How to answer the estimation question in an interview

How to answer the estimation question in an interview

When it comes to interview questions for product managers, there are usually a few different themes that they follow:

  • Analytical or estimations
  • Product design or vision
  • Behaviour or execution
  • Technical understanding
  • Strategic vision

What do we mean by an analytical or estimation question?

These are the questions that are intended to understand how well you approach working out what an answer might be through your deduction and assumption skills.

Examples of analytical questions are:

  • How many people are currently flying at the moment?
  • How many Google searches are performed each second?
  • Twitter tweets have decreased over the past 30 days. Why might this be?
  • How many flat screen televisions have been sold in Australia in the past 12 months?

On the surface, these questions appear impossible to answer if you don’t already know the answer, but with some calm thought you can work through an approach that would give you an approximation of an answer.

Although, to be honest, what the question is designed to identify is the WAY you approach finding the answer, not the answer itself.

How do you approach answering the question?

Let’s pick the example, “How many people are currently flying at the moment?”

Where do you start?

Let’s write down the factors that we think are relevant to knowing how many people are in the air?

  • What’s our definition of “flying”?
  • How many flights come under this definition?
  • How many passengers are on each flight?

Ultimately, this gives us a simple equation of FLIGHTS x PASSENGERS = PEOPLE FLYING

But it’s not that straight forward is it?

As we start to dive into each of these three elements, we find ourselves asking more questions, and in our interview we need to be seen to be asking these questions to enable the interviewer see our thought process.

What’s our definition of flying?
Are we talking about airplanes, or does it include helicopters, microlights, hot air balloons?Are we just talking about commercial passengers, or are we including freight flights? Military flights? Private flights? Crop dusters?Let’s say our definition is ‘commercial airplane passengers only’.

How many commercial flights are there?

  • How many airports are there?

Larger countries might have 10 really large airports, 20 large airports, and 30 small airports

Medium countries might have 2 really large airports, 5 large airports, and 10 small airports

Small countries might have 1 large airport and 1 small airport

Tiny countries might have 1 small airport

How many countries are there in each size category?

There might be 10 large countries, 30 medium countries, and 100 small countries and then 50 tiny countries.

Really large airports might have 20 flights per hour (every 3 minutes) and operate for 18 hours = 360 flights

How many flights take off from each airport in an hour?

Large airports might have 12 flights an hour (every 5 minutes) and operate for 14 hours = 168 flights

Small airports might have 2 flights an hour (every 30 minutes) and operate for 12 hours = 24 flights

What percentage of these flights are in the air at any point in time?

This depends on the planes destination and thus travel time, but lets assume that 10% of these flights are in the air at any point in time.

What do we know now then?

So far we’ve got:

10 large countries each with 5 really large airports (50 airports x 360 flights = 18,000), 10 large airports (100 airports x 168 flights = 16,800) and 30 small airports (300 airports x 24 flights = 7,200) = 42,000

30 medium countries each with 1 really large airports (30 airports x 360 flights = 10,800), 3 large airports (90 airports x 168 flights =15,120) and 6 small airports (180 airports x 24 flights =4,320 ) = 30,240

100 small countries each with 1 large airports (100 airports x 168 flights = 16,800) and 1 small airport (100 airports x 24 flights = 2,400) = 19,200

50 tiny countries each with 1 small airport (50 airports x 24 flights) = 1,200

That’s 92,640 flights per day, but only 10% of them are in the air at any time, giving us 9,264 flights in the air.

We’re nearly there …

Now if we can just figure out how many people were on each flight, then we’d have our number.

So how many is it?

Planes vary in size, from 400+ seats down to less than a hundred, but there’s probably more on the smaller end, so let’s assume an average of 100 passengers are on each flight.

That gives us 9,264 flights multiplied by 100 passengers and crew, which equals a little over 925,000 people.

Now check whether this makes any sense

We need to do a little sanity check to see if what we’re saying really makes sense.

How many people are there in the world? Approximately 7 billion.

If we divide the 1 million passengers (rounded up for ease) by 7 billion people we get in the region of 0.0001% of the world in the air at any one time.

That doesn’t sound too bad a number.

If the number had been something like 5% or 10% you’d have definitely known that something was wrong somewhere along the line.

For full disclosure, the first time I ran the numbers when writing this post the number of passengers I reached was more than 4 million, which I thought looked too high, and so I revisited some of the assumptions that I had made (specifically around the number of countries of the different sizes, and the number of flights from smaller airports).

On completing this task, I used the FlightRadar24 app to look at the real numbers of flights in the air at the current time, and the below was what was the screenshot.

This includes all types of flights, not just commercial, so I’m quite happy with the estimate of 9,264 flights in the air.

What has all this proved?

By walking the interviewer, step-by-step, through your thought process they’ve received an insight into the way that you approach problem solving, when you don’t have much data.

Do you know where to look for the factors that might influence the outcome? Are you able to follow the flow of logic from one point to the next, and are you able to correct yourself if your numbers go wrong?

By knowing this, the interviewer gets to see whether you’ll be able to handle the real world product estimation scenarios where you might be asked to determine the customer usage of this as yet undefined new product feature, or the financial return on the yet to be released new product upgrade path.

It’s an important skill for a product manager to learn, as you’ll need to know some of this information in order to determine whether the feature is worth pursuing, what the potential market size is, whether it should be prioritised, or whether someone is just trying to push a feature on your for their own agenda.

Top tips for handling a question like this

  • Round up or down your numbers where you can to make life easier. Precision of the answer is not the aim of the question.
  • Follow a structure to working out your estimate, and write it down so that you can revisit it if you see there’s a problem with an assumption.
  • Explain your assumptions as you go so the interviewer knows your thought process
  • Keep calm and think clearly

Further information

These types of questions are often called Fermi Questions, after the physicist Enrico Fermi.

There are a few more example questions here where you can try this out, and they also walk you through some of them.