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The **variance** of a set of observation is defined as mean of the squares of deviations of all observations from their mean. When it is calculated from entire population, the **variance** is called the **population variance**, traditionally denoted by (σ is the Greek lower case “sigma”). If instead, the data from the sample are used to calculate the **variance**, it is referred to as the sample variance and is denoted by S² in order to distinguish between the two. The symbol definition of **variance** is

σ² =∑(xi-µ)²/N, for population sample

S²=∑(xi−Ẍ)²/n, for sample data

The **variance** is also denoted by Var(X). **Variance** of sample is calculated by dividing the sum of squared deviations by n. the statistics computed by dividing the sum of squared deviations by n-1 is called the **sample variance** corrected for the mean. Because this ** statistics** is used extensively, we will shorten its name to

**sample variance**. One of the objectives of statistical inference is to estimate the parameter from statistics. For example, we estimate the populations mean µ from the sample mean x. statistics created by dividing ∑(xi- Ẍ)² by n-1 is a better estimator than is the one created by dividing by n.

The term **variance** was introduced in 1918 by R.A Fisher 1890-1962). It should be noted that the **variance** is in square of units in which the observations are expressed and the **variance** is a larger number compared to observations themselves. The **variance** because of its some nice mathematical properties, assumes an extremely important role in statistical theory. Expectation of a random variable X is often called the mean and is denoted by µ. Another quantity of great important in probability and statistics is the variance of a random variable denoted by var(X) or σ². The **variance** is a non –negative number and its unit of measurement is squared units on the origin scale.

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