## Thursday, February 28, 2019

### How to Calculate a Z-Score Using Microsoft Excel

A Z-Score is a statistical value that tells you how many standard deviations a particular value happens to be from the mean of the entire data set. You can use AVERAGE and STDEV.S or STDEV.P formulas to calculate the mean and standard deviation of your data and then use those results to determine the Z-Score of each value.

## What is a Z-Score and what do the AVERAGE, STDEV.S, and STDEV.P functions do?

A Z-Score is a simple way of comparing values from two different data sets. It is defined as the number of standard deviations away from the mean a data point lies. The general formula looks like this:

```=(DataPoint-AVERAGE(DataSet))/STDEV(DataSet)
```

Here’s an example to help clarify. Say you wanted to compare the test results of two Algebra students taught by different teachers. You know the first student got a 95% on the final exam in one class, and the student in the other class scored 87%.

At first glance, the 95% grade is more impressive, but what if the teacher of the second class gave a more difficult exam? You could calculate the Z-Score of each student’s score based on the average scores in each class and the standard deviation of the scores in each class. Comparing the Z-Scores of the two students could reveal that the student with the 87% score did better in comparison to the rest of their class than the student with the 98% score did in comparison to the rest of their class.

The first statistical value you need is the ‘mean’ and Excel’s “AVERAGE” function calculates that value. It simply adds up all of the values in a cell range and divides that sum by the number of cells containing numerical values (it ignores blank cells).

The other statistical value we need is the ‘standard deviation’ and Excel has two different functions to calculate the standard deviation in slightly different ways.

Previous versions of Excel only had the “STDEV” function, which calculates the standard deviation while treating the data as a ‘sample’ of a population. Excel 2010 broke that into two functions that calculate the standard deviation:

• STDEV.S: This function is identical to the previous “STDEV” function. It calculates the standard deviation while treating the data as a ‘sample’ of a population. A sample of a population might be something like the particular mosquitoes collected for a research project or cars that were set aside and used for crash safety testing.
• STDEV.P: This function calculates the standard deviation while treating the data as the entire population. An entire population would be something like all mosquitoes on Earth or every car in a production run of a specific model.

Which you choose is based on your data set. The difference will usually be small, but the result of the “STDEV.P” function will always be smaller than the result of the “STDEV.S” function for the same data set. It is a more conservative approach to assume there is more variability in the data.

## Let’s Look at an Example

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