Standard Deviation

All statistics tools

Measure the dispersion or spread of your dataset.

Data Entry

Input Dataset

Calculation Type

Statistical Results

Standard Deviation15.8114

Mean30

Variance250

Sample Size (n)5

Sum of Squares1,000

Normal Distribution Curve

Visualized normal distribution based on calculated mean and standard deviation.

About this calculator

Overview

Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean. A low standard deviation indicates that the data points tend to be very close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.

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Pro Tips

Use 'Sample' when your data is a subset of a larger population.
Use 'Population' when you have data for every member of the group you are studying.
Standard deviation is sensitive to outliers; a single extreme value can significantly increase the result.

Fun Facts

"The 68-95-99.7 rule: In a normal distribution, about 68% of data falls within one SD of the mean, 95% within two, and 99.7% within three."
"The symbol for population standard deviation is the Greek letter sigma (σ), while sample standard deviation is often denoted by the letter 's'."
"Standard deviation is expressed in the same units as the data itself, whereas variance is expressed in squared units."

Formula: s = √[Σ(x-x̄)² / (n-1)]