*52*

In statistics, a **z-score **tells us how many standard deviations away a value is from the mean. We use the following formula to calculate a z-score:

**z** = (X – μ) / σ

where:

- X is a single raw data value
- μ is the mean of the dataset
- σ is the standard deviation of the dataset

This tutorial explains how to calculate z-scores for raw data values in Google Sheets.

**Example: Z-Scores in Google Sheets**

Suppose we have the following dataset and we would like to find the z-score for every raw data value:

We can perform the following steps to do so.

**Step 1: Find the mean and standard deviation of the dataset.**

First, we need to find the mean and the standard deviation of the dataset. The following formulas show how to do so:

The mean turns out to be **14.375 **and the standard deviation turns out to be **4.998**.

**Step 2: Find the z-score for the first raw data value.**

Next, we’ll find the z-score for the first raw data value by typing the following formula in cell B2:

=(A2–$E$2)/$E$3

**Step 3: Find the z-scores for all remaining values.**

Once we’ve calculated the first z-score, we can highlight the rest of column B starting with cell B2 and press **Ctrl+D **to copy the formula in cell B2 to each of the cells below it:

Now we have found the z-score for every raw data value.

**How to Interpret Z-Scores**

A **z-score **simply tells us how many standard deviations away a value is from the mean.

In our example, we found that the mean was **14.375 **and the standard deviation was **4.998**.

So, the first value in our dataset was 7, which had a z-score of (7-14.375) / 4.998 = **-1.47546**. This means that the value “7” is -1.47545 standard deviations *below *the mean.

The next value in our data, 12, had a z-score of (12-14.375) / 4.998 = **-0.47515**. This means that the value “12” is -0.47515 standard deviations *below *the mean.

The further away a value is from the mean, the higher the absolute value of the z-score will be for that value. For example, the value 7 is further away from the mean (14.375) compared to 12, which explains why 7 had a z-score with a larger absolute value.

**Additional Resources**

How to Calculate Z-Scores in Excel

How to Calculate Z-Scores in R

How to Calculate Z-Scores on a TI-84 Calculator