Variance and standard deviation calculator
Calculator finds out variance and standard deviation from the list of numbers.

Beta version

BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
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Settings

popular sets (click to use):decimal,octal,hexadecimal
Show detailed settings:

Enter your numbers here

Data summary

How many numbers detected3
Detected numbers2, 10, 3.3
Numbers base10 (decimal)
Skipped charactersnone

Results - variance and standard deviation

Variance12.28666666666666666667
Standard deviation3.50523418143020319753

What else can we calculate about your numbers

The numbers sorted in ascending order2, 3.3, 10
The numbers sorted in descending order10, 3.3, 2
Minimal number2
Maximal number10
Sum15.3
Average5.1
Median3.3
Numbers used to compute median2, 3.3, 10
Numbers in words (digit by digit)
  • two (2)
  • one zero (10)
  • three point three (3.3)
Numbers in words (whole number at once)
  • two (2)
  • ten (10)
  • three and three tenths (3.3)

Some facts

  • Measuring variation is commonly used statistical concept. There are various types of variation measures. Simply speaking, if values are more diverse and deviate from the average, the more variation we assign to data set. In particular, if all values in the set are identical, then we will say that there is no variability at all. One of the most popular measures of variation is variance:
    σ2=(x1x)2+(x2x)2++(xnx)2n\sigma^2 = \frac{(x_1 - \overline{x})^2 + (x_2 - \overline{x})^2 + \cdots + (x_n - \overline{x})^2}{n}
    where:
    • σ2\sigma^2 - variance,
    • x\overline{x} - arithmetic mean (the sum of a collection of numbers divided by the count of numbers in the collection),
    • x1x_1 - the first number in the collection,
    • x2x_2 - the second number in the collection,
    • xnx_n - the n-th number in the collection,
    • n - count of numbers in the collection.
  • Other popular measure of variation is standard deviation defined as below:
    σ=(x1x)2+(x2x)2++(xnx)2n\sigma = \sqrt{\frac{(x_1 - \overline{x})^2 + (x_2 - \overline{x})^2 + \cdots + (x_n - \overline{x})^2}{n}}
    where:
    • σ\sigma - standard deviation,
    • x\overline{x} - arithmetic mean (the sum of a collection of numbers divided by the count of numbers in the collection),
    • x1x_1 - the first number in the collection,
    • x2x_2 - the second number in the collection,
    • xnx_n - the n-th number in the collection,
    • n - count of numbers in the collection.
  • We can calculate standard deviation from variance and vice versa. So these are two different measures of the same quantity, which we can use depending on the needs:
    variance=Var=σ2\text{variance} = \text{Var} = \sigma^2
    σ=variance=Var\sigma = \sqrt{\text{variance}} = \sqrt{\text{Var}}
  • In the case of measurement data or data spread over time, the variation measures can be equated with uncertainty or treated as risk factor. For example, the purchase of shares of companies, for which the standard deviation is high, is more risky than other ones. In practice, this means that the share price of such a company is more susceptible to fluctuations. Colloquially, we will say that the share price of such a company is less predictable.
  • ⓘ Hint: Are you looking for statistical calculators? See also:

What is the meaning of each calculator field ?

  • Enter your numbers here - enter numbers, which you're going to use to calculate variance and standard deviation.
  • You can use almost any format you want, numbers can be separated by spaces, commas, semicolons, dashes, end of lines (enters) etc. - it's up to you and your needs.
    More, you can even paste a long text - even lyrics - as long as it contains some numbers. The numbers will be automatically detected, "trapped" and added together.

  • cipher manipulation
    • fill with zeros up to XX ciphers after comma - append zeros at the end of the number, if this number does not have enough digits after the decimal point. For example, if you set here 3, it will show number 15 as 15.000, and the number 15.55 as 15.550.
      A good example of use case is counting the money (accounting), where we have dollars and cents or euros and eurocents. Just type 2 here, and the calculator will supply always two digits after the decimal pennies.
    • consider only XX ciphers after the comma - simply cut the number (of the least accurate part), if the number of digits after the decimal point is greater than desired. For example, to show only decimal, enter here 1. For hundredths enter 2.
  • input parser
    • decimal separators - a list of characters that should be interpreted as decimal separators (colloquially "dot" or "comma" between integer and fraction parts). For example, if you want to treat 1.25 as "one and twenty-five hundredths," you should put comma character here (",").
    • ignored characters - a list of characters that should be ignored while splitting input text into separated numbers. For example, if you want to treat "100 000" as "one hundred thousand", you should put space character here (" "). Similarly, if you have list of hexadecimal numbers in 0x1234 format, you can ignore "x" character, to process them correctly.
  • computer related
    • number base - This calculator works for the number systems based on any base from 2 to 36. It supports the typical systems as decimal, hexadecimal, octal and binary.
      It also allows for calculation of exotic systems (eg. with base 17), up to the base of 36. The order of the characters is consistent with the English alphabet, so starts with 'a', ends with 'z'. 26 letters plus 10 digits gives max base of 36. Of course both upper case and lower case are allowed - input is case insensitive.

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