Z-Scores

Z - Scores

Why is this Important?

How do you compare apples and oranges?

Are you as good a student of French as you are in Physics?

How many people did better than you on a test?
How many did worse?

Are you abnormal or deviant?

Dr So and So, are you going to curve the exam?

If you are going to understand a situation, you will need to able compare things. You will need to present the comparisons in a way that facilitates decision-making. You may be asked:

What percentage of people falls below a given score?

What is the relative standing of a score in one distribution versus another?

What score or scores can be used to define an extreme or deviant situation?

You can do all of these with the Z - Score!

Data Types

For our discussion of the Z-scores, we will be using measurement data (numerical scores).

We Will Need:

Measures of central tendency	The Mean
Measures of variability	Standard Deviation

Our First Intuitive Example

You enter your dorm room and find that one of your roommates has a happy face:

But your other roommate is sad:

What's happened! Why are you so happy! But why are You so sad?

They reply:

They have the same score! Why the different reactions!