Standard Deviation

Create a group of numbers:

x <- c(7, 3, 6.2, 9, 1)
x

## [1] 7.0 3.0 6.2 9.0 1.0

Compute the calculations below.

mean(x)

## [1] 5.24

length(x)

## [1] 5

max(x)

## [1] 9

Find the Standard Deviation. The formula is: \[\sqrt{\frac{1}{N-1}\sum\limits_{i=1}^N(x_i-\bar{x})^2},\]

z={1/(5-1)}
N=5
y=mean(x)
(x-y)^2

## [1]  3.0976  5.0176  0.9216 14.1376 17.9776

sqrt(z*sum((x-y)^2))

## [1] 3.207491

The Standard Deviation above should equal the Standard Deviation when using the sd() function.

sd(x)

## [1] 3.207491

The Standard Deviation calculated using arithmetic operations equals the Standard Devation using the R command.