I went straight to population size and tried to build up from there, which was fine, but I kept second-guessing my assumptions out loud and it made the whole thing feel shaky.
Break down the problem by estimating the U.S. population, segmenting it into likely SMS users (e.g., mobile phone owners), and estimating average daily SMS usage per user. Use a top-down approach with clear assumptions and round numbers to simplify calculations, then validate with a bottom-up check if time permits.
Pro tip: State your assumptions explicitly and round aggressively to keep the math simple; interviewers care more about your structured thinking than the exact number. Also, mention that you'd sanity-check your estimate against known data (e.g., total SMS volume reported by CTIA) to ensure plausibility.
Confirm whether the question refers to person-to-person SMS only or includes application-to-person messages (e.g., notifications, marketing). Clarify if it's for a typical day or a specific day.
Start with the U.S. population (~330 million). Estimate the percentage of people who use SMS (e.g., mobile phone users, excluding young children and some elderly). Assume ~90% have mobile phones, and ~80% actively use SMS, giving ~240 million users.
Divide users into heavy, medium, and light SMS users. For example: heavy (20% of users) send 50 messages/day, medium (50%) send 10 messages/day, light (30%) send 2 messages/day. Calculate weighted average.
Multiply the number of users by the average messages per user per day. For the example: 240M * (0.2*50 + 0.5*10 + 0.3*2) = 240M * (10 + 5 + 0.6) = 240M * 15.6 ≈ 3.7 billion messages per day.
Compare your estimate to known industry data (e.g., CTIA reports ~2 trillion SMS annually in the U.S., which is ~5.5 billion per day). Adjust assumptions if needed and discuss potential sources of error.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.