## Microsoft Interview Question

Program Managers**Country:**India

**Interview Type:**In-Person

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.

So do you think one barber can cut 5000 people's hair in a week. I don't think he can cut more than 50.

So do you think one barber can cut 5000 people's hair in a week. I don't think he can cut more than 50 in a day.

So do you think one barber can cut 5000 people's hair in a week. I don't think he can cut more than 50 in a day.

So do you think one barber can cut 5000 people's hair in a week. I don't think he can cut more than 50 in a day.

Lets assume that there are 100,00,000 people in the city and each people go to barber shop once in a month. So in one month total 100,00,000 person's hair needs to be cut.

Not make assumption that 70% people go for hair cut in weekend i.e. saturday & sunday.

Hence in one month 70,00,000 person's hair needs to be cut. Similarly in one week 70,00,000/4 = 1,750,000 hair needs to be cut on Sat & Sun. So on Sat or Sunday total hair cuts = 875,000. Now lets say one barber cuts 50 hair in a day then total barber required = 875,000/50 = 175,00 approx. Not sure ans was correct or not. Interviewer did not get impressed from this.

So second answer given was lets say total diameter of the city is 50 KM and there should be at least one barber shop in each and every KM. So draw and circle having radius 25 and calculate the circumfrance. Then put barber shop at each KM on outer circumfrance of radius 50. so total number of barber shop = 2 * PI * r = (2 * 22/7 * 50/2 -1).

Again draw another circle inside the bigger one of radius 24 and calculate the barber's shop = ( 2* 22/7 * 24 -1). Now keep on doing till center.

Finally you will get sum as.

So total barber shop = (2*22/7*25 -1) + (2*22/7*24 -1) + (2*22/7*23 -1).......................+1

But interviewer was not impressed from this ans also and got rejected in the first round. This was the only question what i faced in 1st round and returned back empty.

@samaresh: For which position and location you have attended the interview?

Looks like you missed the corner / different category cases to handle:

1. Female (48 / 50% don't go far hair cut, only 2% of modern female go for hair cut that also ~2 months frequency

2. Children (<5 yrs) may not need hair cut

3. 25% of men go for hair cut once in 2 months

4. 60+ age people frequency is different

this question should have been asked to test your estimation skills and identifying all the cases / risks that's needs to be taken care

HI,

This is a management question not a technical question. You are trying to answer it like an engineer by starting with number of people in the first attempt and circumfrence in the second. Ofcourse, the answer will be approximate but what is your approach is the point.

Sol. The answer required is number of barber shops in city.

divide the city into segments - posh area, residential area, maybe developing area.

sample 2 or 3 areas in posh area category and others.

perform a survey in the selected samples and find the number of barber shops in the selected 2/3 posh area samples get the average.

so for posh area the ans obtained in previous step * number of posh areas = the answer for posh area.

do the same for other 2 categories and add up to get an approximate answer.

This is how we solve the estimate issues in Marketing research.

Arun, if you cannt appreciate the cleverness of the answer, then you cannt be a good manager or an engineer. Your solution is really stupid and made me cringe.

@samaresh

I think your answers were really good. Other answers given by people here aren't as clever. One professor I know at stanford was asked the same question and was not able to answer it. You could answer it! Cheers!

What position was this for? You got rejected after this single question!?!

{{}}}

For what it's worth, if this is for SDE/SDET, its a useless question that proves absolutely nothing about your analytical ability.

May be he is expecting sampling here.

1) Send 100 people to different barbers in the city. Mark these barbers

2) Send another 100 people . Let them go to the shops not marked yet.

3) Repeat second step again and again.

4) Now you come to a stage where say only 70 -80 people can find the new shops.

5) continue..

6) At the end only 1-2 or none shops would be left which were unattended

7) From there you can find the number of shops

Assume a barber shop includes all shops that cut hair.

I have 10^7 people in my city.

10 cuts/yr 10^8 cuts/yr

2000 working hrs/yr (40 hrs a week)

5000 barbers at 2000 hrs/yr needed for 10^7 people x 1 hr cuts x10 a yr

Shops are open 5-7 days, 2 to 10 barbers per shop

Pick 5 avg per shop.

1000 shops for a city of 1M

Now, different populations need from 0 hrs/yr (babies) to 40 hrs/year (2 hr cuts)

Need to segment more.

Assume a barber shop includes all shops that cut hair.

I have 10^7 people in my city.

10 cuts/yr 10^8 cuts/yr

2000 working hrs/yr (40 hrs a week)

5000 barbers at 2000 hrs/yr needed for 10^7 people x 1 hr cuts x10 a yr

Shops are open 5-7 days, 2 to 10 barbers per shop

Pick 5 avg per shop.

1000 shops for a city of 1M

Now, different populations need from 0 hrs/yr (babies) to 40 hrs/year (2 hr cuts)

Need to segment more.

Assume a barber shop includes all shops that cut hair.

I have 10^7 people in my city.

10 cuts/yr 10^8 cuts/yr

2000 working hrs/yr (40 hrs a week)

5000 barbers at 2000 hrs/yr needed for 10^7 people x 1 hr cuts x10 a yr

Shops are open 5-7 days, 2 to 10 barbers per shop

Pick 5 avg per shop.

1000 shops for a city of 1M

Now, different populations need from 0 hrs/yr (babies) to 40 hrs/year (2 hr cuts)

Need to segment more.

I have 10^7 people in my city.

10 cuts/yr 10^8 cuts/yr

2000 working hrs/yr (40 hrs a week)

5000 barbers at 2000 hrs/yr needed for 10^7 people x 1 hr cuts x10 a yr

Shops are open 5-7 days, 2 to 10 barbers per shop

Pick 5 avg per shop.

1000 shops for a city of 1M

Now, different populations need from 0 hrs/yr (babies) to 40 hrs/year (2 hr cuts)

Need to segment more.

I have 10^7 people in my city.

10 cuts/yr 10^8 cuts/yr

2000 working hrs/yr (40 hrs a week)

5000 barbers at 2000 hrs/yr needed for 10^7 people x 1 hr cuts x10 a yr

Shops are open 5-7 days, 2 to 10 barbers per shop

Pick 5 avg per shop.

1000 shops for a city of 1M

Now, different populations need from 0 hrs/yr (babies) to 40 hrs/year (2 hr cuts)

Need to segment more.

Male only

Population – 2 crore

1 hair cut – 30 min

Shop open for 10 hours, means – 20 hair cuts a day, 100 per week (considering week off and other factors, like Tuesday etc)

52 weeks means – about 5200 hair cuts per year for one shop

Male:female ratio of 1:1 means 1 crore mails

About 40% over age 60, i.e. would require 1-2 hair cuts a year – 80lakh cuts

About 20% around 40-60,i.e. would require 4-6 hair cuts a year- 1 crore haircuts

About 30% around 15-40, would require around 8-10 hair cuts – 3 crore hair cuts

About 10% around 0-15, would require 10 hair cuts – 1.5 crore hair cuts

Total – 6.3 crore hair cuts

Total barbershops needed – 63000000/5200 = 12115 shops

Calculate Barbershops in your city –

Collect population data in the city or get the data available from a source

Have data organized with information such as –

Male/Female

Age group 1-5, 5-10, 10-15 etc

Occupation

City area

Develop a statistical model to do the analysis

Validate the model for your area and couple of neighborhood area

Find out barbershop required per area

Question is for Barber's shop and not the barber. I think calculating based on population is not possible. It should be done based on sampling and estimation. Do you agree?

- rajeev July 03, 2012