What Happens When Bill Gates Walks Into a Bar

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The mathematician John Allen Paulos in his book Beyond Numeracy writes: “The fourth-grader notes that half the adults in the world are men and half are women and concludes therefrom that the average adult has one breast and one testicle.”

This is a rather extreme example of how the concept of mean or average is misused. An average of X numbers is obtained by adding those numbers and dividing it by X.

Here is another example of a situation where the concept of average is misused.  As Charles Wheelan writes in Naked Statistics—Stripping the Dread from the Data: “Imagine that ten guys are sitting on bar stools in a middle-class drinking establishment…each of these guys earns $35,000 a year, which makes the mean annual income for the group $35,000.”

The software billionaire, Bill Gates, walks into this bar. As Wheelan writes: “Let’s assume for the sake of the example that Bill Gates has an annual income of $1 billion. When Bill sits down on the eleventh bar stool, the mean annual income for the bar patrons rises to about $91 million. Obviously none of the original ten drinkers is any richer. If I were to describe the patrons of this bar as having an average annual income of $91 million, the statement would be both statistically correct and grossly misleading.”

The point being that the average or the mean of a given set of numbers can be very misleading. One thing that clearly comes out of this example is that the majority of the numbers that constitute an average can be lower than the average.

As was clear in this example, ten out of 11 men in the bar had a lower income than the average income of $91 million. Here is another interesting example. As Robert Matthews writes in Chancing It—The Laws of Chance and How They Can Work for You: “The world’s men provide an excellent example – in the shape of their penises. Or, to be more precise, size: according research, the average length is 13.24 centimetres, but the median value is 13.00 centimetres.”

And what is median value? As Paulos writes: “The median of a set of numbers is the middle number in the set.” Let’s go back to the bar example for a moment. Let’s say the eleven individuals in the bar are made to sit in the ascending order of their income. The individual setting on the sixth stool will represent the median income of the group.

Now let’s get back to the penis example. The average length of a man’s penis is 13.24 centimetres. But the median value is 13 centimetres. What does this mean? As Matthews writes: “First, it shows that the global distribution of penis sizes is skewed towards smaller values, and second that most men really do have below-average-sized penises.”

This becomes very important when we are discussing issues like per capita income of a country or the average income earned by a citizen of a country.
The economic health of a nation is also judged by the rise in its per capita income. But should that always be the case? Take the Indian case. A survey carried out by Gallup in December 2013, put India’s median income at $616. Data from the World Bank shows that India’s per capita income during the same year was $1455.

Hence, the median income was around 58% lower than the average income or the per capita income. And that is not a good sign at all. The difference is obviously because the rich (Bill Gates in the example) make substantially more than the poor and drive up the average income. Data from World Bank shows that the top 10% of India’s population makes 30% of the total income.

The point being that economic growth as measured by growth in per capita income is not always the correct way of going about things. Is this growth really trickling down? And that can only become clear if the median income is going up. The tragedy is that no regular data is available on this front.

(Vivek Kaul is the author of the Easy Money trilogy. He can be reached at [email protected])

The column originally appeared in the Bangalore Mirror on April 13, 2016

Mr Jaitley here is why Indians can’t buy a home to live in

Fostering Public Leadership - World Economic Forum - India Economic Summit 2010
Politicians and intellectuals who rarely venture out of their homes in Delhi, seem to have a table top theory to explain everything that is wrong with this country. A favourite theory doing the rounds these days is that India is not progressing because interest rates are too high. And given that, the Reserve Bank of India needs to cut interest rates. Once it does that people will buy homes, cars and what not, and high economic growth will return again. QED.
But is that really the case? Recent data released by the real estate research firm Liases Foras clearly shows that homes in Indian cities are terribly expensive.

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The weighted average price of a flat in Mumbai is Rs 1.34 crore. For Bangalore this stands at Rs 88 lakh and for the National Capital Region at Rs 75 lakh. Nevertheless, this table does not tell us how bad the situation really is. In order to understand that we need to take the per capita income of these cities into account.

The state level economic surveys give out the per capita income of various cities. The only trouble here is that the latest numbers are not available. Hence, in order to account for that I have adjusted these incomes by assuming an average increase in per capita income of 10% per year. (Further, I couldn’t find the average income of Chennai, and hence haven’t taken it into account for making this calculation. Also, for the Mumbai Metropolitan Region I have used the average of the per capita incomes of Mumbai and Thane, respectively. For the National Capital Region, I have used the per capita income of Delhi, and hence the calculation is a little understated to that extent.)

The following table gives the per capita income of five cities in 2014-2015. In order to show how

high the real estate prices are we will basically divide the entries in the first table by the entries in the second table. Hence, we will end up calculating that how many years of current income is needed to buy a flat in a particular city. And the results are very interesting.
It takes 68 years of current income to buy a flat in the Mumbai Metropolitan Region. For Bangalore the number is at an even higher 81.5 years. This seems on the higher side. And there is a reason for it. I have used the per capita income of Bangalore division (which is what I could find in the

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Karnataka Economic Survey of 2013-2014). And Bangalore division includes not just Bangalore but also other places like Kolar, Shimoga, Tumkur etc., where per capita incomes are lower than that in Bangalore.
Even if we assume that per capita income in Bangalore is double the per capita income in Bangalore division, it will take around 40 years of current income to buy a home in Bangalore.
Of the five cities, Pune is the cheapest to buy a home in. But even there is takes close to 32 years of current annual income to buy a home.
Further, home prices continue to remain despite the fact that there is a huge inventory of unsold homes, as the following table from Liases Foras shows us.

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National Capital Region has an inventory of 83 months. What this means is that if the current number of unsold homes is to be sold, it would need nearly 83 months or around seven years for that to happen. One reason for the unsold inventory is that most builders are not interested in developing affordable homes. Everyone wants to cater only to the richer segment of the population.
Also, the tables clearly prove that high interest rates are really not why people are not buying homes. They are not buying homes because homes are very expensive. Fresh home loans can be got these days at anywhere between 10-11 percent. Assuming this interest rate where to fall in the days to come, how much difference would it make? Would people buy homes?
Let’s understand this through an example of an individual who wants to buy a home in Hyderabad. As mentioned earlier the average price of a home in Hyderabad is Rs 75 lakhs. The individual puts in a downpayment of Rs 15 lakh (20% of the value of the home) and takes a home loan of Rs 60 lakh at 10 percent to repaid over 20 years. On this the EMI would work out to around Rs 57,900.
If the interest rates were to fall to 9 percent, the EMI would fall to around Rs 54,000. So, would the individual now buy a home just because the EMI will be around Rs 4,000 per month lower? Unless, home prices fall and builders start concentrating a little more on affordable housing, lower EMIs are not going to help.
This is something that Jaitley and others of his ilk operating out of Delhi, need to realize. To conclude, if Jaitley, the quintessential dilli-wallah, had asked one of his IIT educated babus to do some basic number crunching, he wouldn’t be saying the silly thing that he did.

The article was originally published on Nov 6, 2014 on www.FirstBiz.com 

(Vivek Kaul is the author of the Easy Money trilogy. He tweets @kaul_vivek