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# Standard deviation calculator

This calculator finds the 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 ↓↓
 This is a Sample Whole population
 Standard Deviation (default) Variance Skewness Kurtosis

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examples
example 1:ex 1:
Find the standard deviation for the given set of numbers: $3,~ 4,~ 11,~ 21,~ 23,~ 4,~ 5$.
example 2:ex 2:
Find the variance of the following test results percentages: $73\%,~ 58\%,~ 67\%,~ 92\%,~ 73\%,~ 55\%,~ 85\%, ~54\%$.
example 3:ex 3:
Find the skewness for the following data set: $8, ~6, ~7, ~10, ~14, ~20, ~25, ~30, ~50, ~53$.
example 4:ex 4:
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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