How do you find the number that is a certain percentile when given the percentile, as in, you've been given a data set, and have been asked, what is the 34th percentile?

To find the number that corresponds to a certain percentile in a data set, like the 34th percentile, you need to follow these steps:

### Step-by-Step Process to Find a Percentile:

1. **Sort the Data Set**: Arrange the data in ascending order. This step is crucial because percentiles are based on the position of values within an ordered list.

2. **Determine the Position**: To find the position \( P \) of the data value corresponding to a specific percentile, use the formula:

   \[
   P = \frac{n \cdot p}{100}
   \]

   - \( n \) = total number of data points in the set
   - \( p \) = desired percentile (e.g., for the 34th percentile, \( p = 34 \))

3. **Find the Exact Position**:
   - If \( P \) is an integer, it directly indicates the position of the percentile in the sorted list.
   - If \( P \) is not an integer, round up to the next whole number. The value at this rounded-up position is the 34th percentile.

4. **Locate the Value**:
   - Go to the \( P \)-th position in the sorted data set. This is the number corresponding to the desired percentile.

### Example

Suppose you have a data set: [12, 18, 25, 27, 31, 33, 37, 42, 47].

1. **Sort the Data**: The data is already sorted in ascending order.
2. **Calculate the Position**:
   - Total number of data points \( n = 9 \).
   - Desired percentile \( p = 34 \).

   Find the position:

   \[
   P = \frac{9 \cdot 34}{100} = 3.06
   \]

3. **Determine the Position**:
   - Since 3.06 is not an integer, round up to the next whole number: \( P = 4 \).

4. **Locate the Value**:
   - The 4th value in the sorted data set is **27**. 
   - Thus, the 34th percentile is **27**.

### Summary

- Sort your data.
- Use the formula \( P = \frac{n \cdot p}{100} \) to find the position.
- Round up if necessary and find the corresponding data value.

Would you like further details or have any questions?

---

### 5 Related Questions:
1. How do you calculate the percentile rank of a given data point?
2. What is the difference between the median and the 50th percentile?
3. How do you handle percentiles in a data set with repeated values?
4. What are the steps to calculate percentiles in grouped data?
5. How can I calculate the interquartile range (IQR) using percentiles?

**Tip:** Understanding percentiles helps in interpreting data distribution, particularly in fields like statistics, finance, and medicine.

Learn how to find the 34th percentile in a data set using a step-by-step approach. This guide explains the process of sorting data, calculating the position using the formula P = (n * p) / 100, and determining the corresponding value in the data. 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