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## Measurement & Data - Statistics & Probability 218-221

### Unit 1: Lesson 8

Mean absolute deviation (MAD)

# Mean absolute deviation example

Sal finds the mean absolute deviation of a data set that's given in a bar chart.

## Want to join the conversation?

• Is there a way for the MAD to be negative other than if the data values are negative?
• Actually, regardless of whether data values are zero, positive, or negative, the MAD can never be negative. This is because the MAD is calculated by finding absolute values of the deviations (or differences) from the mean, and then taking the average (or mean) of these absolute values. Note that the absolute value of a quantity is never negative.
• If all the numbers equal the mean will the MAD be 0?
• if all the numbers are equal to mean then there would be no deviation at all and hence mean absolute deviation would be zero
• at , what does Sal mean by deviate?
• Just in case you were wondering, deviate also has a more general application in everyday language, meaning how far you are from the 'original' point. For example, if you're walking on a path in a nature reserve, and you see something far off to your right and start walking off the path and into the bushes, you could say you 'deviated from the path'. Or if you have to do an unprepared speech about horses and start off talking about horses, but end up doing most of your speech about how high kangaroos can jump, then you have 'deviated from the topic'. So basically, it's kinda like if you 'stray' from the topic (or path) or other things. :)
• I'm still confused after the step after calculating the mean. Can someone help me?
• After we calculate the mean, we need to subtract it from every data point and take the absolute value of each result. Adding all that together and dividing by the number of values you have will give you the MAD. Here's an example:

Let's say you have set 1, 2, 3, 4, 5 with a mean of 3. To solve for MAD, you would do the following:

|1 - 3| + |2 - 3| + |3 - 3| + |4 - 3| + |5 - 3| / 5
= |-2| + |-1| + |0| + |1| + |2| / 5

Taking the absolute value eliminates all negative signs.

= 2 + 1 + 0 + 1 + 2 / 5
= 6 / 5
= 1.2

Hope this helps!
• I don't know if this will help anyone else, but it was rather confusing when he kept saying above or below, so I try to think of it as one "unit away" instead.
• what real world situation would you need to find the M.A.D. in?
• Related to that: If you had a budget for the year that is \$450,000. At the end of the year you create a bar graph for each of the months that says how much money was spent monthly. If you wanted to know how much more or less money you spent in each month on average. That would be finding the Mean Absolute Deviation. Hope that helps!
• How many times do we have to practice m.a.d to progress in our levels?
• Could you explain a bit more? Like on khan, or at school, and if on khan, are you doing it through the dashboard or by subject??
• Can you have a MAD less than 1?