Estimating Train Operations in the New York City Subway System

Introduction

Welcome to the quest of acing PRODUCT MANAGEMENT INTERVIEWS, where aspiring product managers delve into the intricate process of prepping for FAANG interviews. The question we are unpacking today is an excellent example of how interviewers assess a candidate’s analytical skills and ability to give educated estimates. We will explore how to estimate the number of trains operating in the NYC subway.

Detailed Guide on Framework Application

1. Choosing the Right Framework

For estimation questions like this one, a logical and structured approach is essential. The framework we’ll employ is the Fermi Estimation technique, named after physicist Enrico Fermi, known for his ability to make good approximate calculations with little or no actual data.

2. Step-by-Step Application of the Fermi Estimation

1. Break down the problem: Start by structuring smaller, more manageable questions whose answers will build up to your final estimate.
2. Gather base data: Identify basic facts and figures that are commonly known or can be reasonably assumed.
3. Make educated guesses: Use your base data to make approximations and fill in the gaps where specific data is not known.
4. Adjust for reality: Critically assess your numbers at each step and adjust for realities, such as peak times and maintenance schedules.

3. Example Using the Framework

Let’s break down the problem into sub-questions:

1. What is the total number of subway stations?
2. How many routes are there?
3. What is the average frequency of trains?
4. How many hours per day does the subway operate?

Now, we apply our base knowledge and make educated guesses:

1. NYC has around 470 subway stations.
2. With known major routes, let’s estimate there are 25 routes.
3. The average frequency might be a train every 5 minutes during peak hours and 10 minutes during off-peak hours.
4. The subway operates 24 hours a day.

Note: These are assumptions and can vary. Always validate your assumptions during the interview process.

Now, let’s do some math:

(60 minutes/5) trains per hour per route during peak hours x 12 peak hours x 25 routes + (60/10) trains per hour per route during off-peak hours x 12 off-peak hours x 25 routes = Estimated daily trains per route. Multiply this by the number of routes to get the total.

4. Fact-checks and Reality Adjustments

Fermi estimations do not need perfection but being in the right ballpark is key. Always question your assumptions and refine the calculation based on the interviewer’s feedback or additional context you might receive.

5. Effective Communication Tips

Clearly articulate your thought process, substantiate your assumptions, and acknowledge uncertainties to show that you understand the estimation is approximated. Be prepared to adjust your calculations if the interviewer provides new data or corrects your assumptions.

Conclusion

Decoding complex estimation questions is all about structure, critical thinking, and adaptability. Fermi Estimation can be your best ally in navigating such questions. Remember, practice makes perfect. Keep engaging with estimation challenges, refine your approaches, and soon you’ll be acing these questions with confidence!