The best example that I have heard as a trainer regarding averages and standard deviation is the following:

If one leg of yours is in the oven, and the other in a freezer, on an average you are comfortable. This is a big learning in statistics – the word average makes no sense if the standard deviation is very high. In cricketing language if you see Shahid Afridi and Rahul Dravid, both have an average of 22 and 58. However, Shahid Afridi has a high standard deviation and Rahul has a low standard deviation.

Which means whenever Shahid Afridi goes out to bat, the probability of his getting 22 is NOT AS HIGH as Rahul Dravid getting 58.

However, you need to remember that over the past 20 years, Rahul has an average of 58 and Shahid has an average of 22. So if you believe in regression to the mean, the average will catch up.

The stock market isn’t much different. Over very long stretches, stocks, on average, have returned around say 18% annually. But in any given year–or even over several years–the stock market can diverge markedly from its long-term average. Throughout the prosperous 1978-79 to 2000, for instance, till 2000 the Sensex rose 24% per year. No wonder Sensex was widely called a can’t-miss investments. However, from the year 1990 to the year 2000 the sensex moved from 1000 to 6000 – giving a return of 20% per annum. How has the sensex fared from the year 2000 (at 6000) to the year 2008? The answer can vary from 11% (index 13700) or 17% (index 21000).

I am sure you understand what I mean. The word average makes no sense at all when we talk equities. Equities gyrate, and gyrate like this. So please do not use the word average when talking average.

If you use the word average, it clearly shows you are mathematically challenged and you do not understand the word standard deviation.

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