Enter your numbers separated by commas and specify the percentile to calculate.
How to Calculate Percentiles
Percentiles are a way to understand the relative standing of a value within a dataset. They tell us what percentage of values fall below a given point.
Percentile Formula
To calculate the \(p\)th percentile:
\[i = \frac{p}{100} \times (n - 1)\]
Where:
\(i\) is the index (which may not be an integer)
\(p\) is the percentile (0-100)
\(n\) is the number of values in the dataset
Calculation Steps
Sort the dataset in ascending order.
Calculate the index \(i\) using the formula above.
If \(i\) is an integer, the percentile is the value at that index.
If \(i\) is not an integer, interpolate between the two nearest values:
Find the values at indices \(\lfloor i \rfloor\) and \(\lceil i \rceil\)
Interpolate between these values based on the fractional part of \(i\)
Example
Let's calculate the 75th percentile for the dataset: 1, 3, 5, 7, 9, 11, 13
The dataset is already sorted.
\(i = \frac{75}{100} \times (7 - 1) = 4.5\)
\(i\) is not an integer, so we interpolate between the 4th and 5th values:
4th value: 7
5th value: 9
Interpolation: \(7 + 0.5 \times (9 - 7) = 8\)
Therefore, the 75th percentile is 8.
Visual Representation
This diagram illustrates the 75th percentile (8) in our example dataset. The green line represents the 75th percentile, showing that 75% of the data points fall below this value.