# Standard Deviation

A standard deviation is a statistic that measures the dispersion of a dataset relative to its mean.

Symbol of standard deviation is σ (the Greek letter Sigma)

`Standard Deviation is also calculated as the square root of the Variance. What is variance and how to calculate it? Check HERE`

It is calculated as the square root of variance by determining each data point’s deviation relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set. Thus, the more spread out the data, the higher the standard deviation.

To calculate the standard deviation follow these steps:

• Step 1: Find the Mean (the simple average of the numbers)
• Step 2: Subtract the Mean from each number
• Step 3: Square the Result (the squared difference) and take sum
• Step 4: Take the average of squared differences.
• Above 4 steps are similar, for both variance and standard deviation.
• Step 5: Take square root of Variance.

## Example

Data = 8, 9, 10, 11, 12

• Step 1: Find the Mean (the simple average of the numbers)
• Mean: (8 + 9 + 10 + 11 + 12) ÷ 5 = 10
• Step 2: Subtract the Mean from each number
• Step 3: Square each deviation from the mean and take sum
• (-2)2 + (1)2 + (0)2 + (1)2 + (2)2 = 10
• Step 4: Divide the sum of squares by n – 1 or N
• Divide the sum of the squares by n – 1 (for a sample) or N (for a population).
• Since we’re working with a sample, we’ll use  n – 1, where n = 5.
• 10/(5-1) = 2.5
• Step 5: Take square root of Variance.
• √ 2.5 = 1.58

## Drawback

The biggest drawback of using standard deviation is that it can be impacted by outliers and extreme values. Standard deviation assumes a normal distribution and calculates all uncertainty as risk, even when it’s in the investor’s favor—such as above-average returns.

## Code

Starting Python 3.4, the standard library comes with the stdev function (sample std. dev or std. dev n-1) as part of the statistics module:

``````# Python code
# stdev() function of Statistics Module

# Import statistics module
import statistics

# Creating a sample of data
sample = [8, 9, 10, 11, 12]

# Print Standard Deviation of the sample set
print(f"Standard Deviation of sample set is {statistics.stdev(sample)}")
``````
`Standard Deviation of sample set is 1.58`

The population std. dev (or std. dev n) can be obtained using the pstdev function:

``````# Python code
# pstdev() function of Statistics Module

# Import statistics module
import statistics

# Creating a sample of data
population = [8, 9, 10, 11, 12]

# Print Standard Deviation of the sample set
print(f"Standard Deviation of population set is {statistics.pstdev(population)}")``````
`Standard Deviation of population set is 1.41`

Univariate Analysis

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