Standard deviation

Do you need calculate the standard deviation of a data set? With our calculator you can obtain the standard deviation by simply typing each figure, separated by a space or a comma. If you are entering decimal numbers, use the period '.' as decimal separator.

When you have typed in all the numbers, click the calculate button and you will automatically get the deviation value as well as other statistical measures such as variance or mean.

What is standard deviation

The standard deviation is a measure of dispersion that is a measure of shows the deviation of the distribution data compared to its arithmetic mean..

This helps us to have a more realistic view of the data. to interpret them correctly, something that positively benefits decision making.

The standard deviation is widely used to see how far the data deviate from the mean of the distribution.

The standard deviation can also be defined as the square root of the variance.

Standard deviation formula

For calculate the standard deviation the following mathematical formula must be applied:

Standard deviation formula

How to calculate the standard deviation step by step

If you do not fully understand how to apply the standard deviation formulaIn this section you will find a step-by-step explanation of how to calculate it. You only have to follow the next steps:

  1. Calculate the arithmetic mean of the numbers in the set
  2. Subtract the average obtained from each number and square the result.
  3. Obtain the average of the previous results
  4. Take the square root of the resulting number

For the sake of clarity, let's take a look at a solved exercise on standard deviation.

Example of standard deviation

Let's calculate the standard deviation of the set of numbers [1, 3, 5, 7, 9].

To do this, we follow the steps seen in the previous point, so the first thing to do is to calculate its average value:

(1 + 3 + 5 + 7 + 9) / 5 = 25 / 5 = 5

Then we subtract the value of the previous average from each number in the set. Then we square it:

(1 – 5)2 = 16

(3 – 5)2 = 4

(5 – 5)2 = 0

(7 – 5)2 = 4

(9 – 5)2 = 16

The next step is to find the average of the previous values:

(16 + 4 + 0 + 4 + 16) / 5 = 8

Finally, we take the square root of the obtained value:

√8 = 2,828

With this we are done.

Standard deviation symbol

Standard deviation symbol

The standard deviation is usually represented by a letter s or with the symbol σ.

Calculate standard deviation in Excel

To calculate the standard deviation in Excel there is a function that does the operation automatically.

To do this, just open the Microsoft spreadsheet program and write each number of the set in a separate cell. For example, let's imagine that we have a set consisting of 10 values that occupies the cell range A1:A10.

To calculate the standard deviation in Excel we write the following formula:


Logically, you will have to adapt the range of cells of the formula to your spreadsheet to cover the cells in which you have written the data of the set.

It is important to note that the above formula is used to calculate the population standard deviation. If you want to calculate the sample standard deviation, then you must write this other formula:


Sample standard deviation

The sample standard deviation is used when it is assumed that the aggregate data are only a sample of the total population..

In this case, the mathematical formula we use is this:

Sample standard deviation formula

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