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Standard deviation calculator

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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.

Standard Deviation Calculator
+ variance, skewness and kurtosis
help ↓↓ examples ↓↓ tutorial ↓↓
This is a Sample Whole population
Standard Deviation (default) Variance
Skewness Kurtosis
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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.

What a is standard deviation?

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.

How to calculate the standard deviation?

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.

$$ \sigma = \sqrt{ \frac{ \sum{\left(x - X\right)} }{ n } } = \sqrt{ \frac{14}{4}} = 1.8708 $$
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