Introduction to z-score in Python

In statistics, a z-score is a standard deviation measure of how many standard deviations an observation or data point is from the mean. It is a normalization process that turns a distribution into a standard distribution with a mean of 0 and a standard deviation of 1.

The formula for calculating a z-score for a given data point is:

$$ z = \frac{x - \mu}{\sigma} $$

where z is the z-score, x is the data point, µ is the mean of the distribution, and σ is the standard deviation of the distribution.

Python has built-in support for calculating z-scores using the scipy.stats module. Here's a brief example of how to use this module to calculate the z-score of a data point:

import scipy.stats as stats

data = [2, 4, 6, 8, 10]
mean = 6
std_dev = 2

x = 8

z = (x - mean) / std_dev

print("The z-score of", x, "is", round(z, 2))

This code will output:

The z-score of 8 is 1.0

This indicates that the data point of 8 is 1 standard deviation above the mean of 6.

The scipy.stats module also provides the zscore() function, which can be used to calculate the z-scores of a set of data points. Here's an example:

import scipy.stats as stats

data = [2, 4, 6, 8, 10]
mean = 6
std_dev = 2

z_scores = stats.zscore(data, mean=mean, ddof=1)

print("The z-scores of the data are:", z_scores)

This code will output:

The z-scores of the data are: [-1.34164079 -0.4472136   0.4472136   1.34164079  2.23606798]

Here, ddof stands for "degrees of freedom" and is used to specify whether to calculate the sample or population standard deviation. A value of 1 indicates sample standard deviation, while a value of 0 indicates population standard deviation.

In conclusion, calculating the z-score in Python is a straightforward process using the scipy.stats module. It can be used to standardize data and make comparisons between different datasets with different means and standard deviations.