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?

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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.