Standard Deviation Calculator

Video guide Information Average calculator Mean Median Mode Q1/Q3/IQR calculator

Step by step calculation.

When entering data, press comma , space or Enter after each value.
Leaving empty cells is okay. The tool doesn't count empty cells or non-numeric cells.
You may use more than one variable.

Dartboard

Following a visual example of standard deviation calculation. More details
The middle of the cycle symbolizes the average. The radius represents the absolute deviation from the average: |𝑥i-x̄|.
Orange circle: each circle represent one value. (r = |value-average|, area = π r2).
Green circle: has the average area of all the orange circles. The standard deviation is the radius of the Green dartboard.

Information

Target: Calculate average, standard deviation, the sample size for several variables. Present histogram chart and average range chart
As you may see in the Sum of squares chart,The outliers may influence dramatically the standard deviation result! as you may see in the sum of squares chart. It is not recommended to exclude outliers unless you know the reason for the outliers.

Statistics

n - Number of values.
Mean- The average.
σ- Population standard deviation, the standard deviation equation is based on the entire population, this is the exact standard deviation.
Variance- Population Variance, if the list of values you entered is the entire population, this is the exact variance.
S- Sample standard deviation, if the list of values you entered is only a sample from the entire population, this is the best estimation for the population standard deviation. The sample standard deviation equation is similar to the population standard deviation equation, but the denominator is n-1 instead of n.
S2- Sample variance, if the list of values you entered is only a sample from the entire population, this is the best estimation for the Population Variance.
MAD- Mean Absolute Deviation, the average of the deviations from the average. For each observation you calculate the distance from the average, MAD is the average of these distances.

Why do we use the standard deviation instead of the MAD?

Formulas

Variance formula
Variance=σ2

Standard deviation formula and sample standard deviation formula
standard deviation formula, sample standard deviation formula

R Code

The following R code should produce the same results except for the skewness. The 'PerformanceAnalytics' package uses a different methods for skewness calculations.