*37*

The **mean absolute deviation** is a way to measure the spread of values in a dataset.

It is calculated as:

**Mean absolute deviation = (Σ |x _{i} – x|) / n**

**Σ**: A fancy symbol that means “sum”**x**: The i_{i}^{th}data value**x**: The mean value**n**: The sample size

A low value for the mean absolute deviation tells us that the data values are concentrated close to each other while a high value tells us that the values are more spread out.

The following step-by-step example shows how to calculate the mean absolute deviation for the following dataset on a TI-84 calculator:

**Dataset:** 8,13,14,16,19,24

**Step 1: Enter the Data**

First, we will enter the data values.

Press Stat, then press EDIT. Then enter the values in column L1:

**Step 2: Calculate the Absolute Deviations**

Next, we will find the absolute deviation of each individual value from the mean.

To do so, highlight the top of column L2 and type in the following formula:

=abs(L1 - mean(L1))

Here’s how to actually type in this formula:

- Press 2nd, then press 0. Then press abs(. This will input
**abs(**in the formula. - Press 2nd, then press 1. Now you will have
**abs(L1**in the formula. - Press the minus – button. Now you will have
**abs(L1-**in the formula. - Press 2nd, then press STAT. Scroll over to “MATH” and then press 3. Now you will have
**abs(L1-mean(**in the formula. - Press 2nd, then press 1. Now you will have
**abs(L1-mean(L1**in the formula. - Press ) twice. Now you will have
**abs(L1-mean(L1))**, which is the final formula.

Once you press Enter, the absolute deviations will appear in column L2:

**Step 3: Calculate the Mean Absolute Deviation**

Lastly, use the following steps to calculate the mean absolute deviation:

- Press 2nd and then press MODE to return to the home screen.
- Press 2nd and then press STAT. Scroll over to “MATH” and then press 3.
- Press 2nd and then press 2.
- Press the ) button.

Once you press Enter, the mean absolute deviation will be displayed:

The mean absolute deviation turns out to be **4**.

This tells us that the average distance between the individual values and the mean value in this dataset is 4.

**Additional Resources**

How to Find a Five Number Summary on a TI-84 Calculator

How to Find Interquartile Range on a TI-84 Calculator

How to Find Coefficient of Variation on a TI-84 Calculator