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## Statistics and probability

### Course: Statistics and probability>Unit 3

Lesson 8: Other measures of spread

Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set. Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are.

## Want to join the conversation?

• I still don't get how to find the MAD, can anyone pls help me
1. finding the mean(average) of the set of numbers
2. find the distance of all the numbers from the mean.
3. Find the mean of those numbers.
• Wait, so we have to find the mean and then the absolute value right?
• Is there an easier way to calculate MAD? So much writing!
• Well, we can solve the writing problem by doing mental math, but we can't solve the easy way part.
• Is this different from standard deviation? I find that I get different answers from both, but they seem like the same concept. Can you please explain the difference and purpose of each?
• The difference between this and standard deviation is that, in standard deviation you are squaring the sum of all the numbers that deviate from the mean; in MAD you don't (you simply divide the sum/# in sample)
(1 vote)
• but how do you do these things and not get them wrong:{
• There are a lot of calculations and it's easy to get one wrong.
Be patient, take your time, and never assume you got it right on your first try.
• I am so confused. Can someone explain how to find the MAD?
• There was a distinction made between a sample variance/standard deviation and a population variance/standard deviation. The population variance is calculated by taking the sum of the squared deviations from each data point to the population mean, and then dividing by the number of data points in the population. On the other hand, the sample variance goes through the same process as above, except it's with respect to the sample mean, and you should also divide by one less than the number of data points in your sample, to correct the bias (Bessel's Correction). I'm wondering if a similar notion exists for the Mean Absolute Deviation (MAD)? In other words, whether it's a sample or population we're dealing with, is there any significant difference in the way that the MAD is calculated for either of them?
• I still don't under stand how you come up with the two different data sets do I split my data in half?
• Sal uses two completely different data sets to show how MAD describes the variability of a single data set.
2,2,4,4 - number of donuts I ate each of the last four days
1,1,6,4 - number of times I scored in my last four soccer games
Both data sets have a mean of 3. On average, I eat 3 donuts a day, and score 3 goals per game [I wish].
The MAD of the donut data is 1, showing that I am pretty consistent on eating donuts. The average day is 2 to 4 donuts (1 donut more or less than 3).
However, The MAD of the soccer data is 2, showing that there is more variability in my goal scoring. An average game is 1 to 5 goals (2 goals more or less than 3).