# Data Science - Statistics Standard Deviation

## Standard Deviation

Standard deviation is a number that describes how spread out the observations are.

A mathematical function will have difficulties in predicting precise values, if the observations are "spread". Standard deviation is a measure of uncertainty.

A low standard deviation means that most of the numbers are close to the mean (average) value.

A high standard deviation means that the values are spread out over a wider range.

Tip: Standard Deviation is often represented by the symbol Sigma: σ

We can use the `std()` function from Numpy to find the standard deviation of a variable:

### Example

import numpy as np

std = np.std(full_health_data)
print(std)
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The output:

What does these numbers mean?

## Coefficient of Variation

The coefficient of variation is used to get an idea of how large the standard deviation is.

Mathematically, the coefficient of variation is defined as:

Coefficient of Variation = Standard Deviation / Mean

We can do this in Python if we proceed with the following code:

### Example

import numpy as np

cv = np.std(full_health_data) / np.mean(full_health_data)
print(cv)
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The output:

We see that the variables Duration, Calorie_Burnage and Hours_Work has a high Standard Deviation compared to Max_Pulse, Average_Pulse and Hours_Sleep.

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