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.

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