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Standard Deviation Calculator for Population or Sample Data Sets

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Standard Deviation Calculator Sign
Standard Deviation Calculator

This calculator will calculate the mean, variance and standard deviation of an entered or pasted-in data set, plus convert the results into a step-by-step tutorial that shows you how to manually solve for the standard depreciation formula. The Learn tab includes answers to:

  • Don't let the formula scare you!
  • What is Standard Deviation?
  • Population vs Sample statistics.
  • Example problem showing 4 simple steps.

Learn More

Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Enter or paste data set:Enter or paste data set:Enter or paste data set:Enter or paste data set:

Data set:

Enter each element of the data set (or paste a copied data set) into this text box. Be sure each number is separated by a space, a comma, a line return, or any combination of the three. Also, if you wish to enter a frequency for each number, enter the number, followed by a lowercase x, followed by the multiplier (for 3 number twos, enter 2x3).

Elements:# of elements:Number of elements in set:Numbers of elements in set:

Number of elements in set:

This is the total number of elements detected in the data set field.

Sum:Sum of numbers:Sum of numbers:Sum of numbers:

Sum of numbers:

This is the sum of elements detected by the Standard Deviation Calculator.

Average:Average (mean):Average (mean):Average (mean):

Average (mean):

This is the average or mean of the items within the data set. This is calculated by summing the items within the set, and then dividing the sum by the number of items.

Population var:Population variance:Population variance:Population variance:

Population variance:

This is the variance of the data set (also called the Mean of Squared Differences) if the items entered represent the entire (population) data set.

Pop std dev:Population std dev:Population standard deviation:Population standard deviation:

Population standard deviation:

This is the population standard deviation, which is calculated by finding the square root of the population variance.

Sample var:Sample variance:Sample variance:Sample variance:

Sample variance:

This is the variance of the data set (also called the Mean of Squared Differences) if the items entered represent only a portion (sample) of the data.

Samp std dev:Sample std dev:Sample standard deviation:Sample standard deviation:

Sample standard deviation:

This is the sample standard deviation, which is calculated by finding the square root of the sample variance.

If you would like to save the current entries to the secure database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

Feedback AppreciatedFeedback Greatly AppreciatedYour Feedback Would Be Greatly AppreciatedYour Feedback Is Greatly Appreciated


Help and Tools

Help and Tools:

This section, which you can Unstick or Hide in the Calculator Preferences (just above the top of the calculator), contains the following tabs (content too long to fit within bordered frame can be scrolled up and down):

About: Click this tab for an introduction to the calculator.

Instructions: Click this tab for step-by-step instructions for using the calculator.

Terms: Click this tab for a list of the descriptions that are located within each popup help button (info icons).

PCalc: Click this tab for a handy "pocket" calculator you can use when you need to calculate an entry needed for the calculator.

Data: Click this tab to save a set of entries or a note in between visits. Entries and notes will be stored to your web browser's local storage (if supported by your browser of choice), meaning they can only be recalled with the same device and web browser you were using when you saved them. If you'd like to save entries and notes between devices you can do so by subscribing to the Ad-Free Member Version.



Add or remove this page to/from my favorites.

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.