Standard Deviation Calculator
Calculate the standard deviation and mean of your data set to understand its variability.
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Table of Contents
Standard Deviation Formula
Standard deviation is a measure of the amount of variation or dispersion in a data set. It tells you how spread out the numbers are from their average value.
Where:
- σ is the standard deviation
- Σ is the sum of
- x is each value in the data set
- μ is the mean of the data set
- n is the number of values
How to Calculate Standard Deviation
To calculate standard deviation, follow these steps:
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1Calculate the mean (average) of the data set
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2Subtract the mean from each value and square the result
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3Calculate the mean of these squared differences
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4Take the square root of the result
Interpreting Standard Deviation
Understanding what the standard deviation tells you about your data:
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1Small Standard Deviation:
Indicates that the data points are close to the mean, showing little variation.
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2Large Standard Deviation:
Indicates that the data points are spread out over a wider range of values.
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3Zero Standard Deviation:
Indicates that all values in the data set are identical.
Practical Examples
Example 1 Test Scores
A class of students has test scores: 85, 87, 89, 91, 93
Mean = 89
Standard Deviation = 3.16
This small standard deviation indicates that the scores are clustered close to the mean.
Example 2 Stock Prices
Daily stock prices over a week: $100, $120, $90, $130, $110
Mean = $110
Standard Deviation = 15.81
This larger standard deviation shows significant price volatility.
Example 3 Temperature Readings
Daily temperatures: 20°C, 20°C, 20°C, 20°C, 20°C
Mean = 20°C
Standard Deviation = 0
Zero standard deviation indicates constant temperature.