📚 Practice With Worksheets
Practice calculating and interpreting mean absolute deviation and comparing the amount of variation in numerical data sets.
🛠️ How to Use This Tool
Enter numerical values for one or both data sets. Values may be separated by commas, spaces, tabs, or line breaks, and each group may be given a custom name.
Select the button for Data Set 1, Data Set 2, or both data sets combined. The tool displays the count, mean, MAD, minimum, maximum, range, and ordered values.
Use the interpretation panel to compare variation, then select Show Step-by-Step MAD Work to examine each distance from the mean and the final average.
🧠 Things to Notice
A smaller MAD means the values tend to remain closer to the mean, while a larger MAD indicates that the data are more spread out.
Two groups may have similar means but very different MADs. Their centers can be alike even when one distribution shows much more variation.
Combining two groups may increase or decrease the overall MAD depending on how far the groups are from one another and from the new combined mean.
📘 Vocabulary
Mean: The sum of all values divided by the number of values.
Deviation: The difference between a data value and the mean.
Absolute Deviation: The nonnegative distance between a data value and the mean.
Mean Absolute Deviation: The average of the absolute distances between the data values and the mean.
MAD: An abbreviation for mean absolute deviation.
Variation: The amount by which data values differ from one another.
Spread: How widely the values are distributed across the number line.
Distance from the Mean: The absolute value of the difference between a data value and the mean.
Distribution: The overall arrangement of values within a data set.
Range: The difference between the maximum and minimum values.
Outlier: A value that is unusually far from most of the other values and may increase the MAD.
Combined Data Set: A single data set formed by joining the values from two groups.
📐 MAD as a Measure of Variation
Mean absolute deviation describes the typical distance between the values in a data set and the mean. It gives one number that summarizes how much the data vary.
First, find the mean. The mean becomes the reference point used to measure the distance of every value.
Next, find each absolute deviation. Absolute value is used because distance is nonnegative; values below and above the mean should not cancel each other.
Finally, average the distances. The resulting MAD represents how far a data value is from the mean on average.
A small MAD describes a distribution whose values are generally clustered near the mean. A large MAD describes a distribution with greater spread and variation.
When comparing groups, MAD should be interpreted together with the mean and the context. Two groups can share the same mean while having very different levels of consistency or variability.
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