# 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:

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)

Try it Yourself »
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.