Standard Deviation Calculator

Standard deviation tells you how much a dataset deviates from the mean value. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.

Calculate Standard Deviation:
Enter your data set below. Each number can be separated by a comma, space, or a new line break.

Standard Deviation:
Based on a sample


Standard Deviation:
Based on population


* Assumes a normal distribution of 50% to calculate your sample size

How to Calculate Standard Deviation?
The standard deviation is found by taking the square root of the average of the squared deviations of the values from their average value. We can use an example of 8 test scores from a class:

The above example can be condensed to the following formulas:

Population Standard Deviation

Sample Standard Deviation

How to Interpret Standard Deviation

Standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values. The standard deviation is a description of the data's spread, how widely it is distributed about the mean. A smaller standard deviation indicates that more of the data is clustered about the mean. A larger one indicates the data are more spread out.

Generally speaking data is normally distributed. This is important as it can be inferred that normally distributed data follows a bell shaped curve. That bell happened curve can tell us more about our data.

bell curve

The above graph shows the rules for normally distributed data. 68% of responses are within 1 deviation of the mean, 95% of responses are within 2 deviations of the mean, while 99.7% of the data is within 3 deviations of the mean.

Example: If a question asks for monthly income the mean could be $35,000 with a standard deviation of $5,000. We could assume that 68% of total responses fall somewhere between $30,000 and $40,000. We could also assume 95% of the data falls between $25,000 and $45,000. From this you can infer what people to target if your survey was looking what customers to sell to.

Survey Questions that Use Standard Deviation

Single text boxes with number, dollar, or percent validation - Useful to gather income, age, or numbers which require analysis.

Continuous Sum gives deviation for each label - Useful to gather budget data, time allocated to projects, or other numerical allocation questions requiring analysis.

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