Calculate standard deviation, variance, and statistical measures for your data set
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Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. A low standard deviation indicates that values tend to be close to the mean, while a high standard deviation indicates that values are spread out over a wider range.
Use when you have data for the entire population. Divides by n in the variance calculation.
Use when working with a sample from a larger population. Divides by n-1 (Bessel's correction) for an unbiased estimate.
Low Standard Deviation
Data points cluster closely around the mean
Medium Standard Deviation
Moderate spread of data around the mean
High Standard Deviation
Data points are widely dispersed from the mean
Measure investment risk and volatility. Higher standard deviation indicates higher risk.
Monitor manufacturing processes and product consistency. Lower values indicate better quality control.
Analyze experimental data and determine measurement precision and reliability.
Evaluate test score distributions and compare student performance across different groups.
The average of squared differences from the mean. Standard deviation is the square root of variance, making it easier to interpret as it's in the same units as the original data.
For normally distributed data: ~68% of values fall within 1 standard deviation of the mean, ~95% within 2 standard deviations, and ~99.7% within 3 standard deviations.
The ratio of standard deviation to the mean (CV = σ/μ), useful for comparing variability between datasets with different units or scales.
Calculate percentages and percentage changes
Calculate percentage increase
Calculate percentage decrease
Calculate percentage difference
Calculate with fractions
Calculate ratios and proportions