# Variance & Standard Deviation

Variance and Standard Deviation are the most frequently used measure of dispersion. Therefore, students of Econometrics should be well-acquainted with these concepts.

Standard Deviation is the square root of Variance. So, we first need to know about Variance before we calculate the Standard Deviation.

Variance is a measure of the average distance of observations from the mean of the data. It is calculated by the following formula:

${\sigma ^2} = \frac{{\sum\limits_{i = 1}^n {\left( {{X_i} – \bar X} \right)} }}{n}$

Where $${\sigma ^2}$$ is a symbol used to represent Variance, $${{X_i}}$$ is the $$ith$$ observation, $${\bar X}$$ is the mean of the given data and $$n$$ is the number of observation in the data.

Since Standard Deviation ($$\sigma$$) is the square root of Variance, its formula is as follows:

$\sigma = \sqrt {\frac{{\sum\limits_{i = 1}^n {\left( {{X_i} – \bar X} \right)} }}{n}}$

For a detailed reading of measures of dispersion, you should consult Fundamentals of Mathematical Statistics by S. C. Gupta and V. K. Kapoor. This book is a standard book on statistics for any postgraduate exam in Indian Universities.

Solved numerical examples will be available soon.