https://file.aiquickdraw.com/mathbot/file/17265164301579wndkudo.jpg

To find the 76th percentile from the sorted list of 27 data points, we can follow these steps:

1. **Calculate the rank for the 76th percentile**:
   \[
   \text{Rank} = \left(\frac{76}{100}\right) \times (n + 1)
   \]
   where \(n\) is the total number of data points. Here, \(n = 27\).

   \[
   \text{Rank} = 0.76 \times (27 + 1) = 0.76 \times 28 = 21.28
   \]

2. **Interpret the rank**:
   Since the rank is not an integer (21.28), we will interpolate between the 21st and 22nd values in the sorted list.

3. **Identify the 21st and 22nd values**:
   From the data table, the 21st value is 393, and the 22nd value is 405.

4. **Interpolate**:
   To interpolate, we use the decimal part of the rank (0.28):
   \[
   \text{76th percentile} = 393 + 0.28 \times (405 - 393)
   \]
   \[
   \text{76th percentile} = 393 + 0.28 \times 12 = 393 + 3.36 = 396.36
   \]

Thus, the 76th percentile is approximately **396.36**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you find the 50th percentile for this dataset?
2. What is the difference between a percentile and a percentile rank?
3. How would you estimate the median from this dataset?
4. What would the 90th percentile be for this same data?
5. How can percentile rank help in comparing scores across different datasets?

**Tip**: Interpolation between values is key when the percentile rank doesn't land exactly on a whole number.

Find the 76th percentile from the following sorted list of 27 data points: [130, 147, 153, 179, 189, 223, 256, 279, 290, 297, 323, 330, 339, 341, 355, 366, 367, 385, 392, 393, 405, 445, 459, 471, 482, 485, 489].

Learn how to find the 76th percentile from a sorted list of 27 data points using interpolation. This problem involves percentile rank calculation and interpolation between data points. Suitable for 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