Monday, February 28, 2011

85% of Statistics Are Made Up On The Spot

I had a good chuckle the other day when I was caught by an example of numerical illiteracy on the part of at least two people: an author and an editor. I had to share.

I was flying with Air Asia from Banda Aceh, Indonesia to Kuala Lumpur, Malaysia. The in flight magazine isn't exactly high production value, as the airline is all about saving. Consider Air Asia to be the Ryan Air of the East. Anyways, here's the tasty treat now:

I can take no issue with the first section on young billionaires as it was actually quite interesting. In the second section, I am entertained by the translation of $122.1k GDP per capita to an average income of about $120,000 per year. Taking the crown though, was the gem at the bottom.

"72% of the 14.5 million population in Mali, Western Africa, earn about $0.003 a day with the average worker's salary of only US$1,500 per year!" Now what is that supposed to mean?

Before you reach for your calculator I can tell you that $0.003/day = $1.10/year.
Also I can tell you that 72% of 14.5 million = 10.44 million.
And that (10.44 million people * $1.10 per person per year ) / $1,500 per worker per year = 7656 workers.
And that 7656/10.44 million = 0.07% employment.

Curiously I can't quite determine what I think they were going for. Anything I try to explain the numbers I see gets destroyed anyway by the strange "72% of 14.5 million". According to Wikipedia, only 43.51 million out of the 81.76 million people in Germany are employed. I suppose I could say that 53% of Germans earn about $0 per day. By adding a dash of real workers I could make that figure $0.003.

Please comment and speculate.

Sunday, February 27, 2011

Faking It On Your Wedding Day

Earlier this month we wrote about our love of podcasts and just last week I was listening to Japan: A Friend In Need from the BBC Documentaries Archive. Here I was in the month of love, listening to a podcast on the subject and I found math in an unexpected place.

The documentary is about an agency in Japan that supplies fake people, or actors I suppose. In particular, this agency will supply people to fill out your side of a wedding. In the given example, we met a young man whose parents were deceased and his siblings were astranged, such that he only had two friends to attend his wedding. So as to keep up appearances, unbeknownest to the bride, he hired parents, friends and relatives. All told, 30 people at his wedding were fake, costing him something like £3,000, equal to his recent redundancy compensation.

The agency claims never to have been caught, and they say that they "research their assignments assiduously", but it got me wondering just how long you could operate such a service without getting caught. How many weddings could you do before a repeat guest noticed that they had seen one of your actors at a wedding before?

The first wedding is simple, and guaranteed to go off without a hitch, but what about the second? Suppose every wedding has on average 30 guests from each family. In the second wedding we need all 30 people to not be from the 30 in the previous wedding. Still pretty easy in a country of 127 million. But what about the 30th wedding when there are 900 previous guests out there in the population? Things are still looking pretty good, but the probabilities are starting to pile up in a similar way to the phenomenon that means that in a group of 23 people there's a 50% chance that two will have the same birthday.

So given a constant wedding size of 60, 30 real and 30 fake, what is the probability that this is the wedding that breaks us? This is the same as the probability that one or more of today's guests attended a previous wedding. This is the same as one minus the probability that none of today's guests attended a previous wedding. For wedding n and a population p:
Assuming 127 million people in Japan...
  • For wedding 1, it's a sure bet as nobody has attended a previous wedding.
  • For wedding 2, we face only a 0.0011% chance of getting caught.
  • Even for wedding 100 our risk is only a 0.11% chance. No problem!
But wait, the above probabilities are conditional probabilites. Our chance of getting caught at wedding 100 given that we got to wedding 99 is 0.11%. What is our chance of getting to wedding 99? This is the the probability that we didn't get caught in one or more of the previous weddings, the probability of a perfect record. Mathematically our chance of getting to and past wedding n is:
  • For wedding 1, it's a sure bet.
  • For wedding 2, it's 99.99%
  • For wedding 100, it's 94.58%.
  • For wedding 500, it's 24.57%.
Even though by the time we get to wedding 500, ony 15,000 people in Japan have been to weddings with our staff, we would be lucky to have made it that far.

If we started this agency today, on average how long can we expect to go before we get caught? Now I'm not going to bother expressing that mathematically, but hacking at it with Excel numerically, I can tell you that it comes to roughly 374. If we were to start such an agency today under such conditions and such assumptions, we would on average expect to do 374 weddings before getting caught.

So I think the moral of the story is, if you're looking to hire fake people for your wedding, you're doing alright, but if you're looking to run a business doing it, you might want to reconsider. Then again, if we're looking for morals in this story, honesty might come first.

Monday, February 7, 2011

I heart smartphones and podcast favourites

I heart smartphones. It is the symbol of the new world, where the world is at your finger tips, and, in your pocket! There is so much information out there, digesting it is a big quest. I'd love to have the time to sit down and browse the net for a couple hours every day to catch up on all the news and events, but now I can do all this while on the move.

I am an owner of an HTC Hero on Android. It is the only digital device I carry in my hand bag (other than my obligatory work phone). Living in a busy city like London means I spend a fair amount of time in transit. If you are a Google fan like me, then Google Reader and Google Listen would be your good friends. My favourite activity during transit when I'm not walking about, is to catch up on the news and my favourite blogs through the RSS reader. My favourite activity during transit when I am walking about, is to plug into one of the following podcasts, which keeps me informed and entertained. If this is not optimising your time, then I don't know what would. I guess the next step is to jog to work while listening to podcasts: information downloading and calorie offloading all at once!

  • LSE lecture and events: London School of Economist half hour to hour long lectures or guest speakers plus Q&A session (frequent publishing of events)

  • The Economist: I like the magazine, but there is so much content to digest. The podcasts do a great job summarising the highlights (weekly publishing or more frequent ones available too)

  • NPR News: short bursts of news that keeps me informed of the North American highlights (hourly publishing)

  • Science of Better: Operations Research podcasts/interviews by INFORMS (monthly publishing)

  • More or Less: BBC radio programme making sense or debunking the numbers behind the news

  • Freakonomics: spin off by the authors of the ever so popular Freakonomics book/movie/blog/etc.

What are some of your favourite podcasts?

Aside from being my RSS reader and podcast player, my smartphone is also my:
- phone (first and foremost)
- email
- calendar
- access to the internet
- Skype to call anyone around the world
- instant messaging to keep in touch with friends
- handy document storage
- camera / video cam
- GPS and compass
- maps (offline maps too)
- ebook reader
- notebook (takes my hand scribbling too)
- news reader
- scanner
- games when I'm bored waiting in a queue somewhere
- MP3 player
- all the other things that come with a phone (alarm clock, calculator, voice recorder, etc.)
- and thousands of other applications available for download (often for free) that keep my life organised and what not