**Population Variance:**\[ \sigma^2 = \frac{\sum (x_i – \mu)^2}{N} \]

**Sample Variance:**

$\[ s^2 = \frac{\sum (x_i – \bar{x})^2}{n – 1} \]โ$

Where \( x_i \) are the individual data points, \( \mu \) is the population mean, \( \bar{x} \) is the sample mean, \( N \) is the size of the population, and \( n \) is the size of the sample.

Variance is not confined to textbooks; it’s evident in various aspects of everyday life:

**Educational Settings:**The variance in students’ test scores can highlight the diversity in learning and understanding within a class.**Financial Markets:**Investors assess the variance in stock prices to gauge market volatility and risk.

Graphs and charts bring variance to life, translating complex numerical concepts into visually intuitive information. Tools like variance plots help in making data-driven decisions more accessible.

Here is how to calculate and visualize variance in plots using python, here is the code:

done

when calculating sample variance we must put a degree of freedom value (ddof=1) for correct variance calculation.

Done

Amazing.

AOA, I found this blog to be a comprehensive and insightful exploration of the concept of variance. And effectively defines variance as a measure of how data points deviate from the mean, emphasizing its importance in understanding data variability. It provides clear formulas for calculating population and sample variances and discusses real-world scenarios where variance plays a significant role, such as in educational settings and financial markets. The inclusion of a Python code example for visualizing variance using bar plots adds practical value to the post. Overall, it was a well-written and informative blog post that enhanced my understanding of variance and its relevance in statistical analysis. ALLAH PAK ap ko dono jahan ki bhalian aata kry AAMEEN.