Question

Calculate the standard deviation for the following data.

3, 4, 5, 6, 7

Options

• `sqrt(3)`

• `sqrt(6)`

• `sqrt(2)`

• 2

Answer 1

`sqrt(2)`

Explanation:

The standard deviation of a data set is given as:

`sigma = sqrt(1/N xx sum_(i = l)^N (x_i - barx)^2`

Where, N `->` Number of data

`barx ->` Mean value

    `->` Data in data set

`barx = (3 + 4 + 5 + 6 + 7)/5 = 25/5` = 5

`(x_i - barx)^2 = (3 - 5)^2 = (- 2)^2` = 4

`(4 - 5)^2 = (1)^2` = 1

`(5 - 5)^2 = (0)^2` = 0

`(6 - 5)^2 = (1)^2` = 1

`(7 - 5)^2 = (2)^2` = 4

Sum is 4 + 1 + 0 + 1 + 4 = I 0

Now, 10 ÷ 5 = 2

Now, `sigma = sqrt(2)`