# Using all available information

In “real-life” problems, it is not necessary to use all the given data.

My mind goes back eleven years, to the first exam in the Quantitative Methods course at IIMB. The exam contained a monster probability problem. It was so monstrous that only some two or three out of my batch of 180 could solve it. And it was monstrous because it required you to use every given piece of information (most people missed out the “X and Y are independent” statement, since this bit of information was in words, while everything else was in numbers).

In school, you get used to solving problems where you are required to use all the given information and only the given information to solve the given problem. Taken out of the school setting, however, this is not true any more. Sometimes in “real life”, you have problems where next to no data is available, for which you need to make assumptions (hopefully intelligent) and solve the problem.

And there are times  in “real life” when you are flooded with so much data that a large part of the problem solving process is in the identification of what data is actually relevant and what you can ignore. And it can often happen that different pieces of given information contradict each other and deciding upon what to use and what to ignore is critical to efficient solution, and the decision is an art form.

Yet, in the past I’ve observed that people are not happy when you don’t use all the information at your disposal. The general feeling is that ignoring information leads to a suboptimal model – one which could be bettered by including the additional information. There are several reasons, though, that one might choose to leave out information while solving a real-life problem:

• Some pieces of available information are mutually contradictory, so taking them both into account will lead to no solution.
• A piece of data may not add any value after taking into account the other data at hand
• The incremental impact of a particular piece of information is so marginal that you don’t lose much by ignoring it
• Making use of all available information can lead to increased complexity in the model, and the incremental impact of the information may not warrant this complexity
• It might be possible to use established models if you were to use part of the information. So we lose precision for a known model. Not always recommended but done.

The important takeaway, though, is that knowing what information to use is an art, and this forms a massive difference between textbook problems and real-life problems.