In this instructable we will learn how to calculate the Z score and use the Z table to find the value for the same. Z score calculation is normally conducted to find out where our value lies in respect to the mean in a normal distribution. Normal distribution is one of the most widely used distribution methods used in statistics and probability and both the normal distribution and Z score calculation is something every single math, statistics and probability student must be well familiarized with.

In this instructable we will learn how to calculate Z score and use the Z Table using a simple example. So without further ado let's go ahead.

### Supplies:

## Step 1: The Example:

500 random strangers are chosen for an IQ test. Samantha scored 120 (X) in total out of 300. The average score for the batch was 110 (µ) and the standard deviation was 30 (σ). Let's see how Samantha fares compared to others in this IQ test.

## Step 2: Z Score Calculation

To fine out the Z score we use the formula

**Z score = ( X – µ ) / σ**

= (120 - 110) / 30

= 10/30

= 0.33

Samantha's Z Score is positive and 0.33

Next we will learn how to map the Z score on the Z table to learn how good or bad Samantha performed on the IQ test compared to others.

## Step 3: Using the Z Table

Since Samantha's Z score value was positive we will use the positive Z Table. Had Samantha's Z score value been negative we would had used the negative Z Table. Both the tables have been added for reference.

To calculate where Samantha's Z score value stands compared to the mean, let us find the value for the first two digits on the Y axis (0.3 for Samantha's Z Score). Next find the value for the second decimal alongside the X axis (0.03 based on Samatha's Z Score). We get the value as 0.62930.

Hence, this means that Samantha's IQ test result is better than 62.93% in comparison with the rest of the batch

## 5 Discussions

4 months ago

Nice tutorial. Thanks for sharing.

Reply 4 months ago

Thank you. I just discovered your DIY hacks instructables and they are so cool and amazing!

Reply 4 months ago

Thank you

4 months ago

I'm not sure what applications this would have in the workshop; still, it was quite interesting to learn!

Reply 4 months ago

Hey Royell. Thank you for your comment. Z Table and normal distribution form the basics of statistics and probability. Let me explain with an example. Most people's height falls somewhere between 5'4'' to 6'1''. If we take a sample of 1000 random people sure we will find few people who are below 5 feet and few people who are let's say near 7 feet but the majority will fall under 5'4'' and 6'1'' and the graph of their heights will look a lot similar to bell curved graph shown above and the graph would peak somewhere around 5'7''. So this helps us better understand and map the data. Whereas the Z Score and Z Table will help you better understand how and where your height stands compared to the others in the sample above. Hope this helps!