Summary  
This chapter explains how to calculate sample variance by summing squared deviations from the mean and dividing by n − 1 to estimate data variability.  

General domain of usage  
Statistical data analysis

Now explore **sample variance**. The concept is similar to **population variance**, but the formula differs slightly because the data represents only a subset of the entire population.


**Formula**
$$
\text{variance} = \frac{\sum^n_{i=1}(x_i-\bar{x})^2}{n-1}
$$

Where:
- $$n$$ - sample size;
- $$i$$ - index of each element;
- $$x_i$$ - each element;
- $$\bar{x}$$ - sample mean value.


Look at the example of variance rounded to two decimal points for the column `'salary_in_usd'`:

The variance of the column `'salary_in_usd'` is **5034932663.18**

## Variance Key Note

The variance of the `'salary_in_usd'` column is quite substantial, indicating that the values in this column are **widely spread out**.

The greater the variance, the more the values are scattered.

Note

Select the one with lower variance from the graphs with an equal number of observations and identical mean values.

Build a strong foundation in statistics using Python. Learn essential statistical concepts and apply them through NumPy and pandas. Move from basic measures like mean and variance to hypothesis testing, confidence intervals, and data-driven insights with hands-on practice.

Discover core statistical principles, including data types, measures of central tendency, and key differences between samples and populations.

Learn to calculate and interpret mean, median, and mode using Python. Practice these operations with pandas to analyze real datasets.

Understand how variance and standard deviation measure data spread. Learn to compute both manually and using Python tools.

Explore how covariance and correlation describe relationships between variables. Practice calculating and comparing both metrics in Python.

Master confidence intervals to estimate population parameters. Use NumPy, pandas, and visualization libraries to calculate and interpret intervals with real data.

Learn the fundamentals of hypothesis testing and the t-test. Understand how to design, perform, and interpret tests using Python to support data-driven decisions.

Sample Variance

Variance Key Note