Skip to main content

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.




Comments

  1. Jyotirmoy SarkarApril 7, 2017 at 10:00 AM

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

    ReplyDelete
  2. RakeshApril 7, 2017 at 11:58 AM

    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.

    ReplyDelete
    Replies
    1. Tomichan MatheikalApril 7, 2017 at 12:07 PM

      “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 :)

      Delete
    2. RakeshApril 7, 2017 at 12:43 PM

      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!

      Delete
  3. Pranju chakrapaniApril 7, 2017 at 12:48 PM

    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? :)

    ReplyDelete
    Replies
    1. Tomichan MatheikalApril 7, 2017 at 8:15 PM

      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.

      Delete
  4. MoonApril 7, 2017 at 9:12 PM

    :D Awesome post!

    ReplyDelete

Post a Comment

Popular posts from this blog

The Adventures of Toto as a comic strip

  'The Adventures of Toto' is an amusing story by Ruskin Bond. It is prescribed as a lesson in CBSE's English course for class 9. Maggie asked her students to do a project on some of the lessons and Femi George's work is what I would like to present here. Femi converted the story into a beautiful comic strip. Her work will speak for itself and let me present it below.  Femi George Student of Carmel Public School, Vazhakulam, Kerala Similar post: The Little Girl
47 comments
Read more

The Little Girl

The Little Girl is a short story by Katherine Mansfield given in the class 9 English course of NCERT. Maggie gave an assignment to her students based on the story and one of her students, Athena Baby Sabu, presented a brilliant job. She converted the story into a delightful comic strip. Mansfield tells the story of Kezia who is the eponymous little girl. Kezia is scared of her father who wields a lot of control on the entire family. She is punished severely for an unwitting mistake which makes her even more scared of her father. Her grandmother is fond of her and is her emotional succour. The grandmother is away from home one day with Kezia's mother who is hospitalised. Kezia gets her usual nightmare and is terrified. There is no one at home to console her except her father from whom she does not expect any consolation. But the father rises to the occasion and lets the little girl sleep beside him that night. She rests her head on her father's chest and can feel his heart...
19 comments
Read more

The Buddha in the Central Vista

Prime Minister Modi was taking a dip in the mineral water pond constructed on the bank of the Yamuna as part of his weekly photo op when Siddhartha Gautama aka the Buddha walked into the office of the National Committee for Correcting Civilizational Narratives (NCCCN) in Central Vista, New Delhi. An email was received by “Dr Sri Siddhartha Gautama Buddha PhD” from the PMO [Prime Minister’s Office] inviting him to attend a meeting “to authenticate and align the curriculum with indigenous perspectives as part of implementing the National Education Policy, NEP.” Siddhartha was amused on receiving the mail. “Is it possible they still wish to learn after proclaiming themselves the Vishwaguru?” He wondered with a wry smile. He was more amused to see the honorary doctorate conferred upon him by the Vishwaguru Vishwavidyala, in Spiritual Sciences. It’d be interesting to make a visit, he decided. When he entered the opulent office, whose floor was paved with Italian marble tiles, he reca...
11 comments
Read more

Sardar Patel and Unity

All pro-PM newspapers carried this ad today, 31 Oct 2025 No one recognised Sardar Vallabhbhai Patel as he stood looking at the 182-m tall statue of himself. The people were waiting anxiously for the Prime Minister whose eloquence would sway them with nationalistic fervour on this 150 th birth anniversary of Sardar Patel. “Is this unity?” Patel wondered looking at the gigantic version of himself. “Or inflation?” Mohandas Karamchand Gandhi chuckled standing beside Patel holding a biodegradable iPhone. “The world has changed, Sardar ji. They’ve built me in wax in London.” He looked amused. “We have become mere hashtags, I’d say.” That was Jawaharlal Nehru joining in a spirit of camaraderie. “I understand that in the world’s largest democracy now history is optional. Hashtags are mandatory.” “You know, Sardar ji,” Gandhi said with more amusement, “the PM has released a new coin and a stamp in your honour on your 150 th birth anniversary.”  “Ah, I watched the function too,” ...
15 comments
Read more

Being Christian in BJP’s India

A moment of triumph for India’s women’s cricket team turned unexpectedly into a controversy about religious faith and expression, thanks to some right-wing footsloggers. After her stellar performance in the semi-final of the Wormen’s World Cup (2025), Jemimah Rodrigues thanked Jesus for her achievement. “Jesus fought for me,” she said quoting the Bible: “Stand still and God will fight for you” [1 Samuel 12:16]. Some BJP leaders and their mindless followers took strong exception to that and roiled the religious fervour of the bourgeoning right wing with acerbic remarks. If Ms Rodrigues were a Hindu, she would have thanked her deity: Ram or Hanuman or whoever. Since she is a Christian, she thanked Jesus. What’s wrong in that? If she was a nonbeliever like me, God wouldn’t have topped the list of her benefactors. Religion is a talisman for a lot of people. There’s nothing wrong in imagining that some god sitting in some heaven is taking care of you. In fact, it gives a lot of psychologic...
13 comments
Read more