The Art and Science of Estimations – Part 1

The vast majority of Indian engineers and scientists do not understand the difference between estimation and random number generation!

In this four series tutorial, I’ll teach you a few tools to make correct estimates.

If someone asked you, “How many car mechanics work in Moscow,” what would you say?

When I ask this question in my workshops, I get instantaneous answers ranging from 10,000 to 1,000,000 in less than 5 seconds, indicating that the participants don’t think such problems could be thoughtfully solved and the best one can do is wildly guess.

Whether they are third-year B.E. students, senior scientists in defence, or experienced engineers from multinational companies, their response is the same.

So, how do you guess intelligently?

The trick is to go from known to unknown systematically, making simple assumptions wherever needed.

What does the number of car mechanics depend on? The number of cars. What does the number of cars depend on? The number of people. So, we need to start with estimating the number of people and then proceed.

Assumption 1: So, which city do you know that is similar to Moscow? Moscow must be pretty large (as we hear it along with other large cities). I live in a large city too—Hyderabad. It definitely is not as extensive as Moscow (geographically speaking, Moscow may be more than double the area of Hyderabad). However, as India is far more populous, I would estimate the population of Moscow to be only 50% higher than Hyderabad. Hyderabad has a population of approximately 8 million; hence, Moscow should be around 12 million. (I just checked in Wikipedia and it happens to be 11.5 million! Not bad for a start.) I also assume a family size of 3 in Moscow (Moscow, like New York, must be more nuclear with regard to family size). So, the number of families in Moscow should be about 4 million.

Assumption 2: In Hyderabad, I expect approximately 40% of the families to own cars. I assume that in a super-rich country like the United States, 85–90% of families own more than 1 car. Russia must be somewhere in between, with 70% of families driving 1 to 2 cars. So, this makes the total number of cars equal to 4 million (families) *0.7 (owning cars) *1.5 (number of cars per family) ~4.2 (or 4) million cars.

Assumption 3: My car stays approximately 7 days a year with mechanics. I expect a slightly lower stay time (say, 4 days) for Russians, as I cannot imagine any other country where people drive so rashly as in India, hitting each other and causing accidents! Also, the roads must be better in Russia. This makes a total of 16 million repair days. Assuming that 2 mechanics must attend to one car, this makes 32 million mechanic days.

A typical mechanic works for 250 days per year. So, Moscow needs ~125,000 mechanics (32,000,000/250). Maybe they have 10–15% more than this in reality. So, I would estimate 130–150,000 mechanics. By the way, I am not using a calculator for the math in this problem. Mental math can take you a long way.

I could be off a bit. But if I research enough and refine my assumptions, this approach will bring me very close to the correct answer. The process is simple. Start with assessing what you need to estimate and make simple and reasonable assumptions.

Great engineers make great estimates! I’m baffled as to why such an important skill is not taught in our curriculum. But, believe me, you are expected to have it and use it in the workplace (all the time, you are asked to estimate how long it takes to complete a project or how much the budget is going to be). So, practice estimations.

To see whether you have the hang of it, here are a couple more questions to practice:

  • How many women engineers work in Silicon Valley?
  • How many hotels does Shanghai have?

The exact answer is only partially important. You should nail the process (there may be more than one right path) and know where you are making assumptions.

So, see you next time with a tutorial on how to make estimations where you do not have anything known to relate to the unknown! .

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