How to Calculate Standard Deviation

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The standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a data set. It tells you how much individual values deviate from the mean (average) of the data.

Steps to Calculate Standard Deviation

1. Find the Mean: Add all the values in the dataset and divide by the total number of values in the dataset.
2. Calculate Deviations: Subtract the mean from each individual value in the dataset to find the deviations.
3. Square the Deviations: Square each deviation to eliminate negative values.
4. Find the Mean of Squared Deviations: Add all the squared deviations together and divide by the total number of values.
5. Calculate the Standard Deviation: Take the square root of the mean obtained in the previous step to obtain the standard deviation.

Standard Deviation Formula

The formula for calculating standard deviation is as follows:

σ = √(Σ(xi - μ)² / N)

• σ: Standard deviation
• Σ: Sum of the values
• xi: Each individual data point
• μ: Mean of the dataset
• N: Total number of values in the dataset

Importance of Standard Deviation

Standard deviation is widely used in statistics and data analysis to measure how spread out data values are. A small standard deviation indicates that most values are close to the mean, while a large standard deviation shows greater variability in the data.

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