Mean, Variance, SD of Five Numbers

Mean $\bar{x}$ is the average of values. Variance $\sigma^2 = \frac{1}{n}\sum(x_i - \bar{x})^2$ measures spread around the mean. Standard deviation $\sigma = \sqrt{\sigma^2}$ brings spread back to the original units. Larger $\sigma$ means more scattered data.

Slide four values $x_1, x_2, x_3, x_4$. The lab returns mean, variance and standard deviation live. Set all four equal: variance is $0$ — no spread. Spread them out and watch $\sigma$ grow.

Cricket bowler economy rates: two bowlers with mean of $5$ runs/over can have very different consistency, captured by $\sigma$. Investment risk, board exam mark distributions, and rainfall variability across Indian monsoon months all use $\sigma$ to quantify how reliable an average is.

Class XI uses the population formula $\frac{1}{n}\sum(x_i - \bar x)^2$. Class XII statistics and some software use the sample formula $\frac{1}{n-1}\sum(x_i - \bar x)^2$ (Bessel's correction). For board exams stick with $n$ unless the question explicitly says sample variance.