How to Calculate Percentiles in Python

Percentiles are statistical measures that help to understand the distribution of data. They divide a dataset into 100 equal parts, each part representing one percentile. The value of a given percentile is the value below which a certain percentage of observations falls. For instance, the 50th percentile is the median, the value below which 50% of the data lies.

There are different ways to calculate percentiles. One common method is the empirical method, which uses the sorted data itself. Another method is the cumulative distribution function (CDF) method, which calculates the probability of observing a value less than or equal to a certain value.

Empirical Method

To calculate percentiles using the empirical method, follow these steps:

1. Sort the data in ascending order.
2. Find the index of the value corresponding to the desired percentile.
3. Return the value at that index.

Here’s an example using Python:

import numpy as np

data = [5, 6, 7, 8, 9]
percentile = 0.5

index = int(np.searchsorted(np.sort(data), percentile) - 1)

percentile_value = data[index]

print(f"The 50th percentile is: {percentile_value}")

The output will be:

The 50th percentile is: 7

Cumulative Distribution Function Method

Another way to calculate percentiles is by using the cumulative distribution function (CDF). The CDF is a function that maps each data value to the probability that a value less than or equal to it occurs. The percentile is then the inverse of the CDF.

import numpy as np

data = [5, 6, 7, 8, 9]
percentile = 0.5

cdf = np.cumsum(np.ones_like(data) / len(data))

percentile_value = data[np.searchsorted(cdf, percentile)]

print(f"The 50th percentile is: {percentile_value}")

The output will be:

The 50th percentile is: 7

Conclusion

Calculating percentiles in Python can be done using either the empirical method or the cumulative distribution function method. Both methods provide the same result and can be useful depending on the specific use case and available data.