# How to calculate standard deviation of a distribution when only know z, xi, x_bar and proportion

I am wondering how I would calculate the standard deviation of a distribution when the values given are as below:

z = -1.08
xi = 120
x_bar = 122
proportion = .14


The missing element here is the standard deviation.

z-score:

z = (xi - x_bar) / std_dev


Using the available data - is there a way to rearrange it to solve for standard deviation?

Using algebra:

z = (xi - x_bar) / std_dev

z(std_dev) = (xi - x_bar)
-1.08 * (std_dev) = -2
-1.08 / -1.08 = -2 / -1.08  # divide both sides by z-score
std_dev = 1.85

• Yes: use algebra. – whuber Apr 25 at 16:07

z = (xi - x_bar) / std_dev