I love interview questions like these because they're seemingly simple, but we can still be organized and thoughtful in our analysis. There's no single correct way to approach this question, but here's how I might think about it:
First, I'd start by asking the interviewer a few clarifying questions. This demonstrates that you're carefully considering the question and the different possible interpretations. Some of these could have a big effect on the solution:
- What do you mean when you say "New York?" Is that Manhattan? New York City? New York State? It's important that we set the appropriate baseline, as there is a big difference is population.
- Do you want me to estimate how many people are wearing a red t-shirt this very moment, or how many people wore or will wear a red t-shirt any time today? This could change the number significantly depending on the time of day, and if we consider that many people change outfits during the day (e.g., going to the gym, getting home from work, etc.)
- When we say t-shirts, I will assume that we are not counting dress shirts, polos, blouses, and other styles of red tops. Does that sound ok?
For the sake of this example, let's assume the interviewer tells us we're looking at New York City, at this very moment, and t-shirts only.
I might set up this equation to start, with three variables we can analyze separately:
# people currently wearing a red t-shirt in NYC =
Number of people currently in NYC * % of people wearing a t-shirt * % of t-shirts that are red
Let's start with the first one: How many people are in NYC right now?
You might ask the interviewer if they happen to know to population of NYC. I'm going to guess that it's approximately 8 million. It's currently 2 PM on a weekday, and I think many people commute into the city from outlying areas (New Jersey, Long Island, Westchester...). NYC is also a popular tourist destination. I'm going to assume there are an additional 2 million non-residents in the city currently. 10 million people total.
Second, what percentage of people in NYC are currently wearing a t-shirt?
I can think of many factors that affect what a person wears:
- Time of day
- Weather (If it's a warm sunny day, more people will probably wear t-shirts)
- Gender (Maybe we think women have more fashion options than men -- dresses, blouses, etc. -- so we might guess that men wear more t-shirts than women)
- Age (Perhaps we think kids wear t-shirts more than working age adults or the elderly)
- Occasion (Many people would wear a t-shirt on their day off, but fewer would wear one to work)
As the candidate, you'll want to demonstrate some analytical thinking here but also your ability to prioritize and not make things overly complicated. It's 2 PM on a late summer weekday, so let's assume the weather is good and a t-shirt would be appropriate and comfortable. Let's use "occasion" to structure our calculation, as that might be the variable with the clearest differences in t-shirt-wearing.
I'm going to estimate the mix of people currently in NYC as follows. I don't know if these are even remotely correct, but the point is to make educated assumptions and explain them:
- Locals who are working today: 60%
- Locals who are not working today: 30%
- Tourists: 10%
I chose these categories because I think there is a sigificant difference in t-shirt-wearing between them. I'm going to estimate that the percentage of people wearing a t-shirt are: 5% of working locals (not very many jobs in NY are that casual), 40% of non-working locals (t-shirts are probably a popular choice on people's days off), and 70% of tourists (practically every tourist I see is dressed very casually).
0.6 * 0.05 + 0.3 * 0.4 + 0.1 * 0.7 = 0.22
By my estimate, 22% of people currently in NYC are wearing a t-shirt.
Third, what percentage of these t-shirts are red?
There are many ways we could approach this question:
- What are the major color categories of t-shirts? (Red, Blue, Green, Black, White, Orange, Yellow, Purple, Pink, Brown, Gray...) Are any of them more popular than others? What percentage do we think are red?
- If I picture the display of t-shirts at a clothing store, what percentage of them are red?
- If I use my own wardrobe of t-shirts as a benchmark, what percentage of my own t-shirts are red? (Be careful using yourself as a sample for the whole population, but this is another data point we can consider.)
- Is there anything that would affect the color of a t-shirt a person chooses to wear today (e.g., is it Valentine's Day? Heart Walk? Are a bunch of Red Sox fans in town for a baseball game?)
This is a great place to demonstrate that you can triangulate to an answer using multiple data points and approaches. Let's assume it's just an ordinary day. My best guess for each of these questions is around 10%.
Finally, putting it all together:
10M people * 22% in t-shirts * 10% red = 220,000 people currently in NYC wearing a red t-shirt
Once you have your answer, I'd suggest doing a few things:
- "Sanity check" the answer. Based on our calculation, 2.2% of people in NYC are wearing a red t-shirt. Does that seem "in the ballpark?" Seems reasonable to me: If we walked through a busy subway station right now, I could imagine 1 in 50 people would be in a red t-shirt.
- Comment on sensitivities: What are the most impactful estimates we made that could significantly affect our answer? Of course, the baseline population is a big one. I've also assumed that only 5% of the largest group of people (working locals) wear t-shirts. That might be low when you consider that some parts of the retail workforce wear t-shirts or that casual offices are becoming more common.
I hope that's helpful! Of course, there are a million other ways you could approach solving this, but the most important thing is to lay out a logical approach, develop reasonable assumptions, and explain your thinking as you build your answer.