Standard Deviation Calculator
Standard Deviation Calculator calculates the standard deviation of a given dataset from the mean. It helps us to know the dispersion of the given set of values with respect to the mean. The positive square root of the variance gives us the standard deviation.
What is a Standard Deviation Calculator?
Standard Deviation Calculator is an online tool that helps to calculate the variation of a given set of values from the mean. The standard deviation will be high if the data points are scattered away from the mean. To use this standard deviation calculator, enter values inside the bracket, separated by a comma.
Standard Deviation Calculator
How to Use Standard Deviation Calculator?
Please follow the steps to find the standard deviation for the given values using the online standard deviation calculator:
 Step 1: Go to Cuemath’s online standard deviation calculator.
 Step 2: Enter the numbers in the input box.
 Step 3: Click on the "Calculate" button to find the standard deviation.
 Step 4: Click on the "Reset" button to clear the fields and enter new values.
How Does Standard Deviation Calculator Work?
Standard deviation is commonly denoted as SD or σ, and it gives a measure of how much a data point has deviated from the mean value. The mean value or average of a given data is defined as the sum of all observations divided by the total number of observations. A low standard deviation tells us that the data point is closer to the mean. Similarly, a high standard deviation tells us that the data point is more spread out relative to the mean. Given below are the steps to calculate the standard deviation of a given data set.
 Determine the mean of the given value.
The mean is calculated using the formula:
Mean or Average(x) = (\(x_{1}\)+ \(x_{2}\) + \(x_{3}\)...+ \(x_{N}\)) / N, where n = total number of terms, \(x_{1}\), \(x_{2}\), \(x_{3}\), . . . , \(x_{N}\) = Different N terms.

We then subtract the mean from each data point.

The values obtained in step 2 are squared and then added.

This is further divided by (N  1). Here, N is the total number of terms.

Finally, the square root of the value obtained in step 4 is taken. This will be the standard deviation of the data set.
The formula for standard deviation is given as:
Standard deviation = √(∑(\(x_{i}\)  x)^{2} / (N  1)),
where \(x_{i}\) denotes individual values in the sample, x is the mean or an average of the sample, and N is the number of terms in the sample.
Solved Examples on Standard Deviation
Example 1: Find the standard deviation for the following set of data: {51,38,79,46,57} and verify it using the standard deviation calculator.
Solution:
Given N =5
Standard deviation = √(∑(\(x_{i}\)  x)^{2}/ (N  1))
Mean(x) = 51 + 38 + 79 + 46 + 57 / 5 = 54.2
Standard deviation = √[(51 − 54.2)^{2} + (38 − 54.2)^{2} + (79 − 54.2)^{2} + (46 − 54.2)^{2} + (57 − 54.2)^{2} / (5  1)
= 15.5
Therefore, the standard deviation is 15.5
Example 2: Find the standard deviation for the following set of data: {28,18,69,35,54}
Solution:
Given N = 5
Standard deviation = √(∑(\(x_{i}\)  x)^{2}/ (N  1))
Mean (x) = ( 28 + 18 + 69 + 35 + 54 ) / 5 = 40.8
Standard deviation = √(28  40.8)^{2} + (18  40.8)^{2} + (69  40.8)^{2} + (35  40.8)^{2} + (54  40.8)^{2} / (51)]
= 20.54
Therefore, the standard deviation is 20.54
Similarly, you can try the standard deviation calculator to find the standard deviation for the following:
 21,14,16,8,2,4,15,8
 25,1,7,15,6,14,14,25,7
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