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## Statistics and probability

### Course: Statistics and probability>Unit 3

Lesson 8: Other measures of spread

# Mean absolute deviation example

This lesson teaches how to calculate the mean and mean absolute deviation (MAD) using a bar graph. The graph shows the number of bubbles blown by four people. The mean is found by adding all the values and dividing by the number of data points. The MAD is calculated by finding the average of the absolute differences from the mean.

## 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.
• 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!
• 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 understand this video but when i try to do it on the acual questions i dont understand because when i do the absoulute deviantion i divid and then i get the same number in the begining
• So you found the mean of the numbers, divided the mean by how many numbers are in the data set then subtracted the answer from the division problem. Maybe you did the math wrong
(1 vote)
• 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.
• All right,
I got a problem that I'm confused on. I will try to solve it right now, narrating all the steps. (If I do something wrong or forget a step, please correct me!)

We have a number line. One dot on 1, one dot on 4, one dot on 5, one dot on 7, and one dot on 8. We know (because the problem tells us) that the mean for the data on the line plot is 5.

What is the absolute deviation for the data point at 7?

When you find the absolute deviation you find the mean of a data set. 1+4+5+7+8=25. 25 divided by 5 is 5.
That is the mean. Then, we get multiple number out of it, which is the step I don't really get.

(I was trying to solve a problem with 47, 45, 44, 41, and 48. When you add them up, you get 225, and divide it by 5. You get 45. And then, all of a sudden, we have the numbers 2, 0, 1, 4, and 3. Where did we get those numbers? How did we go from 45 to 2, 0, 1, 4, and 3?!)

I'm so confused!
Please explain both problems if you can!
(1 vote)
• Hi!

In the first problem, they are asking for the absolute difference between 7 and the mean. Because the mean is 5...

|7 - 5| = 2

The || (absolute value) guarantees that any operation performed inside it will become positive or stay positive.

To solve for the MAD in the second problem, we need to find the mean of the absolute values of (each data point minus the mean of the original data set). Here is the equation:

For a data set with 47, 45, 44, 41, 48 and a mean of 45,

|47-45| + |45-45| + |44-45| + |41-45| + |48-45| / 5
5 is the amount of numbers in the "new data set" that makes up the numerator

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

2 + 0 + 1 + 4 + 3 / 5

10 / 5 = 2

Hope this helps!😄
• Can you have a MAD less than 1?