Statistics How To

Variance and Standard Deviation Calculator

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This standard deviation calculator calculates the standard deviation and variance from a data set. This isn’t your ordinary variance and standard deviation calculator. Type in your numbers and you’ll be given: the variance, the standard deviation, plus you’ll also be able to see your answer step-by-step below.

Data set:


Results

  • Variance:
  • Standard Deviation:
Explanation

  1. First, I added up all of the numbers:
  2. I squared the total, and then divided the number of items in the data set
  3. I took my set of original numbers from step 1, squared them individually this time, and added them all up:
  4. I subtracted the amount in step 2 from the amount in step 3:
  5. I subtracted 1 from the number of items in my data set:
  6. I divided the number in step 4 by the number in step 5:
  7. Finally, I took the square root of the number from step 6 (called the Variance),

variance and standard deviation calculator

Standard deviations are a unit of measurement; they measure how spread out your data is around the mean. The bulk of data (68%) lies within one standard deviation from the mean.

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Variance and Standard Deviation Calculator was last modified: June 20th, 2017 by Stephanie

24 thoughts on “Variance and Standard Deviation Calculator

  1. SS

    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 :(

  2. Sheila

    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.

  3. Tim

    How do I make a graph like the one shown in the photo above? and how do I make a bar graph with error bars to go with it?

  4. Aravind

    Hi Stephanie,

    Thanks in advance.

    I am confused in understanding the biased/unbiased estimator, Can you please share me any link/information on how, dividing by n − 1 instead of n/n+1 makes the sample variance unbiased estimator.

  5. Andale

    It’s a fact that when you divide by n-1, the mean of all sample variance equals the population variance. If you divided by n, then that isn’t true. Does this page help?

  6. Aravind

    Thanks Andale,

    Yeah this page helped me a lot. I have understood the basic concept’s from here.
    Actually i am looking for the derivation of that fact, divide by n-1 making the mean of all sample variance equals the population variance. Because for both of them the distributions will be different.
    Can you help me on this.

  7. Tymillion

    why do we subtracted -1 from the step 5 pls can you please explain…………………. and also if we have data set as: 3,4,5,6,7,8 are we going to say 6-3=3 ….. or everything is going to be minus -1 like this: 6-1=5

    pls help!

  8. daichi

    i have an estimation for a project with different accuracies.
    for example Piping @ + or – 30 % , Equipment at + or – 15 % , Civil At + or – 10 % , Installation cost + or – 40 % , Electrical + or – 15 % ,

    Now how do i make the total mean Variation for the whole project.
    can any one help. ?

  9. Paul ababa

    Please how can we subtract 1 from the number of set data ??..i need an explanation.

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