Interview Question for Analyst at Digitas:

This is a classic market sizing case study question. There are two approached one can take: either estimate the answer based on a small sample and extrapolate to the population of America, or estimate the supply and demand for haircuts.

A sample of the first approach:

- I live in a small town of about 10,000 people, and we have 2 barber shops in the town. Therefore, each one services roughly 5,000 people. Assuming the US population is roughly 300 million, we can estimate that there are (300,000,000 / 2,000) barber shops in the entire country, or 60,000.

A sample of the second approach:

- Assume the population is exactly half male and half female, such that there are 150 million of each gender. Splitting the population into age groups, you can estimate the number of people in each range and determine how many haircuts each group demands per year (for example, there are x people aged 0-15, x people aged 16-31, etc. and each population sample might demand a different number of haircuts/year). Once you have estimated the total demand by aggregating each population sample for both men and women, the next step is to determine how many haircuts a barbershop can supply each year. For example, it might make sense that a barber can cut mens hair at a rate of 1 per hour, and womens at a rate of 1 per 2 hours. If the average shop is open 10 hours a day, and has 2 barbers, it will give a total of 30 daily haircuts (10 male, 5 female for each of the 2 barbers). If a shop is open 5 days a week for 50 weeks, we can assume that, on average, each barbershop will supply a total of 30*5*50 = 7,500 haircuts per year. Using our estimated demand for haircuts/year that we calculated above, we can solve the equation that sets supply equal to demand. If, for example, our total demand was 30,000,000 haircuts per year, we could solve the following equation for "x", which equals the number of barber shops in America:

7,500x = 150,000,000

Therefore, x would be 20,000 barber shops.