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- Standard Deviation

This calculator computes standard deviation, variance, skewness and kurtosis of the given dataset. The calculator shows a step-by-step explanation on how to find these statistics.

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Examples

ex 1:

Find the standard deviation for the given set of numbers:
3, 4, 11, 21, 23, 4, 5.

ex 2:

Find the variance of the following test results percentages:
73%, 58%, 67%, 92%, 73%, 55%, 85%, 54%.

ex 3:

Find the skewness for the following data set:
8, 6, 7, 10, 14, 20, 25, 30, 50, 53.

ex 1:

Calculate standard deviation of: -4, 3.2, 7, 6.1, 2, 8.

Related calculators

**Definition: **The standard deviation measures how close the set of data is to the mean value of the
data set.
If the dataset has a high standard deviation, the values are widely distributed.
If the dataset has a low standard deviation, the data points are quite near to the mean.

We will show how to find the standard deviation using a simple dataset. Take, for example, 1, 4, 5, 6. The process can be separated into four steps.

**Step 1:** Find the mean of the dataset:

X = (1 + 4 + 5 + 6)/4 = 16/4 = 4

**Step 2:** Find the square of the difference between the mean and each data point:

(1 - 4)^{2} = 9

(4 - 4)^{2} = 0

(5 - 4)^{2} = 1

(6 - 4)^{2} = 4

**Step 3: Sum all squares**

9 + 0 + 1 + 4 = 14

**Step 4:** Apply the standard deviation formula.

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