Data Science – Statistics: Standard Deviation

Standard Deviation is a number that describes how spread out the observations are in a dataset. In other words, it measures the variability or uncertainty of a dataset.

What is Standard Deviation?

If the observations in a dataset are close to the mean (average), the standard deviation will be low. However, if the values are spread out over a wider range, the standard deviation will be high. A high standard deviation indicates greater uncertainty in the data, while a low standard deviation shows that the data is more consistent.

Tip: Standard deviation is often represented by the symbol Sigma: σ.

Calculating Standard Deviation Using Python

You can easily calculate the standard deviation of a variable in Python using the std() function from the NumPy library. Here’s an example:

import numpy as np

# Calculate the standard deviation of the full health dataset
std = np.std(full_health_data)

# Print the result
print(std)

The output will give you the standard deviation for the dataset, which shows how spread out the values are.

What Does the Standard Deviation Mean?

When you calculate the standard deviation, the result gives you a sense of the variability in your dataset. For example:

• A low standard deviation means that the values in the dataset are close to the mean.
• A high standard deviation indicates that the values are spread out across a larger range.

Coefficient of Variation

The Coefficient of Variation is another measure that helps you understand the relative size of the standard deviation in relation to the mean. It is calculated as:

Coefficient of Variation (CV) = Standard Deviation / Mean

You can calculate the coefficient of variation in Python using the following code:

import numpy as np

# Calculate the coefficient of variation
cv = np.std(full_health_data) / np.mean(full_health_data)

# Print the result
print(cv)

The output will give you the coefficient of variation, which can help compare the spread of different datasets.

Understanding the Output

In the example above, we compare the standard deviation for different variables in the dataset. For instance:

• The variables Duration, Calorie_Burnage, and Hours_Work may show a high standard deviation, indicating a greater range of values.
• On the other hand, Max_Pulse, Average_Pulse, and Hours_Sleep might have lower standard deviations, indicating a more consistent dataset.

Conclusion

Understanding the standard deviation and coefficient of variation helps you assess the variability and uncertainty of your dataset. By knowing how spread out the data is, you can better understand the trends and patterns within it.