Measures of Dispersion for Ungrouped Data
Enter raw numerical data. This tool computes the range, variance, and standard deviation for an ungrouped data set, treating the values either as a sample or as a population.
Measures of Dispersion for Ungrouped Data
Statistics • Numerical Descriptive Measures
Frequently Asked Questions
What measures of dispersion does this calculator compute?
It computes the range, variance, and standard deviation for an ungrouped (raw) numerical data set. You can also view a deviation table and a step-by-step explanation of the calculations.
What is the difference between sample variance and population variance?
Population variance divides by N, the number of population values. Sample variance divides by n - 1 to correct for bias when estimating population variance from a sample.
How is the range calculated for ungrouped data?
Range is computed as largest value - smallest value. It is simple but very sensitive to outliers because it depends only on the extremes.
How are variance and standard deviation related?
Standard deviation is the positive square root of variance. Variance is measured in squared units, while standard deviation is in the same units as the original data.
Why can the standard deviation change a lot when there are outliers?
Variance uses squared deviations from the mean, so large deviations receive much more weight than small ones. Outliers therefore increase the variance and standard deviation substantially.