Functions > Statistics > Descriptive Statistics > Example: Variance and Standard Deviation
Example: Variance and Standard Deviation
Use the Var and Stdev functions to compare the spread of a Weibull and a normal distribution.
1. Define data sets following a Weibull and a normal distribution.
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2. Plot the distributions.
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The two data sets have different spreads and shapes, even though they have similar means:
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3. Calculate the sample variance of the distributions.
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The smaller variance of the Weibull distribution indicates that it is less spread than the normal distribution.
The sample variance is calculated as follows:
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4. Calculate the sample standard deviation of the Weibull distribution.
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The standard deviation has the same units as those of the original data, making it a slightly more intuitive measure of the dispersion than the variance. It can be considered a measure of the error in a series of measurements that should really be identical.
The sample standard deviation is the square root of the sample variance:
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5. Calculate the population variance and standard deviations for the Weibull distribution:
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The population variance and standard deviation are divided by the sample size, and not by the sample size minus one:
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The sample variance, or function Var, is the more commonly used definition in quantitative data analysis.
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