I've learned how to find out the answers of variances, deviations, MADs. But, I don't understand what are these answers "saying", they're meaningless to me. Can anyone tell me what are these answers about?

Range, MAD, variance, and standard deviation are all measures of spread. They tell you how spread out the data are. Data that are very similar will have a small spread, whereas data that are wildly different from each other will have a large spread. Range and MAD are very basic measures. Since the variance takes the square of each deviation, large deviations (>1) will cause the variance to become very large indeed.

Why is the MAD a part of so many everyday activities (Grocery store sales, average daily likes for a clip, etc.), but it isn't actually used everyday?

It is so you can relate to what happens and aren't drowning in aerospace technicalities while learning statistics. While you would not actually calculate the MAD for fun, it is just so you have a bit more interest, as just having a set like Data Set A: [#, #, #, #] would make people even more bored than how often the likes on a cat video differ.

what is the difference between mean absolute deviation and variance?

Mean absolute deviation is the average of the *deviations* from the mean. Variance is the average of the *squared deviations* from the mean.

what does the like E shaped symbol means in the above rule?

∑ is the Greek capital letter sigma, and represents a sum. Sal explains the sigma notation here: www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/sigma-notation-sum Notice that in the video, Sal says we need to define an index. In this case the index isn't explicitly stated, instead it's to be understood that we sum over 𝑖 as it goes from 1 through 𝑛, and if we were to write the sum out it would look like this: MAD = (|𝑥₁ − 𝑥̅| + |𝑥₂ − 𝑥̅| + |𝑥₃ − 𝑥̅| + ... + |𝑥_𝑛 − 𝑥̅|)∕𝑛

Ok, I'm a pretty fast learner and I even answer questions, but what is the formula in plain English? I always write formulas on sticky notes so I understand and remember them but I can't find a way to simplify the formula! HALP Thank you in advance ~Green Bear

Hey um I had this question in class and I had no idea how to do it: *For which class would mean be a better indicator of a test score in the class* Class A, Mean: 85.2%, MAD: 14 Class B, Mean: 85.2%, MAD: 2 pls help

Class B, because the data points are closer together.

Main content

Statistics and probability

Course: Statistics and probability > Unit 3

Lesson 8: Other measures of spread

Mean absolute deviation (MAD) review

Google Classroom

Mean absolute deviation

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

Here's how to calculate the mean absolute deviation.

Step 1: Calculate the mean.

Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

Step 3: Add those deviations together.

Step 4: Divide the sum by the number of data points.

Following these steps in the example below is probably the best way to learn about mean absolute deviation, but here is a more formal way to write the steps in a formula:

MAD = \frac{\sum | x_{i} - \bar{x} |}{n}

Example

Erica enjoys posting pictures of her cat online. Here's how many "likes" the past

6

pictures each received:

10

15

15

17

18

21

Find the mean absolute deviation.

Step 1: Calculate the mean.

The sum of the data is

96

total "likes" and there are

6

pictures.

mean = \frac{96}{6} = 16

The mean is

16

Step 2: Calculate the distance between each data point and the mean.

Data point	Distance from mean
$10$ ‍	$\| 10 - 16 \| = 6$ ‍
$15$ ‍	$\| 15 - 16 \| = 1$ ‍
$15$ ‍	$\| 15 - 16 \| = 1$ ‍
$17$ ‍	$\| 17 - 16 \| = 1$ ‍
$18$ ‍	$\| 18 - 16 \| = 2$ ‍
$21$ ‍	$\| 21 - 16 \| = 5$ ‍

Step 3: Add the distances together.

6 + 1 + 1 + 1 + 2 + 5 = 16

Step 4: Divide the sum by the number of data points.

MAD = \frac{16}{6} \approx 2.67

likes

On average, each picture was about

3

likes away from the mean.

Want to learn more about mean absolute deviation? Check out this video.

Practice problem

The following table shows the number of lemons that grew on Mary's lemon tree each season.

Season	Number of lemons
Winter	$3$ ‍
Spring	$15$ ‍
Summer	$21$ ‍
Fall	$13$ ‍

Find the mean absolute deviation (MAD) of the data set.

lemons

Want to practice more problems like these? Check out this exercise.

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Hann
Posted 5 years ago. Direct link to Hann's post “I've learned how to find ...”
I've learned how to find out the answers of variances, deviations, MADs. But, I don't understand what are these answers "saying", they're meaningless to me. Can anyone tell me what are these answers about?
Button navigates to signup pageComment on Hann's post “I've learned how to find ...”
(10 votes)
Answer
- Greg
  Posted 5 years ago. Direct link to Greg's post “Range, MAD, variance, and...”
  Range, MAD, variance, and standard deviation are all measures of spread. They tell you how spread out the data are. Data that are very similar will have a small spread, whereas data that are wildly different from each other will have a large spread.
  
  Range and MAD are very basic measures. Since the variance takes the square of each deviation, large deviations (>1) will cause the variance to become very large indeed.
  Button navigates to signup page
  (11 votes)
Carlos Kieliszewski
Posted 7 years ago. Direct link to Carlos Kieliszewski's post “Why is the MAD a part of ...”
Why is the MAD a part of so many everyday activities (Grocery store sales, average daily likes for a clip, etc.), but it isn't actually used everyday?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- h.khanacademy.user
  Posted 6 years ago. Direct link to h.khanacademy.user's post “It is so you can relate t...”
  It is so you can relate to what happens and aren't drowning in aerospace technicalities while learning statistics. While you would not actually calculate the MAD for fun, it is just so you have a bit more interest, as just having a set like Data Set A: [#, #, #, #]
  would make people even more bored than how often the likes on a cat video differ.
  Button navigates to signup page
  (6 votes)
Rajat
Posted 3 years ago. Direct link to Rajat's post “_*What is Sample MAD*_ Sh...”
What is Sample MAD
Should we use the concept of dividing by n-1 for calculating the Mean Absolute Deviation of a Sample Data too? Why in the formula above in this article divides the sum of differences of individual data points from the sample mean by n, not n-1?
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(4 votes)
Answer
dena escot
Posted 7 months ago. Direct link to dena escot's post “what is the difference be...”
what is the difference between mean absolute deviation and variance?
Button navigates to signup pageComment on dena escot's post “what is the difference be...”
(3 votes)
Answer
- ANB
  Posted 5 months ago. Direct link to ANB's post “Mean absolute deviation i...”
  Mean absolute deviation is the average of the deviations from the mean. Variance is the average of the squared deviations from the mean.
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  (3 votes)
Juliepotatoe83
Posted 4 years ago. Direct link to Juliepotatoe83's post “How can you tell if a dat...”
How can you tell if a data set is more widespread or clustered based off of the MAD?
Button navigates to signup pageComment on Juliepotatoe83's post “How can you tell if a dat...”
(3 votes)
Answer
OJBear
Posted 3 years ago. Direct link to OJBear's post “Ok, I'm a pretty fast lea...”
Ok, I'm a pretty fast learner and I even answer questions, but what is the formula in plain English? I always write formulas on sticky notes so I understand and remember them but I can't find a way to simplify the formula! HALP

Thank you in advance

~Green Bear
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(1 vote)
Answer
- green_ninja
  Posted 3 years ago. Direct link to green_ninja's post “Hi! Here's the written-o...”
  Hi!
  
  Here's the written-out version of the formula:
  
  (|x1 - mean| + |x2 - mean| + ... + |xn - mean|) / n
  
  In words, MAD is the mean of the absolute values of (each data point minus the original mean).
  
  Hope this clears things up!😊
  Comment on green_ninja's post “Hi! Here's the written-o...”
  (5 votes)
Aditi
Posted 9 months ago. Direct link to Aditi's post “Hey um I had this questio...”
Hey um I had this question in class and I had no idea how to do it: For which class would mean be a better indicator of a test score in the class

Class A, Mean: 85.2%, MAD: 14
Class B, Mean: 85.2%, MAD: 2

pls help
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Lucas
  Posted 6 months ago. Direct link to Lucas's post “Class B, because the data...”
  Class B, because the data points are closer together.
  Comment on Lucas's post “Class B, because the data...”
  (4 votes)
Marvin M. M. Museum
Posted a year ago. Direct link to Marvin M. M. Museum's post “i used to think MAD was t...”
i used to think MAD was the same as the mean... i was probably getting many questions incorrect haha
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(2 votes)
Answer
gheed msw
Posted 3 years ago. Direct link to gheed msw's post “what does the like E shap...”
what does the like E shaped symbol means in the above rule?
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(2 votes)
Answer
- Jerry Nilsson
  Posted 3 years ago. Direct link to Jerry Nilsson's post “∑ is the Greek capital le...”
  ∑ is the Greek capital letter sigma, and represents a sum.
  
  Sal explains the sigma notation here:
  https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/sigma-notation-sum
  
  Notice that in the video, Sal says we need to define an index.
  In this case the index isn't explicitly stated, instead it's to be understood that we sum over 𝑖 as it goes from 1 through 𝑛,
  and if we were to write the sum out it would look like this:
  MAD = (|𝑥₁ − 𝑥̅| + |𝑥₂ − 𝑥̅| + |𝑥₃ − 𝑥̅| + ... + |𝑥_𝑛 − 𝑥̅|)∕𝑛
  Comment on Jerry Nilsson's post “∑ is the Greek capital le...”
  (2 votes)
Jonathan
Posted 2 years ago. Direct link to Jonathan's post “what sort of situations c...”
what sort of situations could we use mad in?
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(2 votes)
Answer
- Simran
  Posted 2 years ago. Direct link to Simran's post “The mean absolute deviati...”
  The mean absolute deviation (MAD) is the mean (average) distance between each data value and the mean of the data set. It can be used to quantify the spread in the data set and also be helpful in answering statistical questions in the real world.
  Many professionals use mean in their everyday lives. Teachers give tests to students and then average the results to see if the average score was high, in between, or too low. Each average tells a story. Absolute deviation can further help to see the distance between each of the scores and the beginning average scores, since A small mean absolute deviation tells us that most of the data values are very close to the mean (since the expected distance from each data value to the mean is small).
  Got from Google. I am no expert.
  But I hope this helps!
  Button navigates to signup page
  (1 vote)