Calculate Standard Deviation from Mean and N
Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of values. Calculating standard deviation from the mean and sample size (n) is crucial in understanding the spread of data around the mean.
- Enter the mean (average) of your data set.
- Enter the sample size (n), which is the total number of values in your data set.
- Enter each data point in the ‘Data’ textarea, separated by commas.
- Click ‘Calculate’ to see the standard deviation and a visual representation of your data.
The formula to calculate standard deviation (σ) from mean (μ) and sample size (n) is:
σ = √[(∑(xi - μ)²) / (n - 1)]
Where:
xiis each data point in the set.μis the mean of the data set.nis the sample size.
| Method | Formula | Advantages | Disadvantages |
|---|---|---|---|
| Population Standard Deviation | σ = √[(∑(xi - μ)²) / n] |
Used when the entire population is available. | Not suitable for sample data. |
| Sample Standard Deviation | σ = √[(∑(xi - μ)²) / (n - 1)] |
Used when only a sample of the population is available. | Underestimates the population standard deviation. |
- Always use the correct formula based on whether you’re working with a population or a sample.
- Be cautious when interpreting standard deviation. It’s sensitive to outliers and may not be the best measure of dispersion for all data sets.
- Consider using other measures of dispersion, such as range, interquartile range, or variance, depending on your data and research question.
What is the difference between population and sample standard deviation?
Population standard deviation is used when the entire population is available, while sample standard deviation is used when only a sample of the population is available. The formulas differ in the denominator: n for population and n – 1 for sample.
How does standard deviation relate to variance?
Standard deviation is the square root of variance. Variance measures the average of the squared differences from the mean, while standard deviation measures the square root of that average.
Learn more about standard deviation from Stats NZ
Khan Academy’s guide to standard deviation