mean absolute deviation following, absolute

smartpants

hello
i m stuck with MAD
calculate the MAD for the following set over the last 6 years
4%, 1%, 8%, 10%, 3% ande 15%
it will appreciate if any one will tell me the steps to calculate MAD on BA 2 plus professional
regards

stockjaguar

There is no specific way to do it with the BAII plus calculator, you simply need to know the formula and go from there.
MAD = SUM [(X - Mean)]/N
The difference with MAD is that if for example your expected return/mean was 5% and you had a return of 4% thus equaling (4-5 = -1), you would then reverse your given answer from a negative to positive, in this case equaling 1. There are no negatives when using MAD.
Your ER = 6.8, lets use 7 instead.
= (4-7) + (1-7) + (8-7) + (10-7) + (3-7) + (15-7) / 6
= -3 + -6 + 1 + 3 + -4 + 8 / 6
= 3 + 6 + 1 + 3 + 4 + 8 / 6 (This is where you make any negative into a positive)
= 25/6
= 4.16 (may be a bit more as I rounded the mean to 7)

sabaruch

thank you so much for your help
1 question…whats the logic behind replacing all the negetive figures into positive?

Viceroy

MAD is exactly what it sounds like–MEAN (meaning average) ABSOLUTE (absolute value being a positive number, by definition) DEVIATION (how much it changes from the “benchmark”–here, the average).
So to find Mean Absolute Deviation, first get a simple average of the data points.  (Somebody said it was 6.8.  I’ll go with that.)
Then, take the difference between #1 and the average.  Write that down.  (4-6.8 = 2.8)  2.8 is a positive number, because it is 2.8 units away from the mean.  We don’t care if it’s +2.8 or -2.8.  The fact is–it’s 2.8 units away from the mean.
Then, take the difference between #2 and the average.  Write that number down.  (1-6.8 = 5.8)  Again, 5.8 is a positive number.
Once you have found the absolute values of the differences between the data points and the mean, simply average them to get the MEAN ABSOLUTE DEVIATION.
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BTW–don’t spend more than about five minutes on this.  I’ll be surprised if it shows up on the test.  For the exam (and in real life) nobody uses MAD for anything.  It’s all about Standard Deviation.
You DO need to spend significant time on Standard Deviation.  If you don’t know how to calculate a variance and standard deviation, then don’t waste a precious First Saturday in June, because you’ll never finish the CFA exam.

Carson

^I don’t really know myself.  I think the point of StDev is to “punish” those that are further away from the mean.  That is, a deviation of 20 should be “punished” more than 10 deviations of 2.
And facts being what they are–other than one part of one paragraph in Level 1, you’ll probably NEVER see MAD again in the CFA curriculum.

CFA4Techie

This is one of the classic examples where people who are math-savvy can intuitively understand the concept where most others have a hard time grasping the idea (even if they “understand” the forumla, it’s hard for them to remember for the exam).
A lot of people find statistics very challenging (esp when it comes to time series), but it’s one of the easier topics for me ^_^
NANA