Fundamental normality test

Imagine you have a group of numbers, like 2, 5, 6, 8, and 10. These numbers are called data. Now, you want to know if these numbers are "normal" or not. But what does normal mean in this case?

Normal here means that the numbers are behaving in a typical or expected way. For example, if you have a group of numbers that represent the heights of people, you would expect most people to have heights in a certain range. If someone's height is very far away from that range, it might be considered abnormal.

Now, let's say you want to test if your group of numbers is normal. To do this, you can use something called the fundamental normality test. This test helps you figure out if your data is behaving in a normal or expected way.

To perform the fundamental normality test, you need to follow a few steps. First, you find the average of all the numbers in your group. In our example, the average would be (2 + 5 + 6 + 8 + 10) divided by 5, which is 31 divided by 5, which is 6.2.

Next, you calculate something called the standard deviation. This is a fancy math term, but it basically tells you how spread out your numbers are. The standard deviation is like a measure of how much the numbers move away from the average. In our example, assuming you know a bit of calculation, the standard deviation is approximately 2.39.

Once you have the average and the standard deviation, you can use these numbers to help determine if your data is normal. You can compare each number in your group to the average. If a number is close to the average, it's behaving normally. But if a number is very far away from the average, it might be considered abnormal.

To decide if a number is far away from the average, we can use the standard deviation. If a number is more than a few times the standard deviation away from the average, it might be considered abnormal. The specific number of times (or standard deviations) can vary depending on the situation or what you're trying to find out.

For example, if you have a number in your group that is three times the standard deviation away from the average, it might be considered abnormal. In our example, three times the standard deviation is 3 x 2.39, which is approximately 7.17. So, any number in our group that is more than 7.17 away from the average might be considered abnormal.

By performing this fundamental normality test, you can get a better understanding of whether your group of numbers is behaving in a normal or expected way. It helps you identify any numbers that might be unusual or different from the rest of the data.