When should I pick Sample vs. Population?

Use Sample when your data is a subset of a larger group, and Population when it covers the entire group.

Why do the symbols change?

Statistics use σ and μ for populations and s and x̄ for samples, so the notation updates with your choice.

It's the square of the standard deviation — the average squared deviation from the mean.

How do I enter my data?

Type your numbers separated by commas or spaces; both work.

Online Advanced Deviation Calculator

Standard Deviation Calculator computes the standard deviation, variance, mean, count, and sum of squares for a data set, with a sample or population option.

Data Set

Comma separated numbers

Group

Result
Standard Deviation	s = 4.5
Variance	s² = 20.24
Count	n = 7
Mean	x̄ = 14.29
Sum of Squares	SS = 100

What Is This Tool?

This Standard Deviation Calculator measures how spread out a set of numbers is, for either a sample or a whole population. Enter your values separated by commas or spaces and choose Sample or Population: the sample option divides by n−1 and uses the symbols s, s², and x̄, while the population option divides by n and uses σ, σ², and μ. Along with the standard deviation it reports the variance, count, mean, and sum of squares. The result can be downloaded as a PDF.

How to Use This Tool?

Enter your numbers separated by commas or spaces.
Choose Sample or Population.
Click Calculate to see the statistics.
Download a PDF of the result if you'd like.

Key Features

Computes standard deviation for either a sample or a population.
Switches the divisor and notation between sample (s, x̄) and population (σ, μ).
Also reports variance, mean, count, and sum of squares.
Accepts numbers separated by commas or spaces.
Offers a one-click PDF download of the result.

Examples

The set 9, 11, 13, 13, 15, 16, 23 has a mean of 14.29.
As a sample, its standard deviation is about 4.5.
Its sample variance is about 20.24.
Choosing Population divides by n instead of n−1, lowering both figures slightly.

Common Use Cases

Measuring variability in a sample of data.
Calculating population standard deviation for a complete set.
Checking variance for statistics coursework.
Comparing the spread of two data sets.
Reporting summary statistics with the correct notation.

Tips & Best Practices

Choose Sample when your data is part of a larger group.
Choose Population when your data covers the whole group.
Enter every value and separate them consistently.
Note that the symbols change to match your selection.
Check the mean and count before trusting the result.

Limitations

Results depend entirely on the numbers you enter.
Non-numeric entries are ignored rather than flagged individually.
At least two values are required to compute a standard deviation.
Nothing is saved between sessions — only the current result can be exported as a PDF.

Frequently Asked Questions

When should I pick Sample vs. Population?: Use Sample when your data is a subset of a larger group, and Population when it covers the entire group.
Why do the symbols change?: Statistics use σ and μ for populations and s and x̄ for samples, so the notation updates with your choice.
What is variance?: It's the square of the standard deviation — the average squared deviation from the mean.
How do I enter my data?: Type your numbers separated by commas or spaces; both work.

Key Terminology

Standard deviation: A measure of how spread out the values in a data set are.
Variance: The square of the standard deviation; the average squared deviation from the mean.
Sample: A subset of a larger group; its standard deviation divides by n−1.
Population: The entire group of interest; its standard deviation divides by n.
Mean: The arithmetic average of all the values.

Quick Knowledge Check

What divisor does the sample option use?

n − 1

n + 1

Which symbol denotes population standard deviation?

x̄

Variance is the standard deviation…

squared

halved

doubled