Question

Standard deviation of 4,5 and 7?

Answer 1

The standard deviation is about `1.24721...`

Explanation:

Using the standard deviation formula:

`S_x=sqrt((sum_(i=1)^n(x_i-barx)^2)/n)`

We can calculate the average then plug in our numbers:

`barx=(4+5+7)/3=16/3`

`S_x=sqrt((sum_(i=1)^3(x_i-16/3)^2)/3)`

`color(white)(S_x)=sqrt(((4-16/3)^2+(5-16/3)^2+(7-16/3)^2)/3)`

`color(white)(S_x)=sqrt(((12/3-16/3)^2+(15/3-16/3)^2+(21/3-16/3)^2)/3)`

`color(white)(S_x)=sqrt(((-4/3)^2+(-1/3)^2+(5/3)^2)/3)`

`color(white)(S_x)=sqrt((16/9+1/9+25/9)/3)`

`color(white)(S_x)=sqrt((42/9)/3)`

`color(white)(S_x)=sqrt(42/27)`

`color(white)(S_x)~~1.24721...`

Answer 2

Standard Deviation`=1.25`

Explanation:

Given -

`x: 4, 5, 7`
Mean `barx=(4+5+7)/3=16/3=5.3`
Variance `sigma^2 = [(4-5.3)^2+(5-5.3)^2+(7-5.3)^2]/3`
`=(1.69+0.09+2.89)/3=4.67/3=1.56`

Standard Deviation `sigma =sqrt(sigma^2)=sqrt1.56=1.25`