Standard deviation calculator

The standard deviation calculator is a tool which can be used to calculate standard deviation of the data. The  standard deviation is calculated by taking square root of the variance. This calculator give accurate answer verified by statistics expert also provide steps for each output.

Standard Deviation Calculator



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How to Use the Standard Deviation Calculator

  1.   Enter the data value in the given designated field separated by comma or space i.e ( 1,2,3 or 1 2 3 )
  2.   Select which type of standard deviation required ( population or sample )
  3.   Click on the calculate button to get desired standard deviation
  4.   The calculator will display the standard deviation along with steps for easy understanding.

Formula for the standard deviation

Sample standard deviation :

\(\mathrm{s = \sqrt{\frac{\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}{n-1}}}\)

where:

  • s is the sample standard deviation
  • \(\mathrm{x_{i}}\) is a data point
  • \(\mathrm{\bar{x}}\) is the mean of the data set
  • n is the number of data points.   

Population standard deviation :

\(\mathrm{\sigma = \sqrt{\frac{\sum_{i=1}^{n}(x_{i}-\mu)^{2}}{n}}}\)

where:

    • \(\sigma\) is the population  standard deviation
    • \(\mathrm{x_{i}}\) is a data point
    • \(\mathrm{\mu}\) is the mean of the data set
    • n is the number of data points

What is standard deviation?

Standard deviation is a measure of how spread out a set of data is. It is calculated by taking the square root of the variance, which is the average of the squared deviations from the mean.

Why is standard deviation important?

The standard deviation is important because it can be used to compare the variability of different sets of data.

For example : 

If the two data set has a same mean but one set has higher standard deviation then the second set of data is more spread out.

what is the standard deviation of the data given below (Example)

A standard deviation calculator is a tool that can be used to calculate the standard deviation of a set of data.

T0 find sample standard deviation in our calculator follow below step

  1. Enter the given data into the input field (20, 12, 6, 7, 9)
  2. As the data is sample data so select sample option
  3. Click on calculate button
  4. The calculator will display the sample standard deviation along with steps

Frequently asked question ( Faqs)

how to calculate mean and standard deviation in excel ?

To calculate mean in excel use the below formula 

=AVERAGE(data) 

To calculate standard deviation in excel use the below formula 

For sample :

=STDEV.S(data)

For population :

=STDEV.P(data )

Note : Replace the data with your data separated by comma ( 1,2,3,4)

how to calculate variance from standard deviation in excel ?

To calculate variance from standard deviation in  excel simply twice the standard deviation 

For eg. if your standard deviation is 2 then your variance will be 2*2 = 4

can standard deviation be negative ?

No, standard deviation cannot be negative. because it is calculated by taking the square root of the variance. Variance is always non-negative, so the standard deviation must also be non-negative.

Disclaimer

This calculator provides results for educational and informational purposes only. Please validate the results and consult with a professional statistician for critical data analysis.