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
44 comments
Read more

The Rebellion of Christmas

One of the biggest ironies of Buddhism is that Buddha never endorsed the belief in God as done by organised religions but he ended up becoming one such God. Buddha did not advocate for prayer in the sense of appealing to a divine entity for favours or intervention. But his followers of today seem to be giving undue importance to rituals and offerings. Something similar happened to Jesus and his teachings too. Jesus was trying to reform his religion, Judaism, by making it more humane. He wanted to redeem Judaism from its meaningless rituals and displays of devotion . Religion is meaningless and even dangerous unless it touches the believer’s heart and transforms it. Jesus was not interested in the rubrics and the regulations prescribed by the priests of his religion. His primary concern was love and relationships. What good is religion unless it helps you to love your fellow human beings? “If anyone says ‘I love God’ and hates his brother, he is a liar,” Jesus’ beloved disciple Jo...
10 comments
Read more

Koorumala Viewpoint

  Koorumala is at once reticent and coquettish. It is an emerging tourist spot in the Ernakulam district of Kerala. At an altitude of 169 metres from MSL, the viewpoint is about 40 km from Kochi. The final stretch of the road, about 2 km, is very narrow. It passes through lush green forest-looking topography. The drive itself is exhilarating. And finally you arrive at a 'Pay & Park' signboard on a rocky terrain. The land belongs to the CSI St Peter's Church. You park your vehicle there and walk up a concrete path which leads to a tiled walkway which in turn will take you the viewpoint. Below are some pictures of the place.  From the parking lot to the viewpoint The tiled walkway A selfie from near the view tower  A view from the tower Another view The tower and the rest mandap at the back Koorumala viewpoint is a recent addition to Kerala's tourist map. It's a 'cool' place for people of nearby areas to spend some leisure in splendid isolation from the hu...
30 comments
Read more

Remedios the Beauty and Innocence

  Remedios the Beauty is a character in Gabriel Garcia Marquez’s novel, One Hundred Years of Solitude . Like most members of her family, she too belongs to solitude. But unlike others, she is very innocent too. Physically she is the most beautiful woman ever seen in Macondo, the place where the story of her family unfolds. Is that beauty a reflection of her innocence? Well, Marquez doesn’t suggest that explicitly. But there is an implication to that effect. Innocence does make people look charming. What else is the charm of children? Remedios’s beauty is dangerous, however. She is warned by her great grandmother, who is losing her eyesight, not to appear before men. The girl’s beauty coupled with her innocence will have disastrous effects on men. But Remedios is unaware of “her irreparable fate as a disturbing woman.” She is too innocent to know such things though she is an adult physically. Every time she appears before outsiders she causes a panic of exasperation. To make...
4 comments
Read more

Christmas Hijacked

Has Christmas been hijacked by Santa Claus and his snow cap? And also by plastic? This is a concern raised by a friend who is also a Catholic priest. Watching the Christmas celebrations around me in the last few days in various places – religious as well as secular – I know my friend’s concern is genuine. Christmas has been “Caesarianized,” he says. The spiritual preparation during the Advent season has given way to Santa Claus and his jingle bells. To discount sales in shopping malls. What’s worse, various Christian organisations send out carol teams on floridly decorated open vehicles equipped with high decibel loudspeakers that shatter all the peace while blaring out carols on ‘Peace to people with goodwill.’ It is a Christmas without Jesus. Santa Clauses tower far above the diminutive figure of infant Jesus, if the latter is there at all in the carol teams and other celebrations. Look at any commercial brought out during the season and you will think that Christmas is all abo...
12 comments
Read more