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# Frequency Distribution Definition and Tutorial

This is often the first topic when covering investment risk. We break observations into groups and from there the dispersion around a central point starts to appear.
1. Define - Define a frequency distribution.
2. Context - Use frequency distribution in a sentence.
3. Video - See the video for examples in Excel.
4. Script - Follow along with the transcript below.
5. Quiz - Test yourself. by Paul Alan Davis, CFA
Updated: February 17, 2021
The frequency distribution is best visualized with a histogram. In Excel here we create both.

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## Frequency Distribution for Investment Modeling

Beginner

Frequency Distribution is a table showing the number, or frequency, of observations within ranges of data. Ranges may also be called bins or buckets. As an example, in a two-bin case, count the number of observations in each of two bins: a less-than-zero bin, and a zero-or-greater bin. The same tabular data can be presented in chart form using a histogram.

Synonym: frequency table

For context, it is descriptive statistics, like variance and standard deviation, that allow you to understand the absolute risk of an investment based on observations from the past. These calculations can hide outliers, so it is a good idea for the financial modeler to utilize a frequency distribution and histogram to be certain that takeaways associated with descriptive statistics are valid.

### In a Sentence

Joy:  So to get a frequency distribution in Excel, it ends with Ctrl+Shift+Enter?
Doc:  That's music to my ears. Exactly! It's called the =FREQUENCY function.

### Video

This video can be accessed in a new window or App , at the YouTube Channel or from below.

Frequency distribution definition for investment modeling (4:31)

### Video Script

The script includes two sections where we visualize and demonstrate the creation of a frequency distribution.

#### Visualize

We're sitting right here in Excel and this is a snippet from our boot camp course.

Our goal is to analyze 60 monthly returns on four stocks, located on a tab called Returns.

And in this table we listed six ranges, or bins. So we now can see. There were 2 returns of less than -10% for Microsoft, and eBay returned greater than 10%, 12 times.

It can be easier to grasp this by using a histogram. This visual perspective will help you spot errors and trends. It will also let you see if the distribution is in alignment with your statistical tests. See how eBay, in orange, had more observations away from the center, than Microsoft and Abbott Labs? So eBay would have higher risk, if we measured it by standard deviation. Next, let's demonstrate.

#### Demonstrate

There are eight steps to generate a frequency distribution and histogram in Excel. First, estimate breakpoints by reviewing the data. I sorted the returns in rather arbitrarily-selected buckets.

From there, set up labels and a blank table for the numeric output.

Third, set up the bins_array, or cut off points. Each horizontal line here, refers to a breakpoint for the bins, so you need one less than the number of bins, so 5 bins, instead of 6. These aren't used as labels, so no need to be fancy here.

Fourth, set up the data array. In this case we'll select the range `C7:F66` on the Returns tab.

Fifth, select and highlight the output block, or `F8:I13`.

Sixth, type `=FREQUENCY` open parenthesis, select the data_array, comma, the bins_array, closed parenthesis, then the `Ctrl+Shift+Enter` keystroke combination, telling Excel it is an array calculation, meaning calculate everything at once. The array formula is identified by curly braces. There you have it.

Seventh, create a row with the `=SUM` function to verify totals.

Last, highlight the range of data, including labels, click Insert, then Column. Edit the histogram as you see fit.

### Quiz

The histogram presents data in tables and the frequency distribution presents data in charts. | True or False?

False, the other way around.

The bins array in Excel has the same number of rows as the output array. | True or False?

False, the bins array is for the breakpoints and has one less row.

Still unclear on the frequency distribution? Leave a question in the comments section on YouTube or check out the Quant 101 Series, specifically Stock return frequency distributions and histograms in Excel.

### Related Terms

Our trained humans found other terms in the category statistics basics you may find helpful.

## What's Next?

• To see all terms in the Glossary, click Outline.
• To learn the term Forecast Return, click Back.
• Contribute to new content for this free site, click Tip.
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