
- NumPy - Home
- NumPy - Introduction
- NumPy - Environment
- NumPy Arrays
- NumPy - Ndarray Object
- NumPy - Data Types
- NumPy Creating and Manipulating Arrays
- NumPy - Array Creation Routines
- NumPy - Array Manipulation
- NumPy - Array from Existing Data
- NumPy - Array From Numerical Ranges
- NumPy - Iterating Over Array
- NumPy - Reshaping Arrays
- NumPy - Concatenating Arrays
- NumPy - Stacking Arrays
- NumPy - Splitting Arrays
- NumPy - Flattening Arrays
- NumPy - Transposing Arrays
- NumPy Indexing & Slicing
- NumPy - Indexing & Slicing
- NumPy - Indexing
- NumPy - Slicing
- NumPy - Advanced Indexing
- NumPy - Fancy Indexing
- NumPy - Field Access
- NumPy - Slicing with Boolean Arrays
- NumPy Array Attributes & Operations
- NumPy - Array Attributes
- NumPy - Array Shape
- NumPy - Array Size
- NumPy - Array Strides
- NumPy - Array Itemsize
- NumPy - Broadcasting
- NumPy - Arithmetic Operations
- NumPy - Array Addition
- NumPy - Array Subtraction
- NumPy - Array Multiplication
- NumPy - Array Division
- NumPy Advanced Array Operations
- NumPy - Swapping Axes of Arrays
- NumPy - Byte Swapping
- NumPy - Copies & Views
- NumPy - Element-wise Array Comparisons
- NumPy - Filtering Arrays
- NumPy - Joining Arrays
- NumPy - Sort, Search & Counting Functions
- NumPy - Searching Arrays
- NumPy - Union of Arrays
- NumPy - Finding Unique Rows
- NumPy - Creating Datetime Arrays
- NumPy - Binary Operators
- NumPy - String Functions
- NumPy - Matrix Library
- NumPy - Linear Algebra
- NumPy - Matplotlib
- NumPy - Histogram Using Matplotlib
- NumPy Sorting and Advanced Manipulation
- NumPy - Sorting Arrays
- NumPy - Sorting along an axis
- NumPy - Sorting with Fancy Indexing
- NumPy - Structured Arrays
- NumPy - Creating Structured Arrays
- NumPy - Manipulating Structured Arrays
- NumPy - Record Arrays
- Numpy - Loading Arrays
- Numpy - Saving Arrays
- NumPy - Append Values to an Array
- NumPy - Swap Columns of Array
- NumPy - Insert Axes to an Array
- NumPy Handling Missing Data
- NumPy - Handling Missing Data
- NumPy - Identifying Missing Values
- NumPy - Removing Missing Data
- NumPy - Imputing Missing Data
- NumPy Performance Optimization
- NumPy - Performance Optimization with Arrays
- NumPy - Vectorization with Arrays
- NumPy - Memory Layout of Arrays
- Numpy Linear Algebra
- NumPy - Linear Algebra
- NumPy - Matrix Library
- NumPy - Matrix Addition
- NumPy - Matrix Subtraction
- NumPy - Matrix Multiplication
- NumPy - Element-wise Matrix Operations
- NumPy - Dot Product
- NumPy - Matrix Inversion
- NumPy - Determinant Calculation
- NumPy - Eigenvalues
- NumPy - Eigenvectors
- NumPy - Singular Value Decomposition
- NumPy - Solving Linear Equations
- NumPy - Matrix Norms
- NumPy Element-wise Matrix Operations
- NumPy - Sum
- NumPy - Mean
- NumPy - Median
- NumPy - Min
- NumPy - Max
- NumPy Set Operations
- NumPy - Unique Elements
- NumPy - Intersection
- NumPy - Union
- NumPy - Difference
- NumPy Random Number Generation
- NumPy - Random Generator
- NumPy - Permutations & Shuffling
- NumPy - Uniform distribution
- NumPy - Normal distribution
- NumPy - Binomial distribution
- NumPy - Poisson distribution
- NumPy - Exponential distribution
- NumPy - Rayleigh Distribution
- NumPy - Logistic Distribution
- NumPy - Pareto Distribution
- NumPy - Visualize Distributions With Sea born
- NumPy - Matplotlib
- NumPy - Multinomial Distribution
- NumPy - Chi Square Distribution
- NumPy - Zipf Distribution
- NumPy File Input & Output
- NumPy - I/O with NumPy
- NumPy - Reading Data from Files
- NumPy - Writing Data to Files
- NumPy - File Formats Supported
- NumPy Mathematical Functions
- NumPy - Mathematical Functions
- NumPy - Trigonometric functions
- NumPy - Exponential Functions
- NumPy - Logarithmic Functions
- NumPy - Hyperbolic functions
- NumPy - Rounding functions
- NumPy Fourier Transforms
- NumPy - Discrete Fourier Transform (DFT)
- NumPy - Fast Fourier Transform (FFT)
- NumPy - Inverse Fourier Transform
- NumPy - Fourier Series and Transforms
- NumPy - Signal Processing Applications
- NumPy - Convolution
- NumPy Polynomials
- NumPy - Polynomial Representation
- NumPy - Polynomial Operations
- NumPy - Finding Roots of Polynomials
- NumPy - Evaluating Polynomials
- NumPy Statistics
- NumPy - Statistical Functions
- NumPy - Descriptive Statistics
- NumPy Datetime
- NumPy - Basics of Date and Time
- NumPy - Representing Date & Time
- NumPy - Date & Time Arithmetic
- NumPy - Indexing with Datetime
- NumPy - Time Zone Handling
- NumPy - Time Series Analysis
- NumPy - Working with Time Deltas
- NumPy - Handling Leap Seconds
- NumPy - Vectorized Operations with Datetimes
- NumPy ufunc
- NumPy - ufunc Introduction
- NumPy - Creating Universal Functions (ufunc)
- NumPy - Arithmetic Universal Function (ufunc)
- NumPy - Rounding Decimal ufunc
- NumPy - Logarithmic Universal Function (ufunc)
- NumPy - Summation Universal Function (ufunc)
- NumPy - Product Universal Function (ufunc)
- NumPy - Difference Universal Function (ufunc)
- NumPy - Finding LCM with ufunc
- NumPy - ufunc Finding GCD
- NumPy - ufunc Trigonometric
- NumPy - Hyperbolic ufunc
- NumPy - Set Operations ufunc
- NumPy Useful Resources
- NumPy - Quick Guide
- NumPy - Cheatsheet
- NumPy - Useful Resources
- NumPy - Discussion
- NumPy Compiler
NumPy std() Function
The NumPy std() function computes the standard deviation of the elements in an array along a specified axis. It returns the standard deviation, which measures the spread or dispersion of a distribution. By default, the standard deviation is calculated over the flattened array, but it can also be computed along a specified axis.
In statistics, the standard deviation is the square root of the variance. The formula is std = sqrt(sum((x_i - mean)^2) / N), where x_i is each data point, mean is the mean of the data, and N is the number of data points.
For a one-dimensional array, the standard deviation is computed over all elements. For multi-dimensional arrays, the standard deviation is computed along the specified axis.
Syntax
Following is the syntax of the NumPy std() function −
numpy.std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=<no value>, where=<no value>, mean=<no value>, correction=<no value>)
Parameters
Following are the parameters of the NumPy std() function −
- a: Input array or object that can be converted to an array. It can be a NumPy array, list, or a scalar value.
- axis (optional): Axis or axes along which the standard deviation is computed. Default is None, which means the standard deviation is computed over the entire array.
- dtype (optional): Data type to use in computing the standard deviation. If None, it is inferred from the input array.
- out (optional): A location into which the result is stored. If provided, it must have the same shape as the expected output.
- ddof (optional): Delta Degrees of Freedom. The divisor used in the calculation is N - ddof, where N is the number of elements. Default is 0.
- keepdims (optional): If True, the reduced dimensions are retained as dimensions of size one in the output. Default is False.
- where(optional): The elements that to be included in the standard deviation
- mean(optional): It provide's the mean to prevent its re-calculation. The mean should have a shape as if it was calculated with keepdims=True. The axis for the calculation of the mean should be the same as used in the call to this std function.
- correction(optional): This function calculates the standard deviation of elements in an array, measuring the dispersion or spread of data around the mean, with options to compute along specified axes, apply degrees of freedom (`ddof`), and retain dimensions.
Return Values
This function returns the standard deviation 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 standard deviation of an array using the NumPy std() function −
import numpy as np # input array x = np.array([1, 2, 3, 4, 5]) # applying std result = np.std(x) print("Standard Deviation Result:", result)
Output
Following is the output of the above code −
Standard Deviation Result: 1.4142135623730951
Example: Specifying an Axis
The std() function can compute the standard deviation along a specific axis of a multi-dimensional array. In the following example, we have computed the standard deviation 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 std along axis 0 (columns) result_axis0 = np.std(x, axis=0) # applying std along axis 1 (rows) result_axis1 = np.std(x, axis=1) print("Standard Deviation along axis 0:", result_axis0) print("Standard Deviation along axis 1:", result_axis1)
Output
Following is the output of the above code −
Standard Deviation along axis 0: [2.44948974 2.44948974 2.44948974] Standard Deviation along axis 1: [0.81649658 0.81649658 0.81649658]
Example: Usage of 'ddof' Parameter
The ddof(Delta Degrees of Freedom) parameter allows us to adjust the degrees of freedom for the calculation. By default, ddof=0, but we can set it to a different value to change the divisor used in the calculation. In the following example, we have computed the standard deviation with ddof=1 −
import numpy as np # input array x = np.array([1, 2, 3, 4, 5]) # applying std with ddof=1 result = np.std(x, ddof=1) print("Standard Deviation with ddof=1:", result)
Output
Following is the output of the above code −
Standard Deviation with ddof=1: 1.5811388300841898
Example: Plotting 'std()' Function
In the following example, we have plotted the behavior of the std() function. We have calculated and plotted the standard deviation 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.std(x) plt.plot(x, np.full_like(x, y), label="Standard Deviation") plt.title("Standard Deviation Function") plt.xlabel("Input") plt.ylabel("Standard Deviation Value") plt.legend() plt.grid() plt.show()
Output
The plot demonstrates the constant nature of the standard deviation value across the input range −
