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Estimate the number of Facebook users in India.

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I'd ask clarifying questions first: 

1. Are we talking about active users of Facebook or registered users in India?

2. Are we interested in the access pattern of these users e.g. mobile or website users?

I'd assume the answer to #1 is registered users and #2 is irrespective of access pattern, we are looking at the overall number.

I'd then look at breaking the problem into manageable subsets: 1. we need to look at what's the popluation having access to internet and then 2. out of the ones having internet access, what %age of users must be using facebook.

So to solve the problem, I'd define the top level equation:

total number of FB users = # people having internet access x % of internet connected population having FB account

lets solve both of these one by one:

1. #people having internet access - since india is having huge rural population (~70%), these people are directly connecting to internet through their phones. Urban population (30%) connects to internet using both phone and computer.

70% Urban population can safely be assumed to have internet access while the rural population may be around 40%

population of India: 1.3B

#people having internet access = # rural population having internet access + # urban population having internet access

= 1300M * 70% * 60% + 1300M * 30% * 40%

= 546M + 156M

=702M

2. % of internet connected population having FB account - this one can be calculated using age/ demographics of the indian population.

Facebook has an age restriction of 13 years.

Lets assume:

  • 10% of India's population is < 13 years - can be assumed to have near zero FB accounts
  • 25% of India's population is > 60 years - can be assumed to have ~25% FB accounts
  • 65% of India's popluation is between 13-60 years - can be assumed to have 70% FB accounts

Now let's feed this data to our earlier equation:

% of internet connected population having FB account = 10%*0 + 25%*25% + 65%*70%

= 6.25% + 45.5%

= 52%

Since we have estimate for both the key variables of our top equations for estimating the FB users in India, lets get to the final answer:

total number of FB users = 702M people having internet access x 52% of internet connected population having FB account

= 365.04M

Now that we have our final answer, lets also assess whether this estimate seems ok or do we need to go back and correct some of our earlier assumptions.

365M out of 1300M people means 1/3 people in India using FB which to my mind is pretty reasonable number. I dont think we need to go back and correct any of our assumption. We can proceed with the estimate.

 

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You did a mistake in calculating the number of people with internet access. Please edit the answer. Apart from that, your structure is great.
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My best answer to this Facebook estimation question is below.

Number of Facebook Users in India:
Total Population of India: 130 crore
Segregation of user base: Total population will then be segregated based upon age and geographical areas.
Accesibility: Users will then be counted based upon their probability of access to internet. Following three means will be included:
  • Accesibility of only Smartphone
  • Accesibility of only Laptop/Computer
  • Accesibility of only internet cafe
Lastly I would try to determine probability of joining social media or facebook.
 
Total PopulationAge DemographyGeographySmartphone Only PenetrationLaptop/Computer Only PenetrationInternet Only CafeTotal AccesibilitySocial Media PenetrationFacebook PenetrationTotal facebook Users
  Rural
(70%)
Urban
(30%)
RuralUrbanRuralUrbanRuralUrban    
130 Crore0-15 (10%)13cr940%10%-0.4cr0%10% 0.4cr0%5% 0.2cr1 cr20% 0.2cr80% 0.16cr23.36cr
 15-25 (20%)26cr18820%-3.5cr75%-6cr10% 1.8cr10%1.8 cr5% 1cr15% 1.2 cr15.380% 12cr70% 8.4cr
 25-35 (20%)26cr18830%-5.4cr75%-6cr10% 1.8 cr10% 1.8cr 5% 1 cr15% 1.2 cr17.170% 12cr70% 8.4cr
 35-50 (20%)26cr18820% 3.6cr50% 45% 1 cr5% 1 cr5% 1 cr5% 1 cr11.660% 7cr80% 5.6cr
 50-70 (20%)26cr18810% 1.8cr20% 1.6cr0%5% 0.4 cr0%0%3.830% 1cr80% 0.8cr
 70+ (10%)13cr940%0% 0%0%0%0% 0%0%
               
 
23.36 Crore should be the user base for Facebook in India. i.e 17.7% of total population. For Facebook this number look okayish.
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I: Are we estimating people who have FB account or people who actually use FB?

Interviewer: People who have FB account is good enough.

I: Are we counting people who use it on cell phones or desktop?

Interviewer: Well since we are just looking at people who have FB accounts, there is no question of device since we aern't looking at usage.

I: True. Ok, India's population is 1.3 billion.

Let's assume 30% of India's population doesn't have internet access considering it being a developing country infrastrucutre is still poor in many parts and poverty level in india. So that brings us to 910 million with internet access.

Out of those, 20% are little kids, 20% are old people and rest 60% are youngsters and young adults. That 60% = 546 million. From those 546 million, let's assume there are about 20% who don't have FB account due to people being concered about privacy so much. So 80% who would have a FB account = 436.8 million.

This is just an ambigious problem, I wonder if I have calculated accurately. 436.8 million out of 1300 million is 33.6%. That sounds about right considering 30% don't have internet access and 40% dont have FB account ...so that's 70%. I think I am pretty close but when you look at that 33.6% it just seems so low given the life we live here in the western world.
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