In this section we’ll look at how to calculate **Variance in R**.

Variance is defined as the sum of squares of deviations of the set of numbers from the mean value. It is a measure of how far a set of data are dispersed out from their mean value . It is always a non -negative number. It is generally denoted by sigma squared `σ2`

(sigma squared)

Where

`x`

= Data set values`µ`

= Mean value`N`

= Total number of observations

Let’s have a look at an example that we considered for calculation of mean `3, 5, 7, 9, 11, 13, 15`

.

The mean value in this case is `(3 + 5 + 7 + 9 + 11 + 13 + 15 ) / 7 = 9`

- Squares of the deviations from the mean value µ is calculated as
`(3-9)^2 = 36, (5-9)^2 = 16, (7-9)^2 = 4, (9-9)^2 = 0, (11-9)^2 = 4, (13-9)^2 = 16, (15-9)^2 = 36`

- Sum all the squares of deviation and divide it by the number of observations
`(36 + 16 + 4 + 0 + 4 + 16 + 36 ) / 7 = 16`

. Hence the variance in this example is`16`

.

R provides an in-built function `var()`

to compute the variance of all data values in the dataset with respect to the mean. The function takes numeric or integer vector as an argument and returns the result.

`x`

is a variable that takes the integer vectors using`c()`

function- The result of
`var(x)`

is displayed using`print`

In the next section we’ll look at Standard Deviation

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