and quartiles?
4. How would the percentile value change if the data contained extreme outliers?
5. What role does interpolation play when finding percentiles in a small dataset?

**Tip**: Percentiles help you understand the relative standing of a particular value within a dataset, providing insight into the data distribution.

Find the 24th percentile, P24, from the following data

Discover how to find the 24th percentile (P24) from a dataset of 27 values, including interpolation between data points. Learn the formula for calculating percentile position and follow a step-by-step solution. Perfect for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation