*45*

The **Empirical Rule**, sometimes called the 68-95-99.7 rule, states that for a given dataset with a normal distribution:

**68%**of data values fall within one standard deviation of the mean.**95%**of data values fall within two standard deviations of the mean.**99.7%**of data values fall within three standard deviations of the mean.

In this tutorial, we explain how to apply the Empirical Rule in Excel to a given dataset.

**Applying the Empirical Rule in Excel**

Suppose we have a normally-distributed dataset with a mean of **7** and a standard deviation of **2.2**. The following screenshot shows how to apply the Empirical Rule to this dataset in Excel to find which values 68% of the data falls between, which values 95% of the data falls between, and which values 99.7% of the data falls between:

From this output, we can see:

- 68% of the data falls between
**4.8**and**9.2** - 95% of the data falls between
**2.6**and**11.4** - 99.7% of the data falls between
**0.4**and**13.6**

The cells in columns *F *and *G *show the formulas that were used to find these values.

To apply the Empirical Rule to a different dataset, we simply need to change the mean and standard deviation in cells C2 and C3. For example, here is how to apply the Empirical Rule to a dataset with a mean of **40** and a standard deviation of **3.75**:

From this output, we can see:

- 68% of the data falls between
**36.25**and**43.75** - 95% of the data falls between
**32.5**and**47.5** - 99.7% of the data falls between
**28.75**and**51.25**

And here is one more example of how to apply the Empirical Rule to a dataset with a mean of **100 **and a standard deviation of **5**:

From this output, we can see:

- 68% of the data falls between
**95**and**105** - 95% of the data falls between
**90**and**110** - 99.7% of the data falls between
**85**and**115**

**Finding What Percentage of Data Falls Between Certain Values**

Another question you might have is: *What percentage of data falls between certain values?*

For example, suppose you have a normally-distributed dataset with a mean of 100, a standard deviation of 5, and you want to know what percentage of the data falls between the values **99 **and **105**.

In Excel, we can easily answer this question by using the function **= NORM.DIST()**, which takes the following arguments:

**NORM.DIST**(x, mean, standard_dev, cumulative)

where:

*x*is the value we’re interested in*mean*is the mean of the distribution*standard_dev*is the standard deviation of the distribution*cumulative*takes a value of “TRUE” (returns the CDF) or “FALSE” (returns the PDF) – we’ll use “TRUE” to get the value of the cumulative distribution function.

The following screenshot shows how to use the **NORM.DIST()** function to find the percentage of the data that falls between the values **99 **and **105 **for a distribution that has a mean of 100 and a standard deviation of 5:

We see that **42.1% **of the data falls between the values 105 and 99 for this distribution.

**Helpful Tools:**

Empirical Rule Calculator

Empirical Rule (Practice Problems)