# Physics of Poverty: Who cares about the average income?

March 13, 2011, Updated on : Thu Sep 05 2019 07:31:23 GMT+0000
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Read Dr. Tara's previous post on It's not a Pyramid before reading this column, as both are interrelated.

Apparently this last year the per capita income of Indians increased to Rs. 46,492 per year. That’s Rs. 3874 (\$85) per month. Glory days! The ‘average’ Indian is no longer living in ‘poverty’. But really, per capita income is an average and who cares about the average income when the average Indian hardly exists. The distribution of income is highly skewed and looks like this (see my last related post ‘It’s not a pyramid’). You can see where that places the average.

Yet when we think of an average we make certain assumptions about the spread or distribution of the values that go into this number. If you say the average height of people in India is around 5’ 5” with a standard deviation of 5”, it’s pretty intuitive what that means – that when you arrive in India you will find most people around 5’5” with about 5 inches variation this way and that. In large part it means that we all look similar and can fit in the same seats, sleep on the same size beds and fit through the same doorways. So if we hear that the average height of Indians has increased, we think immediately that we are collectively growing taller as a population and not that a small group of freak giants suddenly emerged. Similarly, reports of an increase in the average income suggest to us that we are collectively better off. Are we?

Now instead, imagine if the distribution of heights was not a bell curve but looked like the distribution of income in the picture above. What this would mean is that most people are less than a foot tall (at the base) while a few are absolutely enormous giants of 50 to 100 feet (in the point) with the rest somewhere in between. In this scenario there is no one size fits all and it would be impossible for a randomly selected group to be comfortable sitting at the same sized table. The enormous giants the height of multi-storey apartment buildings would have to live in a different sort of world of much larger proportion where they could barely see the underfoot base scurrying around lest they get unwittingly crushed. The average height in this distribution would still be around 5’5” but knowing this average, and even the standard deviation, would be completely uninformative. A single giant of 100’ might raise the average by a few feet. Similarly a single person with an annual income of 2.5 Crores among a million people earning just Rs.21,500 per year (below that arbitrary poverty line of \$2/day) would give you that per capita income figure of Rs. 46,492.

So if you knew nothing about India and you wondered what single number would best prepare you for the economic landscape, average or per capita income is really quite uninformative. Rather If you knew the exponent that described how fast the point tapers, or better still, had a good visual of the distribution, you would come prepared to find Mukesh Ambani in a 27 storey house on Altamount road surrounded by millions of abysmally poor people with barely a roof over their heads (and some of everything in between).

Really, who cares about the average income!

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