Friday, April 7, 2017

Average Problems

Here’s why you shouldn’t walk on escalators is one of the headlines in today’s Times of India.  The report, written by Christopher Mele and originally published in New York Times two days back, is an excellent example of how statistics and mathematics can create imaginary worlds which appear real. 

Take an example.  Suppose a man wants to calculate the average income of people living on Altamount Road in Mumbai.  He will arrive at a figure which will astound almost all the people living there until they realise that Mukesh Ambani’s house, Antilia, is also situated on their road. 

From the New York Times
The researcher in Mele’s report did just that.  Let me simplify the findings.  Imagine yourself in a metro railway station which has escalators. Don’t imagine Connaught Place in Delhi whose escalators are so overcrowded at any time that nobody can even dream of walking up or down any of those escalators.  Imagine a sparsely populated metro station.

There are ten passengers on an escalator.  Two of them are walking up in order to save time while 8 are standing steady for the escalator to reach them atop.  The one who stands still takes 30 seconds to reach the top while the one who walks on the escalator takes 15 seconds.  Now, what’s the average time taken by a random passenger? 

Average time = Total time ÷ Number of passengers.
Total time = (30x8) + (15x2) = 270 seconds
Number of passengers = 8+2 = 10
Therefore, average time = 270÷10 = 27 seconds

Now, imagine 4 passengers are walking and 6 are standing still.  The average time will reduce to 24 seconds.

As the number of walkers increases, the average time will decrease.  Can we then say that the standers lose more time as the number of walkers increases?

The report makes a similar claim.  “When 40% of the people walked, the average time for standers was 138 seconds and 46 seconds for the walkers,” says the report. “When everyone stood, the average time fell to 59 seconds.  For walkers, that meant losing 13 seconds but for standers, it was a 79-second improvement.”  So walkers stand to lose!

Got the logic?  If you didn’t, don’t worry.  Such logic makes up a lot of reality in our world.  For example, economic statistics.  Our government gives us this kind of averages to show how much our economic standard has improved.  And you may be left wondering where the improvement is seen in your personal life.  Now you know where the improvement actually lies.


  1. Did not get the logic as well as the improvement in my personal life as shown by the economic statistics.
    Very nice post.

  2. Law of averages is only helpful to casinos. We can never handle people by that law. And, if we consider it gospel and make rules according to that, we are in for a huge surprise. Which is what today's politicians doing. Blindingly following something, which they don't really understand.

    1. “Statement: A girl and a boy jump into a river. The boy swims over to the girl and says, "God, it's cold."
      Question: What's the probability they will kiss?”
      ― Jenny Downham, You Against Me

      Life's relation to statistics is as good as that :)

    2. Hahahah! Absolutely my thoughts! A statistician is the Rahul Gandhi of science! I'm more of factual data oriented. Statistics is just to present an average picture. Unfortunately, nowadays people treat it as the whole truth!

  3. There is also a theory called wisdom of the crowd. As the opinion of the majority of the crowd tends to a common point the truth shifts towards that point. The outliers at both the extremes cancel each other. Your take? :)

    1. Absolutely. Psychology has a technical term for that crowd wisdom though I can't recall it now. I have seen people standing still on the escalators in Delhi's metro stations until one young lad or lass makes the first move. Once the first move is made many more follow. The crowd mentality is not very visible on escalators because of logistical and other reasons. But it is there.

      Outliers belong to a different category, always. Even if they don't cancel each other, they make little difference in the social behaviours.


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