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