NumPy median() Function

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The NumPy median() function computes the median of the input array along a specified axis. The median is the value separating the higher half from the lower half of the data. It is a measure of central tendency that is less sensitive to outliers compared to the mean.

In statistics, median is the middle value of the given list of data when arranged in an order. The arrangement of data or observations can be made either in ascending order or descending order. If the number of terms n is odd, then the median value is the n+1/2-th value. If n is an even number, the median is the average value of the two middle numbers, specifically the values at positions n/2 and n/2 + 1.

For a one-dimensional array, the median is the middle value when the data is sorted. For multi-dimensional arrays, the median is computed along the specified axis. If the data has an even number of elements, the median is the average of the two middle elements.

Syntax

Following is the syntax of the NumPy median() function −

numpy.median(a, axis=None, out=None, overwrite_input=False, keepdims=False)

Parameters

Following are the parameters of the NumPy median() function −

• a: Input array, it can be a NumPy array, list, or a scalar value.
• axis (optional): The axis along which to compute the median. Default is None, which means that the median is computed over the entire array.
• overwrite_input (optional): If True, the input array is modified in place. Default is False.
• out (optional): A location into which the result is stored. If provided, it must have the same shape as the expected output.
• keepdims (optional): If True, the reduced dimensions are retained as dimensions of size one in the output. Default is False.

Return Values

This function returns the median of the input array. The result is a scalar if the input is one-dimensional, and an array if the input is multi-dimensional.

Example

Following is a basic example to compute the median of an array using the NumPy median() function −

import numpy as np
# input array
x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
# applying median
result = np.median(x)
print("Median Result:", result)

Output

Following is the output of the above code −

Median Result: 5.0

Example: Specifying an Axis

The median() function can also compute the median along a specific axis of a multi-dimensional array. In the following example, we have computed the median along axis 0 (columns) and axis 1 (rows) of a 2D array.

import numpy as np
# 2D array
x = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
# applying median along axis 0 (columns)
result_axis0 = np.median(x, axis=0)
# applying median along axis 1 (rows)
result_axis1 = np.median(x, axis=1)
print("Median along axis 0:", result_axis0)
print("Median along axis 1:", result_axis1)

Output

Following is the output of the above code −

Median along axis 0: [4. 5. 6.]
Median along axis 1: [2. 5. 8.]

Example: Multi-dimensional Array

The median() function operates on multi-dimensional arrays. In the following example, we have created a 2D NumPy array and computed the median of each element along a specific axis −

import numpy as np
# 2D array
x = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
result = np.median(x, axis=1)
print("Median Result for 2D Array:", result)

Output

Following is the output of the above code −

Median Result for 2D Array: [2. 5. 8.]

Example: Usage of 'keepdims' Parameter

The keepdims parameter allows the result to retain the reduced dimensions as size one. This is useful for broadcasting the result back to the original shape. In the following example, we have computed the median along axis 0 and retain the reduced dimensions −

import numpy as np
# 2D array
x = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
result = np.median(x, axis=0, keepdims=True)
print("Median with keepdims=True:", result)

Output

Following is the output of the above code −

Median with keepdims=True: [[4. 5. 6.]]

Example: Plotting 'median()' Function

In the following example, we have plotted the behavior of the median() function. We have calculated and plotted the median for different sizes of input arrays by importing Numpy and matplotlib.pyplot module −

import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0, 10, 100)
y = np.median(x)
plt.plot(x, np.full_like(x, y), label="Median")
plt.title("Median Function")
plt.xlabel("Input")
plt.ylabel("Median Value")
plt.legend()
plt.grid()
plt.show()

Output

The plot demonstrates the constant nature of the median value across the input range −