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Of Media and Mathematics

How mathematics is used incorrectly in the media, which leads to the formation of erroneous notions

One of the perils of growing up in erstwhile Bihar, in the mid to late 1990s, was that a three- year graduation degree used to take four years. And so, I ended up taking four years to complete a degree in mathematics.

Also, some of the subjects taught seemed so disconnected with the real world, maybe because of the way they were taught more than anything else, that one just mugged up and wrote the exams. Hence, the chances of ever retaining anything were simply not there.

This makes me sad because I actually love the subject despite the lousy teachers I have had over the years.

Though I do remember some of the mathematics that I was taught before and in the tenth standard, the general mathematical skills of most people are not very good. I might be generalising here but that's what I have observed.

This lack of mathematical skills shows up in the media all the time. Indeed, extremely basic mathematical mistakes are made while reporting news. Take the recent case of the West Indies team pulling out of a cricket tour to India. A Mumbai Mirror report pointed out that "WICB [West Indies Cricket Board] officials and team management told Mirror that the dispute is over payments to the players. A senior West Indian player said the board has cut each player's fee by over 75 per cent and in some cases by even 1,000 per cent, though we do not know how that is possible."

The question here is how someone's fee can be cut by 1,000 per cent. Any fall in fee cannot go beyond zero. If a cricketer was being paid $100,000 and his fee was cut to zero dollars, it would be a fall of 100 per cent. If a cricketer was making a million dollars and his fee was cut to zero dollars, it would "still" be a fall of 100 percent. On the flip side, a rise in fee can be infinite.

In fact, there have been other instances also where a newspaper has fallen victim to such a basic mathematical error. The Economic Times, the largest-read business newspaper in the country, published a report in January 2012, in which it said "Network18's market cap is down 171.57 per cent since January 5, 2009 while TV18's has fallen 560.23 per cent in the same period."

Like a fee, how can the market capitalisation of a company fall more than 100 per cent?

These were rather basic mistakes. Let's now look at a slightly more complicated mistake that mathematician Jordan Ellenberg discusses in How Not to Be Wrong: The Hidden Maths of Everyday Life.

He shares an example about the Republican Party of Wisconsin issuing a new release in June 2011, which talked about how half of the total new jobs generated in the United States that month came from the state of Wisconsin.

The state of Wisconsin had managed to generate 9,500 jobs during the month and the United States as a whole had managed to generate only 18,000 jobs. Hence, the conclusion was drawn that Wisconsin had generated 50 per cent of the jobs in the United States.

This seems quite straightforward. What is wrong here? Ellenberg explains this through an example of a coffee shop. As he writes, "For example, say, I run a coffee shop. People, sad to say, are not buying my coffee; last month I lost $500 on that part of my business. Fortunately, I had the prescience to install a pastry case and a CD rack, and those two operations made $750 each."

Hence, the coffee shop made $1000 in total ($750 it made from the CD rack plus $750 it made from the pastry case minus the $500 it lost on selling coffee).

So 75 per cent of the profit came from the pastry case. Nevertheless, it is equally correct to say that 75 per cent of the profit came from the CD rack. As Ellenberg writes "Imagine I'd lost $1,000 more on coffee, then my total profits would be zero, infinity percent of which would be coming from pastry!" And that would be absurd.

Now let's get back to the job example. Wisconsin created 9,500 jobs in June 2011. But Minnesota created more than 13,000 jobs during the same month. Does that mean that Minnesota created 72 per cent of the jobs during the month? And Wisconsin created 50 per cent? And the two states together created 122 per cent of the jobs?

It needs to be pointed out here that states like California, Michigan, Texas and Massachusetts created even more jobs. So, many states created more jobs than Wisconsin did.

Nevertheless, the overall US economy created only 18,000 jobs because jobs were lost in other states. As Ellenberg puts it, "In fact, what was going on is that job losses in other states almost exactly balanced out jobs created in places like Wisconsin, Massachusetts, and Texas."

Hence, it is not right to talk about percentages when numbers may be negative, because they lead to results which might seem correct but which are actually absurd.

These examples dealt with basic mathematical mistakes. Then there is also the case of people using numbers to justify things which aren't really true. Stock market experts are an excellent example of the same. Mathematician John Allen Paulos makes this point in A Mathematician Reads the Newspaper.

As he writes, "Almost never does a stock pundit say that the market's or a particular stock's activity for the day or the week or the month was largely a result of random fluctuations." And he manages to make himself sound impressive by throwing a wealth of data at the audience.

"The business pages, companies' annual reports, sales records, and other widely available statistics provide such a wealth of data from which to fashion sales pitches that it's not difficult for a stock picker to put on a good face...All that's necessary is a little filtering of the sea of numbers that washes over us," writes Paulos. And this leaves us impressed.

To conclude, it's worth remembering these tricks and being aware of the mathematical mistakes and tricks that make their way into the mainstream media.

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

This column appeared in the January 2015 Issue of Mutual Fund Insight.