Answer:
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:
\text{MAD}=\dfrac{\sum{\lvert x_i-\bar{x} \rvert}}{n}MAD= ∑∣ xi -x /n
start text, M, A, D, end text, equals, start fraction, sum, open vertical bar, x, start subscript, i, end subscript, minus, x, with, \bar, on top, close vertical bar, divided by, n, end fraction
Example
Erica enjoys posting pictures of her cat online. Here's how many "likes" the past 666 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.
\text{mean}=\dfrac{96}{6}=16
mean= 96/6=16
start text, m, e, a, n, end text, equals, start fraction, 96, divided by, 6, end fraction, equals, 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.
\text{MAD}=\dfrac{16}{6}\approx2.67MAD=
MAD=16/6 =2.67 Likes
On average, each picture was about 333 likes away from the mean.