Standard Deviation Calculator

Standard deviation is the most widely used measure of statistical dispersion, quantifying how spread out data points are from the mean.

Population vs. Sample Standard Deviation:

• Population standard deviation (sigma): Used when your data set includes the entire population. Variance = Sum of squared deviations / N.
• Sample standard deviation (s): Used when your data is a sample from a larger population. Variance = Sum of squared deviations / (N - 1). The N-1 denominator (Bessel's correction) provides an unbiased estimate of the population variance.

Step-by-Step Calculation:

1. Calculate the mean (average) of the data set.
2. Subtract the mean from each value to get the deviation.
3. Square each deviation.
4. Sum all the squared deviations.
5. Divide by N (population) or N-1 (sample) to get the variance.
6. Take the square root of the variance to get the standard deviation.

Coefficient of Variation (CV):

The CV is the standard deviation expressed as a percentage of the mean: CV = (SD / |Mean|) x 100%. It allows comparison of variability between data sets with different units or scales.

Interpreting Standard Deviation:

For a normal distribution, approximately 68% of data falls within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs (the 68-95-99.7 rule, or empirical rule).