Variance and standard deviation for ungrouped data
Let $x_i, i=1,2, \cdots , n$ be $n$ observations.
Formula
Sample variance of $X$ is denoted by $s_{x}^2$ and is given by
$s_x^2 =\dfrac{1}{n-1}\sum_{i=1}^{n}(x_i -\overline{x})^2=\dfrac{1}{n-1}\bigg(\sum_{i=1}^{n}x_i^2-\dfrac{\big(\sum_{i=1}^n x_i\big)^2}{n}\bigg)$
where,
$\overline{x}=\dfrac{1}{n}\sum_{i=1}^{n}x_i$is the sample mean
The sample standard deviation of $X$ is defined as the positive square root of the sample variance. The sample standard deviation of $X$ is given by
