Standard Deviation Calculator

Enter the comma separated values in the box to find standard deviation using standard deviation calculator.

RESULT
Count	Sum	Mean
0	0	0
Sum of Differences²
0
POPULATION
Standard Deviation	Variance
0	0
SAMPLE
Standard Deviation	Variance
0	0
Differences Every Number minus the Mean	Differences² Square of each difference
0	0

Finding standard deviation was never so simple, thanks to the sample standard deviation calculator. The calculations offered by sample mean calculator are:

Sample Variance
Sample Standard Deviation
Population Variance
Population Standard Deviation
Differences, and
Square of Differences

Let’s explore a few key points such as standard deviation definition, how to find standard deviation without using relative standard deviation calculator, and standard deviation equation.

What is standard deviation?

A measure of extent to which numbers are spread out.

Standard Deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. It is denoted by the Greek symbol sigma σ.

Below, you can find the plot of normal distribution with width of 1 band.

Standard Deviation Formula

Standard deviation formula can be expressed by taking the square root of the variance.

Sample Standard Deviation Formula

s refers to sample standard deviation
N is the number of observations
x_i is the observed values of sample item, and
x̄ is the mean value of the sample

Population Standard Deviation Formula

σ refers to population standard deviation
N is the size of population
x_i is the observed values from population, and
μ is population mean

How To Calculate Standard Deviation?

Standard Deviation Calculation can be carried out using mean and standard deviation calculator above. However, we will explain the method to calculate SD with an example

Example:

Find the standard deviation of the given sample:
$30, 20, 28, 24, 11, 17$

Step 1: Calculate the mean value of sample data:

$N = 6$

$\frac{∑X}{N} = \frac{(30+20+28+24+11+17)}{6} = \frac{130}{6} = 21.67$

Step 2: Calculate $(x i - x̄)$ by subtracting mean value from each value of data set.

$x 1 - x̅ = 30 - 21.67 = 8.33$

$x 2 - x̅ = 20 - 21.67 = -1.67$

$x 3 - x̅ = 28 - 21.67 = 6.33$

$x 4 - x̅ = 24 - 21.67 = 2.33$

$x 5 - x̅ = 11 - 21.67 = -10.67$

$x 6 - x̅ = 17 - 21.67 = -4.67$

Step 3: Now, take the square of $(x i - x̄)$ for each value to find $(x i - x̄) 2$ .

$(x 1 - x̅) 2 = 8.33 2 = 69.4$

$(x 2 - x̅) 2 = -1.67 2 = 2.78$

$(x 3 - x̅) 2 = 6.33 2 = 40$

$(x 4 - x̅) 2 = 2.33 2 = 5.43$

$(x 5 - x̅) 2 = -10.67 2 = 113.85$

$(x 6 - x̅) 2 = -4.67 2 = 21.80$

Step 4: Get the sum of all values for $(x i - x̄) 2$ .

$(x i - x̅) 2$
$69.4$
$2.78$
$40$
$5.43$
$113.85$
$21.80$
$\sum (x i - x̅) 2 = 253.26$

Step 5: Divide $\sum (x i - x̅) 2$ with $(N-1)$ .

$\frac{∑(x_i - \overline x)^2 }{N - 1} = \frac{253.26}{5} = 50.65$

Variance = $50.65$

Step 6: Take the square root of $\frac{∑(x_i - \overline x)^2 }{N - 1}$ to get the standard deviation.

$\sqrt{\frac{∑(x_i - \overline x)^2 }{N}} = \frac{(30+20+28+24+11+17)}{6} = \frac{130}{6} = 21.67$

$s = 7.11$

Use the population standard deviation calculator above to cross-check the values for SD calculations.

Standarddeviationcalculator.io is a free calculator website that finds the standard deviation of an entered set of data. Using this online calculator, you can find the variance, Standard Deviation, Differences, Sum, and Square of Differences

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