This standard deviation calculator calculates the standard deviation and variance from a data set. In addition, you’ll also be able to see your answer step-by-step below.

Data set:

**Results**

- Variance:
- Standard Deviation:

**Explanation**

- First, I summed all the numbers:

- I squared the sum, and divided the number of items in the data set
- I took my set of original numbers from step 1, squared them individually this time, and added them all up:

- I subtracted the amount in step 2 from the amount in step 3:

- I subtracted 1 from the number of items in my data set:

- I divided the number in step 4 by the number in step 5:

- Finally, I took the square root of the number from step 6 (called the Variance),

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Very helpful to me.

I love whoever designed this website and this calculator. It’s more useful than going to class.

Awesome – love the step by step instructions! Thank you

what happens when the value in step 4 is negative?

11.00 7.50 8.50 10.00 10.00 10.50 5.50 10.00 9.00 9.50 5.25 8.00

Could you solve for above 12 numbers please? I tried and could not :(

Variance: 3.4938446969696937

Standard Deviation: 1.8691828955374308

I’d check your math. Variances can’t be negative.

Super-helpful calculator, especially with the step-by-step instructions!

Very helpful calculator, especially with the step-by-step instructions!

Can you please give me the formula for this calculation? I want to see what it looks like, in order to follow it with the above calculations.

Sure! See: for the formula.