Letters to a friend...




THIS PAGE HAS MY WRITINGS FROM MAY TO AUGUST,2005.
MY WRITINGS SINCE THEN ARE POSTED AT:

A Curious Mind W(o/a)nders...- http://ayanwonders.blogspot.com/

Tuesday, May 17, 2005

Misunderstanding the Mean

The account below is fictional and is a piece of the writer's imagination
-
A: On an average, how many hours do you work in office?
B: 9 hrs
A: How many hours have you already put in today?
B: 5 hrs
A: So you'll be free in the evening today, why don't you join me for dinner?
(Office starts at 09:30 hrs, this talk takes place around 14:30 hrs)

Again a misunderstanding of the meaning of 'mean'. If I work for 9 hrs a day on an average and I've worked for 5hrs today, it tells you nothing about how long I'm going to work today till you know the distribution.

As Taleb writes in that delightful book ('Fooled by Randomness'), if the average life expectancy is 72, then does that mean my grandma who's 80 has a life-expectancy of -8....funny eh?
As your age increases, so does the life-expectancy because there are correspondingly people dying younger and 72 is the expected value (p1*X1+p2*X2+....). So if some of the Xs are small and you've lived long, you still have more years to live...how many...for that you need to know how many have died at exactly what ages.

Similarly for you to get an estimate of how long I'm going to be in office today, knowing that I've worked for 5hrs isn't enough (along with the mean and current time). You need to know over what period the mean is being calculated and the time interval for which I have been working on the other days.
And I won't tell you that :-). So probabilities will earn me my freedom from tasteless food and discussion :-).

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