Question

How do you convert z to x and x to z in Statistics? An explanation would be great. Thank you!

Answer 1

There are two formula we need to remember:

$\small z=\frac{x-\mu}{\sigma}$

and $\small x=\mu+z*\sigma$

We normally have three values given out of four $\small x, z, \mu, \sigma$ and we need to find the 4th one.

$\small \mu$ is mean, $\small \sigma$ is population standard deviation.

We just need to use these and we can convert x to z or z to x as per our requirement.

Example:

mean = 5, population standard deviation = 2, x = 7 then z = ?

$\small z=\frac{7-5}{2}=\frac{2}{2}=1$

Same way, mean = 5, sd = 2, z = 1 then x = ?

$\small x=5+1*2 = 5+2=7$

That's how we convert. Please remember $\small \sigma$ is population standard deviation.

I hope this will help. Thank you.