How to Find Standard Deviation: A Step-by-Step Guide

If you’re dealing with a set of data and you want to measure the amount of variation or dispersion within that data, then you’ll want to learn how to find the standard deviation. This statistical concept is essential for fields ranging from finance to healthcare, and it can help you analyze your data and make informed decisions based on your findings. In this article, we’ll break down the process of finding standard deviation into clear, easy-to-follow steps.

Step 1: Find the Mean

Mean CalculatorSource:

The first step in finding standard deviation is to calculate the mean, or average, of your data set. To do this, add up all the values in your data set and divide by the number of values. For example, if you have the data set {2, 4, 6, 8, 10}, the mean would be (2+4+6+8+10)/5 = 6.

Step 2: Subtract the Mean from Each Data Point

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Next, subtract the mean from each data point. This will give you a new set of numbers that represent how far each value is from the mean. For example, if your data set is {2, 4, 6, 8, 10} and the mean is 6, you would subtract 6 from each value to get {-4, -2, 0, 2, 4}.

Step 3: Square the Differences

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Now, square each of the differences you calculated in step 2. This is because we want to measure the absolute value of these differences, and squaring them ensures that they are all positive. For example, if your differences are {-4, -2, 0, 2, 4}, squaring them would give you {16, 4, 0, 4, 16}.

Step 4: Find the Mean of the Squared Differences

Mean CalculatorSource:

The next step is to find the mean of the squared differences. To do this, add up all the squared differences and divide by the number of values. For example, if your squared differences are {16, 4, 0, 4, 16}, the mean would be (16+4+0+4+16)/5 = 8.

Step 5: Take the Square Root

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Finally, take the square root of the mean of the squared differences to find the standard deviation. For example, if the mean of the squared differences is 8, the standard deviation would be the square root of 8, which is approximately 2.83.

Additional Tips


Now that you know the basic steps for finding standard deviation, here are a few additional tips to keep in mind:

  • The formula for finding standard deviation is often represented as σ (sigma) for a population or s for a sample.
  • Standard deviation can be used to identify outliers in your data set. An outlier is a value that is significantly different from the other values in the set.
  • If your data set is very large, it may be more efficient to use a calculator or statistical software to find the standard deviation.


Now that you’ve learned how to find standard deviation, you can start using this powerful statistical tool to analyze your data and make informed decisions. Remember to follow each step carefully and use additional resources if needed. With practice, you’ll soon be able to calculate standard deviation with ease.

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