- Machine Learning Basics
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- Machine Learning Data Visualization
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- Statistics for Machine Learning
- Machine Learning - Statistics
- Machine Learning - Mean, Median, Mode
- Machine Learning - Standard Deviation
- Machine Learning - Percentiles
- Machine Learning - Data Distribution
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- Regression Analysis In ML
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- Classification Algorithms In ML
- Machine Learning - Classification Algorithms
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- Machine Learning - Naïve Bayes Algorithm
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- Clustering Algorithms In ML
- Machine Learning - Clustering Algorithms
- Machine Learning - Centroid-Based Clustering
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- Machine Learning - Mean-Shift Clustering
- Machine Learning - Hierarchical Clustering
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- Machine Learning - DBSCAN Clustering
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- Machine Learning - HDBSCAN Clustering
- Machine Learning - BIRCH Clustering
- Machine Learning - Affinity Propagation
- Machine Learning - Distribution-Based Clustering
- Machine Learning - Agglomerative Clustering
- Dimensionality Reduction In ML
- Machine Learning - Dimensionality Reduction
- Machine Learning - Feature Selection
- Machine Learning - Feature Extraction
- Machine Learning - Backward Elimination
- Machine Learning - Forward Feature Construction
- Machine Learning - High Correlation Filter
- Machine Learning - Low Variance Filter
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- Machine Learning - Discussion
Machine Learning - Standard Deviation
Standard deviation is a measure of the amount of variation or dispersion of a set of data values around their mean. In machine learning, it is an important statistical concept that is used to describe the spread or distribution of a dataset.
Standard deviation is calculated as the square root of the variance, which is the average of the squared differences from the mean. The formula for calculating standard deviation is as follows −
$$\sigma =\sqrt{\left [\Sigma \left ( x-\mu \right )^{2}/N \right ]}$$
Where −
$\sigma$is the standard deviation
$\Sigma$ is the sum of
$x$ is the data point
$\mu$ is the mean of the dataset
$N$ is the total number of data points
In machine learning, standard deviation is used to understand the variability of a dataset and to detect outliers. For example, in finance, standard deviation is used to measure the volatility of stock prices. In image processing, standard deviation can be used to detect image noise.
Types of Examples
Example 1
In this example, we will be using the NumPy library to calculate the standard deviation −
import numpy as np
data = np.array([1, 2, 3, 4, 5, 6])
std_dev = np.std(data)
print('Standard deviation:', std_dev)
Output
It will produce the following output −
Standard deviation: 1.707825127659933
Example 2
Let's see another example in which we will calculate the standard deviation of each column in Iris flower dataset using Python and Pandas library −
import pandas as pd
# load the iris dataset
iris_df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learningdatabases/iris/iris.data',
names=['sepal length', 'sepal width', 'petal length', 'petal width', 'class'])
# calculate the standard deviation of each column
std_devs = iris_df.std()
# print the standard deviations
print('Standard deviations:')
print(std_devs)
In this example, we load the Iris dataset from the UCI Machine Learning Repository using Pandas' read_csv() method. We then calculate the standard deviation of each column using the std() method of the Pandas dataframe. Finally, we print the standard deviations for each column.
Output
On executing the code, you will get the following output −
Standard deviations: sepal length 0.828066 sepal width 0.433594 petal length 1.764420 petal width 0.763161 dtype: float64
This example demonstrates how standard deviation can be used to understand the variability of a dataset. In this case, we can see that the standard deviation of the 'petal length' column is much higher than that of the other columns, which suggests that this feature may be more variable and potentially more informative for classification tasks.