Question

How to calculate mean, variance from meadian absolute deviation

Answer 1

In calculating the mean variance from median absolute deviation you can use this formula;

MAD = median(| x - median(x)|)

where x represents the collection of numbers.
Steps:
First, find the median of x
Then, subtract this median from each value in x
Then, take the absolute value of these differences
Find the median of these absolute differences

Example.

First, the 9 scores are 83, 83, 84, 85, 85, 86, 86, 83, and 86.
©The mean of these scores is the sum 761 divided by 9. The mean is 84.6.
©The deviation is a measure of how each score differs from some average. To
calculate the standard deviation , we take each score and subtract the mean from it.
This gives
83-84.55556 =-1.5556
83-84.55556=-1.5556,
84-84.55556=-0.5556,
85-84.5556=0.4444,
85-84.5556=0.4444,
86-84.5556=1.4444,
86-84.5556=1.4444,
83-84.5556 -1.5556,
86-84.5556=1.4444.
The next step
in calculating the standard deviation is to square these differences:
2.4198, 2.4198, 0.3086, 0.1975, 0.1975, 2.0864, 2.0864, 2.4198, and
2.0864.
We add these positive numbers to get 14.2222. Then, we divide by 9
to get 1.5802. This is the mean of the squared differences.
The last step is to take the square root. This gives us 1.2571, which
is the standard deviation.