NumPy - Mean

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What is Mean?

In mathematics, the mean is the average value of a set of numbers. The most common type is the arithmetic mean, which is the sum of the numbers divided by the count of the numbers.

Other types include the geometric mean (nth root of the product of the numbers) and the harmonic mean (number of values divided by the sum of reciprocals).

These different means are used based on the nature of the data and specific needs of the analysis.

The NumPy mean() Function

The mean() function in NumPy calculates the arithmetic mean (average) of the elements in an array. By default, it computes the mean of all elements, but you can specify an axis to compute the mean along rows or columns.

It can also handle different data types and allow you to define the output type. For example, np.mean([1, 2, 3, 4]) returns 2.5.

Following is the basic syntax of the mean() function in NumPy −

numpy.mean(a, axis=None, dtype=None, out=None, keepdims=False)

Where,

• a: The input array containing the elements for which the mean is to be calculated.
• axis: The axis along which to compute the mean. If None, it computes the mean of all the elements in the array. For multi-dimensional arrays, you can specify an axis (0 for rows, 1 for columns, etc.).
• dtype: The data type to use in computing the mean. If not specified, it defaults to the data type of the input array.
• out: A location where the result will be stored. If provided, it must be of the same shape and type as the expected output.
• keepdims: If True, the reduced axes are kept in the result as dimensions with size one. This is useful for broadcasting.

Calculating the Mean of a 1D Array

If you have a one-dimensional array, you can use the numpy.mean() function to calculate the mean of its elements. Here is an example −

import numpy as np

# Define a 1D array
arr = np.array([1, 2, 3, 4, 5])

# Calculate the mean of all elements
mean_value = np.mean(arr)

print("Mean of the array:", mean_value)

Following is the output obtained −

Mean of the array: 3.0

Mean Along a Specific Axis in a 2D Array

In a two-dimensional array, you can compute the mean along a specific axis. For example, calculating the mean along rows or columns −

import numpy as np

# Define a 2D array
arr_2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# Mean along rows (axis=1)
mean_rows = np.mean(arr_2d, axis=1)

# Mean along columns (axis=0)
mean_columns = np.mean(arr_2d, axis=0)

print("Mean along rows:", mean_rows)
print("Mean along columns:", mean_columns)

Following is the output obtained −

Mean along rows: [2. 5. 8.]
Mean along columns: [4. 5. 6.]

Calculating Mean with a Specified Data Type

You can also specify the data type in which you want the mean to be computed. This is especially useful when dealing with large numbers or when you need the result in a specific precision (such as float64). Here is an example −

import numpy as np

# Define an array of integers
arr_int = np.array([10, 20, 30])

# Calculate the mean with a specified data type (float64)
mean_float = np.mean(arr_int, dtype=np.float64)

print("Mean with dtype float64:", mean_float)

Following is the output obtained −

Mean with dtype float64: 20.0

Calculating Mean with Keepdims Parameter

The keepdims parameter helps preserve the dimensionality of the original array after the mean operation. If set to True, the result will have the same number of dimensions as the input array, but the size of the reduced axes will be one.

import numpy as np

# Define a 2D array 
arr_2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# Mean along columns while keeping dimensions
mean_keepdims = np.mean(arr_2d, axis=0, keepdims=True)

print("Mean with keepdims=True:", mean_keepdims)

Following is the output obtained −

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

Applications of NumPy Mean

The numpy.mean() function has a wide range of applications in scientific computing, data analysis, and machine learning. Some common use cases are −

• Calculating average values in datasets: The mean provides a central value for datasets, which is crucial in statistics and data analysis to understand the data distribution.
• Feature scaling: In machine learning, computing the mean of features helps in normalization and standardization, ensuring that each feature contributes equally to the model.
• Financial analysis: Calculating the mean of financial data, such as stock prices or sales figures, helps identify trends and make informed decisions.
• Scientific measurements: The mean is used in scientific research to summarize experimental data, providing a measure of central tendency.

Optimizing the Mean Calculation

NumPy is optimized for fast array operations, and the numpy.mean() function is highly efficient. However, there are a few ways to further optimize your mean calculations −

• Using the out parameter: If you want to store the result of the mean in a pre-existing array, you can use the out parameter, which avoids creating a new array and helps save memory.
• Using axis wisely: Specify the axis only when necessary. Calculating the mean over the whole array by default is the fastest operation, but computing the mean along specific axes might be slower depending on the data.