Standardizing Z scores simple explanation

Standardizing a value, or a z-score, is a way of expressing how many standard deviations a value is from the mean of a distribution.

To standardize a value, you can use the following formula:

z = (x - μ) / σ

Where x is the value you want to standardize, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

For example, let's say you have a distribution with a mean of 100 and a standard deviation of 10. If you want to standardize the value 110, you would do the following calculation:

z = (110 - 100) / 10 = 1

This means that the value 110 is 1 standard deviation above the mean of 100.

Standardizing values can be useful in comparing values from different distributions or in identifying unusual values that fall outside of the normal range.

A more simple example 

To standardize your age of 10 years, you would need to know the mean and standard deviation of the age distribution you are comparing it to. For example, if you are comparing your age to the age of students in your class and the mean age of the students is 10 years and the standard deviation is 2 years, you can standardize your age as follows:

z = (10 - 10) / 2 = 0

This means that your age of 10 years is exactly the average age of the students in your class. If the mean age of the students was 9 years and the standard deviation was still 2 years, your standardized age would be:

z = (10 - 9) / 2 = 0.5

This means that your age is 0.5 standard deviations above the mean age of the students in your class.

It's important to note that standardizing a value only makes sense if you are comparing it to a distribution with a known mean and standard deviation. Without this information, you cannot accurately standardize a value.