How to Calculate Percentile in Python

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  4. How to Calculate Percentile in Python
Azaz Farooq Feb 02, 2024
Python Python Math Python NumPy
  1. Calculate Percentile in Python Using the scipy Package
  2. Calculate Percentile in Python Using the NumPy Package
  3. Calculate Percentile in Python Using the math Package
  4. Calculate Percentile in Python Using the statistics Package
  5. Calculate Percentile in Python Using the NumPy’s Linear Interpolation Method
  6. Calculate Percentile in Python Using the NumPy’s Lower Interpolation Method
  7. Calculate Percentile in Python Using the NumPy’s Higher Interpolation Method
  8. Calculate Percentile in Python Using the NumPy’s Midpoint Interpolation Method
How to Calculate Percentile in Python

Percentiles indicate the percentage of scores that fall below a certain value. An individual with an IQ of 120, for instance, is at the 91st percentile, which means that his IQ is greater than 91% of other people.

This article will discuss some methods to calculate percentile in Python.

Calculate Percentile in Python Using the scipy Package

This package will calculate the score of the input series at a given percentile. The syntax of the scoreatpercentile() function is given below:

scipy.stats.scoreatpercentile(
    a, per, limit=(), interpolation_method="fraction", axis=None
)

In the scoreatpercentile() function, the parameter a represents a 1-D array, and per specifies the percentile ranging from 0 to 100. The other two parameters are optional. The NumPy library is used to get the numbers on which we calculated percentile.

The complete example code is given below.

from scipy import stats
import numpy as np

array = np.arange(100)

percentile = stats.scoreatpercentile(array, 50)

print("The percentile is:", percentile)

Output:

The percentile is: 49.5

Calculate Percentile in Python Using the NumPy Package

This package has a percentile() function that will calculate the percentile of given array. The syntax of the percentile() function is given below.

numpy.percentile(
    a,
    q,
    axis=None,
    out=None,
    overwrite_input=False,
    interpolation="linear",
    keepdims=False,
)

The parameter q represents the percentile calculation number. a represents an array while the other parameters are optional.

The complete example code is given below.

import numpy as np

arry = np.array([4, 6, 8, 10, 12])

percentile = np.percentile(arry, 50)

print("The percentile is:", percentile)

Output:

The percentile is: 8.0

Calculate Percentile in Python Using the math Package

The math package with its basic function - ceil can be used to calculate different percentiles.

The complete example code is given below.

import math

arry = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]


def calculate_percentile(arry, percentile):
    size = len(arry)
    return sorted(arry)[int(math.ceil((size * percentile) / 100)) - 1]


percentile_25 = calculate_percentile(arry, 25)
percentile_50 = calculate_percentile(arry, 50)
percentile_75 = calculate_percentile(arry, 75)

print("The 25th percentile is:", percentile_25)
print("The 50th percentile is:", percentile_50)
print("The 75th percentile is:", percentile_75)

The math.ceil(x) rounds off the value and returns the smallest integer greater than or equal to x, while the sorted function sorts the array.

Output:

The 25th percentile is: 3
The 50th percentile is: 5
The 75th percentile is: 8

Calculate Percentile in Python Using the statistics Package

The quantiles() function in the statistics package is used to break down the data into equal probability and return a distribution list of n-1. The syntax of this function is given below.

statistics.quantiles(data, *, n=4, method='exclusive')

The complete example code is given below.

from statistics import quantiles

data = [1, 2, 3, 4, 5]

percentle = quantiles(data, n=4)

print("The Percentile is:", percentle)

Output:

The Percentile is: [1.5, 3.0, 4.5]

Calculate Percentile in Python Using the NumPy’s Linear Interpolation Method

We can calculate different percentiles using the interpolation mode. The interpolation modes are linear, lower, higher, midpoint and nearest. These interpolations are used when the percentiles are in between two data points, i and j. When the percentile value is i, it is lower interpolation mode, j represents higher interpolation mode, and i + (j - i) * fraction represents the linear mode where fraction indicates the index surrounded by i and j.

The complete example code for linear interpolation mode is given below.

import numpy as np

arry = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

print("percentiles using interpolation = ", "linear")

percentile_10 = np.percentile(arry, 10, interpolation="linear")
percentile_50 = np.percentile(arry, 50, interpolation="linear")
percentile_75 = np.percentile(arry, 75, interpolation="linear")

print(
    "percentile_10 = ",
    percentile_10,
    ", median = ",
    percentile_50,
    " and percentile_75 = ",
    percentile_75,
)

We use numpy.percentile() function with additional parameter interpolation. You can see that we get float values for this interpolation.

Output:

percentiles using interpolation =  linear
percentile_10 =  1.9 , median =  5.5  and percentile_75 =  7.75

Calculate Percentile in Python Using the NumPy’s Lower Interpolation Method

The complete example code for lower interpolation mode is given below.

import numpy as np

arry = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

print("percentiles using interpolation = ", "lower")

percentile_10 = np.percentile(arry, 10, interpolation="lower")
percentile_50 = np.percentile(arry, 50, interpolation="lower")
percentile_75 = np.percentile(arry, 75, interpolation="lower")

print(
    "percentile_10 = ",
    percentile_10,
    ", median = ",
    percentile_50,
    " and percentile_75 = ",
    percentile_75,
)

Output:

percentiles using interpolation =  lower
percentile_10 =  1 , median =  5  and percentile_75 =  7

You can see that the final percentile is rouded-off to the lowest value.

Calculate Percentile in Python Using the NumPy’s Higher Interpolation Method

This method will give percentiles of the given array to the highest round-off value.

The complete example code for higher interpolation mode is given below.

import numpy as np

arry = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

print("percentiles using interpolation = ", "higher")

percentile_10 = np.percentile(arry, 10, interpolation="higher")
percentile_50 = np.percentile(arry, 50, interpolation="higher")
percentile_75 = np.percentile(arry, 75, interpolation="higher")

print(
    "percentile_10 = ",
    percentile_10,
    ", median = ",
    percentile_50,
    " and percentile_75 = ",
    percentile_75,
)

Output:

percentiles using interpolation =  higher
percentile_10 =  2 , median =  6  and percentile_75 =  8

Calculate Percentile in Python Using the NumPy’s Midpoint Interpolation Method

This method will give midpoints of the percentile values.

The complete example code for midpoint interpolation mode is given below.

import numpy as np

arry = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

print("percentiles using interpolation = ", "midpoint")

percentile_10 = np.percentile(arry, 10, interpolation="midpoint")
percentile_50 = np.percentile(arry, 50, interpolation="midpoint")
percentile_75 = np.percentile(arry, 75, interpolation="midpoint")

print(
    "percentile_10 = ",
    percentile_10,
    ", median = ",
    percentile_50,
    " and percentile_75 = ",
    percentile_75,
)

Output:

percentiles using interpolation =  midpoint
percentile_10 =  1.5 , median =  5.5  and percentile_75 =  7.5

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