How to solve estimation questions in a PM Interview?

Intro

If you are looking to apply for a PM interview, chances are you'll be asked to solve an Estimation type of question.

For example:

  • Calculate the number of queries answered by Google per second?
  • How many dentists are there in New York?
  • Estimate the number of passengers arriving in SF airport everyday.
  • Estimate the number of WhatsApp chats occurring in India.

Here's a broad framework on how to solve such questions:

  1. Clarify the scope of the question
  2. Create the main equation
  3. Break down the unknowns in the equation into simpler equations
  4. Calculate the numbers
  5. Do a sanity check
  6. Submit.

Let's take a look at one such problem and try to solve it.

Problem Statement

How many people are currently online in Europe?

Base Assumptions

First, I would like to state my assumptions below:

  1. When we say currently online, the data will vary depending on what time of the day/week. However, we’ll assume the answer will give us an average number of people online at any given standard time of the day.
  2. Also by online, I am assuming they are actively surfing & using some device (Mobile, Laptop, Streaming a movie, etc.).
  3. The Population of Europe in 2020: ~750 Million (Source)

Further assumptions will be stated as we solve the problem.

Clarification

I would also like to clarify that this question can be approached in several ways: the number of users who have an email account in Europe, the number of smart devices owned per person, the number of users who have a Facebook account in Europe, etc.

However, we’ll keep the approach more straightforward and approach it via the population of Europe. The reason is it’ll have fewer chances of making a wrong assumption.

Central Equation

Next, I would like to create the central equation:

People Online in Europe
= (Euros having net X Ratio of being Online) + 
   (Non-Euros having net X Ratio of being Online)

The above equation breaks down the people currently online in Europe into two categories. First is the European population who lives in Europe. Second, are those people who are traveling to Europe for various reasons: Tourists, Businessmen, Govt officials, etc.

We’ll treat the two parts on RHS as Equation 1 and Equation 2, respectively.

People Online in Europe
= (Equation 1) + (Equation 2)

Equation 1

Let’s breakdown the Equation 1 first:

We’ll create a new formula to calculate,

Europeans having internet access
= Population of Europe in 2020 *
  Percentage of People having Internet

As we have already established above, the population of Europe in 2020 is roughly 750M.

Regarding internet penetration, I believe Europe has a very high internet penetration compared to a country like India. It would be safe to assume that the penetration would be as high as 90-95%. For simplicity’s sake, let’s assume 90%. As there will be remote villages, poor countries where internet penetration would be poor. Hence,

Europeans having internet access
= 750M X 0.90
= 675M

Now, Let’s look at the other part of the Equation 1 i.e.

Ratio of being online
= (Avg. time spent online) / (24hrs in a day)

Since the ratio of time spent online would vary depending on the age group, we’ll need to further break this down via age group:

Age Group (yrs) % of Population Avg time spent online in a day (hrs) 
0 - 12  15
13-20 25 
21-39  20 
40-50  30 
50+  30 


The above population age ratio is based on the fact that the median age of Europe is 42.5.

Explanation of Avg. time spent assumptions:

  • 0-12yrs: Since this age group is heavily monitored by their parents, my assumption is they would have less exposure to online screen time, hence 2hrs on average.
  • 13-20yrs: Teenagers are almost always on. They have the highest usage on social media, binge-watching shows on Netflix, etc. On average, they can spend anywhere between 2-8hrs a day. It’s safe to assume they are spending 5hrs every day.
  • 21-39yrs: This age group is the working class. Since they are using laptops to get their work done, they are likely to be connected almost all the time while working and later surfing movies. Hence 6hrs a day on average is a safe assumption.
  • 40-50yrs: This age group will also be part of the working group but likely to be working in traditional sectors; hence their avg time spent online would be less than above, hence 4hrs a day is a safe assumption.
  • 50+ yrs: This age group is likely to be spending time on tools like WhatsApp, Facebook, etc. but not heavy on binge-watching. Also, they are less adaptive to new tech, new apps, etc. hence consumption would be less. Hence 3hrs per day.

Based on the above, we can calculate the ratio of being online:

Ratio of being online
= [ (Percentage of 0 to 12yrs * Avg. time spent in a day)
+ (Percentage of 13 to 20yrs * Avg. time spent in a day)
+ (Percentage of 21 to 39yrs * Avg. time spent in a day)
+ (Percentage of 40 to 50yrs * Avg. time spent in a day)
+ (Percentage of 50+yrs * Avg. time spent in a day) ]
/ (24hrs in a day)
Ratio of being online
= [ (0.15 * 2) + (0.25 * 5) + (0.20 * 6) + (0.30 * 4) + (0.30 * 3) ] / 24
Ratio of being online
= 4.85 / 24
= 0.20

Equation 1 Calculation

Now that we have all the values for the first equation, let’s roll it back up.

Equation 1
= Population of Europe X Percentage of People having Internet X Ratio of being Online
= 750M X 0.90 X 0.20
= 135M

Equation 2

Now let’s take a look at Equation 2:

Equation 2
= Non Euros having internet X Ratio of being online

Non-Europeans having internet access:

We can break down the Non-Europeans having internet access as:

Non Europeans having internet access
= (Leisure Tourists X Ratio of internet access) + (Work Tourists X Ratio of Internet Access) + (Misc. Tourists X Ratio of internet access)

Based on this tourism statistics, 139 million inbound arrivals to destinations within the EU are from outside of European countries.

Out of this, 60% of these visitors were for travel, 15% for businesses, 25% for other misc reasons.  Almost all of them are likely to have internet access. Hence we’ll assume 95%, 98%, and 90% ratio of internet access.

Hence:

Non Europeans having internet access
= (Leisure Tourists X 0.95) + (Work Tourists X 0.98) + (Misc. Tourists X 0.90)
= ((139M X 0.60) X 0.95) + ((139M X 0.15) X 0.98) + ((139M X 0.25) X 0.90)
= 130M

However, these stats are for a year and not at any given point in time.

It would be safe to assume roughly 10% of these stats are in Europe at any given time (For simplicity sake, I am not considering the impact of COVID-19).

Hence 13M Non-resident Europeans are in Europe that have internet access.

Since this number is tiny compared to the overall population, we can assume their online ratio is roughly the same as that of Europeans, i.e., 20%.

Equation 2 Calculation:

Hence Equation 2:

Equation 2
= Non Euros having internet access X Ratio of being online
= 13M X 0.20
= ~3M

Final Calculation:

People currently online
= Equation 1 + Equation 2
= 135M + 3M
= 138M

Sanity Check:

Let’s do a sanity check to see if this number makes sense.

Total number of people in Europe
= 750M (Europeans) + 13M (Non Europeans)
Ratio of being online right now in Europe
= 138M / (750M + 13M)
= 0.18
= Roughly 20% people are online right now

20% sounds reasonable. With everyone having access to an internet-connected device, 1/5th of the people currently online is a fair number.

Conclusion

Hope you enjoyed reading this blog post on estimation. To learn more about how to do estimation, I recommend this website Product Management Exercises where you can learn and practice such (and other types of) problems.