Statistics & Probability calculator
Mean Absolute Deviation Calculator
Calculate mean absolute deviation from raw data, frequency or grouped data, and forecasting tables, with step-by-step work, deviation tables, and focused companion statistics.
Mean absolute deviation calculator results
Your mean absolute deviation will appear here
Enter your data and click Calculate.
Mean Absolute Deviation
Dataset MAD, grouped-data MAD, and forecasting MAD answer related but different questions. Grouped class-interval results are midpoint-based estimates.
Calculator overview
Quick Mean Absolute Deviation Calculator Overview
Use this mean absolute deviation calculator to find MAD from raw data, frequency tables, grouped intervals, or forecasting errors. It shows the average absolute distance or forecast error with step-by-step work.
Choose the data mode, enter values, and calculate MAD with supporting steps.
Guide
Mean Absolute Deviation Calculator Guide
Use this guide to understand dataset MAD, grouped-data MAD, and forecasting MAD without mixing up the formulas or the meaning of the results.
What This Calculator Does
This mean absolute deviation calculator helps users calculate MAD from raw data, exact frequency tables, grouped class intervals, and actual-versus-forecast tables. It also shows the worked steps so you can see the mean, each absolute deviation, the deviation sum, and the final average.
The page is also an absolute deviation calculator for common classroom and business workflows, including grouped-data estimates and the MAD forecasting formula.
What Mean Absolute Deviation Means
Mean absolute deviation is the average absolute distance between values and the mean. A smaller MAD means values usually sit closer to the mean. A larger MAD means values are more spread out.
This calculator focuses on mean absolute deviation. Median absolute deviation is a different statistic that measures distance from the median.
How to Calculate MAD for Raw Data
Start by finding the mean. Then calculate each distance from the mean using an absolute value, add those distances, and divide by the number of values.
Grouped Data MAD
Frequency-table MAD uses each exact value and its frequency. The weighted mean is sum(f x value) divided by sum(f), and the weighted MAD is sum(f x |value - mean|) divided by sum(f).
Grouped class intervals are different. When only intervals are available, the calculator uses each class midpoint as the representative value. That makes grouped-data MAD useful, but approximate.
Forecasting MAD
Forecasting MAD is the average absolute forecast error. For each period, subtract forecast from actual, take the absolute value, add the absolute errors, and divide by the number of forecast periods.
This meaning is separate from dataset MAD. Dataset MAD measures spread around a mean; forecasting MAD measures how far forecasts were from actual values.
How to Use
- 1Choose the input mode
Select raw data, frequency or grouped data, forecasting MAD, or companion stats.
- 2Enter your data
Paste a list, fill frequency rows, add class intervals, or enter actual and forecast values.
- 3Click Calculate
Results stay hidden until you submit the calculator.
- 4Review MAD first
Then check the mean, deviation table, supporting values, and step-by-step work.
Tips / Notes
- MAD is often easier to interpret than variance because it stays in the same unit as the data.
- Grouped-data MAD is approximate because class intervals use representative midpoints.
- Forecasting MAD is useful when comparing forecast accuracy across similar series.
- Larger MAD generally means more variability or larger forecast errors.
- Use raw data when available; use frequency or grouped data when the original observations are summarized.
FAQ
Frequently Asked Questions
Clear answers about finding mean absolute deviation, grouped-data estimates, forecasting MAD, and worked steps.
What does the Mean Absolute Deviation Calculator do?
It calculates mean absolute deviation from raw data, value-frequency tables, grouped class intervals, and actual-versus-forecast tables, with worked steps for each mode.
How do I find mean absolute deviation from a list of numbers?
Find the mean, subtract the mean from each value, take the absolute value of each difference, then average those absolute deviations.
Can this calculator handle grouped data?
Yes. The grouped-data mode estimates MAD using class midpoints and frequencies. It labels the result as an estimate because the original raw values are not fully known.
What is the difference between dataset MAD and forecasting MAD?
Dataset MAD measures average distance from a dataset mean. Forecasting MAD measures average absolute error between actual and forecast values.
Why is grouped-data MAD only an estimate?
Class intervals summarize many possible raw values. The calculator uses each class midpoint as a representative value, so the result is approximate.
Does this calculator show the steps?
Yes. Each mode shows the mean or forecasting error setup, the absolute deviations or absolute errors, the total, and the final MAD calculation.