Tutoring some high school math courses, statistics is prominent.  The tutor introduces an important definition.

 
Statistics focuses on the mean and the standard deviation. But why is that? The reason is that while most phenomena follow a normal distribution, very few follow the standard normal distribution. Yet, the standard normal distribution is what we have tables for.

The z-score of a measurement “standardizes” it; i.e., it tells where that measurement would fall in the standard normal distribution, based on its placement in its own distribution.

The z-score of measurement x is given by

z=(x-μ)/σ

where

μ = mean of population x is from
σ = standard deviation of the population x is from

Example:

Find the z score of the exam mark 72 if the mean mark is 61 and the standard deviation is 12.

Solution:

z = (x-μ)/σ = (72-61)/12 = 11/12 = 0.9167

Looking at a z-score table or else the Sharp EL-520W (see here), we get the answer 0.82035: 82% of the students got that mark or below. Therefore, only 18% got above it.

z-scores can be seen as leading to the “bell curve” people refer to in connection with exam marks.

HTH:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.