mean absolute deviation calculator

What is mean absolute deviation?

Mean absolute deviation is a measure of spread. It tells you, on average, how far each value in your data set is from the mean. In plain language: it gives you the typical distance from the average.

If the MAD is small, your data points are clustered close to the mean. If the MAD is large, your data points are more spread out.

MAD formula

MAD = (Σ |x_i − x̄|) / n

• x_i = each data value
• x̄ = arithmetic mean of the data
• n = number of values
• |x_i − x̄| = absolute distance from the mean

How this calculator works

This tool performs the full calculation automatically:

• Parses your input values
• Computes the mean of the data set
• Finds each absolute deviation from the mean
• Averages those absolute deviations to get MAD
• Displays a step-by-step table so you can verify the result

Step-by-step example

Suppose your data set is: 10, 14, 18, 18, 20

1) Calculate the mean

(10 + 14 + 18 + 18 + 20) / 5 = 16

2) Find each absolute deviation from the mean

• |10 − 16| = 6
• |14 − 16| = 2
• |18 − 16| = 2
• |18 − 16| = 2
• |20 − 16| = 4

3) Average the absolute deviations

(6 + 2 + 2 + 2 + 4) / 5 = 16 / 5 = 3.2

So the mean absolute deviation is 3.2.

Why use MAD?

MAD is useful because it is intuitive and easy to explain. Instead of squared units, everything stays in the original unit of the data.

• In finance, MAD can summarize average daily movement in returns.
• In quality control, MAD can capture average process drift from target levels.
• In education, MAD can show how spread out student scores are around class average.
• In analytics, MAD is a quick variability metric for dashboards and reports.

MAD vs variance and standard deviation

Mean Absolute Deviation (MAD)

• Uses absolute distances from mean
• Easier to interpret directly
• Less influenced by extreme values than squared methods

Variance / Standard Deviation

• Uses squared distances from mean
• Penalizes large outliers more strongly
• Very common in statistical modeling and inference

If you need a practical “average distance from average,” MAD is often the cleanest choice.

Input tips

• You can enter integers, decimals, and negative numbers.
• Use commas, spaces, or semicolons as separators.
• Avoid text symbols inside the list (for example, “12 apples”).
• If your list is long, paste it directly and click Calculate MAD.

Frequently asked questions

Is MAD ever negative?

No. Absolute deviations are always zero or positive, so their average cannot be negative.

What if all values are identical?

Then every deviation from the mean is zero, so MAD = 0.

Can I use MAD with a single value?

Yes. The mean equals that value, the deviation is 0, and MAD is 0.

Final takeaway

Mean absolute deviation is one of the best “quick clarity” statistics for spread. Use the calculator above whenever you want a transparent, readable measure of variability for a numeric data set.