A clickstream table receives 2 billion events per day, and product needs user sessions split after 30 minutes of inactivity to decide whether a new onboarding flow reduced median time to activation by at least 10 percent. How would you build the SQL output for the last 90 days?

I would sessionize in SQL with a deterministic window sequence, then aggregate at the generated session grain. - Use LAG over each user ordered by event_ts and event_id, and mark a new session when the prior event is absent or the gap exceeds 30 minutes. - Cumulatively sum that marker over the same partition to create a stable session number, keeping event_id as the tie-breaker for equal timestamps. - Group by user_id and session number to return session start, session end, event count, and the first activation timestamp. - Filter event_date before the windows so only 90 partitions scan, then compare median activation duration for the old and new onboarding variants.

Your warehouse ingests 800 million mobile events per day, and network retries duplicate about 0.7 percent of them before the daily purchase report is produced at 09:00. How would you deduplicate the events in SQL so finance can trust the reported order count?

I would select one canonical row per event before any joins or purchase aggregation. - Apply ROW_NUMBER partitioned by event_id and ordered by source_updated_at descending, ingestion_ts descending, then keep row number 1. - If legacy clients lack event_id, build a documented fingerprint from user_id, event_name, client_ts, order_id, and payload hash, while reporting its collision rate separately. - Restrict the scan to the report date plus the three-day retry window, but allow a scheduled seven-day restatement for late events. - Reconcile distinct order_id and summed revenue against the payment table, and block the 09:00 report if either differs by more than 0.1 percent.

A subscription product has 20 million signups across 18 months, and growth will pause channels whose week-4 retention is below 18 percent. How would you write the SQL for signup-month cohorts with week 1 through week 12 retention by acquisition channel?

I would fix each user's cohort and denominator once, then join activity to an explicit week spine. - Assign each user their earliest valid signup timestamp, signup month, and acquisition channel before joining the 6 billion activity rows. - Reduce activity to distinct user_id and activity_date, then calculate week_number from the user's signup date and keep weeks 1 through 12. - Cross join every cohort and channel to a 1-to-12 week spine so weeks with zero retained users remain visible instead of disappearing. - Divide distinct active users by the original cohort size, exclude incomplete week-4 cohorts from the decision table, and output channels below the 18 percent threshold.

An e-commerce site records 600 million events per day, and the checkout team must measure users who completed view_item, add_to_cart, begin_checkout, and purchase in that order within 24 hours before deciding on a rollout. How would you query this ordered funnel without counting out-of-order events?

I would chain each funnel step to the earliest qualifying event after the prior step at a defined attempt grain. - Start from one view_item per user and checkout attempt, retaining item_id, variant, and its timestamp as the denominator row. - For each next step, take the minimum timestamp greater than the previous step and no later than 24 hours after the initial view, using order_id or attempt_id to prevent cross-purchase matching. - Left join the chained steps so abandoners stay in the denominator, and count a stage only when every preceding timestamp is present. - Return stage conversion and step-to-step drop-off by device and variant, with the rollout table flagging variants whose purchase conversion improves by at least 2 percent.

You have 400 million historical transactions and a customer-risk table whose tier changes over time, and credit operations needs each transaction labeled with the tier valid at purchase time to set next quarter's limits. How would you implement the point-in-time join in SQL?

I would join each transaction to the single risk-tier version whose validity interval contains the purchase timestamp. - Represent tier history with valid_from inclusive and valid_to exclusive, using a far-future value only for the current version. - Join on customer_id with valid_from less than or equal to purchased_at and purchased_at less than valid_to, or use the warehouse's native ASOF join with the same semantics. - Assert that intervals never overlap and use version_id as a deterministic tie-breaker while routing unmatched transactions to an explicit unknown tier. - Prune transactions to the planning quarter and prefilter tier versions to intersect that period, then output default rate and exposure by the historical tier for limit setting.

A marketplace stores 1.2 billion daily inventory snapshots, and operations needs every seller-SKU with at least 14 consecutive out-of-stock days to decide which listings to suppress. How would you solve this gaps-and-islands problem in SQL while distinguishing missing snapshots from real stockouts?

I would create a complete daily series, classify data gaps explicitly, and form islands only from confirmed out-of-stock days. - Cross join active seller-SKU ranges to a calendar for the 60-day review window, then left join snapshots so a missing row becomes unknown rather than zero inventory. - Mark an island boundary when the status changes, the prior calendar date is not yesterday, or either day is unknown, using LAG within each seller_id and sku_id. - Cumulatively sum the boundary marker to assign an island id, then group confirmed out-of-stock islands to get start_date, end_date, and day_count. - Return islands with day_count at least 14 for suppression and send unknown runs longer than two days to a separate data-quality queue.

A latency table contains 12 billion rows per month and 500 country-device groups, but the release gate needs p50, p95, and p99 within 10 minutes and blocks any group whose p95 exceeds 2.5 seconds. When would you use exact versus approximate percentiles in SQL?

I would use approximate percentiles for the broad gate scan, then calculate exact percentiles only for groups near the 2.5-second boundary. - Exact PERCENTILE_CONT requires large per-group sorts and gives interpolated quantiles suitable for audited final numbers, but it is unlikely to meet the 10-minute scan target on 12 billion rows. - APPROX_PERCENTILE or APPROX_QUANTILES uses bounded-memory sketches and should return p50, p95, and p99 for all 500 groups within the dashboard SLA. - Calibrate the approximation monthly against exact results on representative partitions and record absolute p95 error, requiring it to stay below 50 milliseconds. - Recompute exact p95 for groups whose approximate result is between 2.4 and 2.6 seconds, then block the release only from that exact boundary table.

Merchandising needs the top five products by net revenue within each of 120 categories from 250 million order lines, with all fifth-place ties included for an assortment decision. How would you write the SQL and make tie behavior explicit?

I would aggregate to one row per category and product, then use DENSE_RANK within each category. - Sum line revenue minus refunds at category_id and product_id grain before applying any window function, with revenue rounded to accounting cents. - Compute DENSE_RANK partitioned by category_id and ordered by net_revenue descending, then keep ranks 1 through 5. - Do not use ROW_NUMBER because it would arbitrarily discard fifth-place ties, and do not use RANK because gaps can return fewer than five distinct revenue levels. - Return rank, net revenue, and category revenue share, warning merchandising that a category may contain more than five output products when rank 5 is tied.

A B2B company has an 8 million-node account hierarchy with parent_account_id and annual recurring revenue, and sales needs ARR rolled up to every ancestor plus a list of structures deeper than eight levels before redesigning territories. How would you query it with recursive SQL?

I would build an ancestor-descendant closure with a recursive CTE, then aggregate descendant ARR to each ancestor. - Seed every account as both ancestor and descendant at depth 0, then recursively follow parent_account_id while carrying ancestor_id, descendant_id, depth, and a visited-id path. - Stop a branch when an id repeats or depth reaches 50, and output cycles and missing parents separately instead of silently dropping them. - Sum each descendant's ARR once by ancestor_id from the closure, and calculate maximum depth without adding parent ARR repeatedly at intermediate levels. - Materialize the validated closure incrementally for 8 million nodes, then provide rolled-up ARR and ancestors with maximum depth above eight for territory redesign.

A weekly attribution query scans 15 TB of clickstream data, joins orders and campaign history, runs for 70 minutes, and costs $180, but marketing needs it under 10 minutes before reallocating $5 million of spend. How would you optimize the analytical SQL without changing its result?

I would use the query profile to remove scanned and shuffled data before changing warehouse size. - Inspect bytes scanned, join cardinalities, spill, and stage timing, then push event_date and valid campaign predicates into the earliest clickstream scan so partition pruning still works. - Reduce clicks to the required user-session-campaign grain before joining orders, and join small campaign dimensions only after that reduction to prevent fan-out and network shuffle. - Cluster or sort the large intermediate by event_date and user_id, and incrementally materialize daily attribution inputs if the same 15 TB history is reread every week. - Compare row counts, attributed order ids, and revenue checksums with the original query, accepting the rewrite only if it runs under 10 minutes with identical business totals.

A local-services marketplace has 500,000 weekly visitors, 40,000 completed jobs, and $8 million in weekly GMV. What north star metric would you choose?

I would use weekly successfully completed jobs because it records value delivered to both customers and providers. - Count a job once when payment settles and it has neither a cancellation nor a refund within 7 days; the current baseline is 40,000. - Decompose it as 500,000 eligible visitors times 12% request creation, 80% matching, and 83% completion, which yields about 39,840 jobs. - Protect quality with a 7-day dispute rate below 3%, median provider earnings of at least $24 per hour, and p90 time to match below 48 hours. - Publish the count by city and service category, and flag any segment contributing over 20% of growth while its repeat-booking rate falls by more than 2 percentage points.

A subscription product has 100,000 paid seats and $2 million in MRR, with a target to grow MRR by 20% in 6 months. Build the metric tree you would use.

I would root the tree in ending MRR and connect every branch through identities that reconcile to the $2.4 million target. - The stock branch starts at $2 million, equal to 100,000 paid seats times $20 realized MRR per seat, and ends at the $2.4 million goal. - The monthly bridge is opening MRR plus $50,000 new and $30,000 expansion, minus $20,000 contraction and $25,000 churn, for a current net gain of $35,000. - Acquisition owns the $50,000 new-MRR branch as 1,000 new accounts times $50 first-month MRR, with trial volume and paid conversion beneath it. - Retention owns gross MRR churn of 1.25%, while expansion owns the $30,000 branch; keeping current flows adds only $210,000 in 6 months, leaving a $190,000 gap to assign.

A web and mobile collaboration product reports 1.2 million MAU, but only 430,000 users meaningfully edit content. Write the exact active-user contract you would adopt.

I would define MAU as distinct canonical human users who create at least 1 persisted content change during a UTC calendar month. - Qualifying actions are exactly 3 successful events: document_created, edit_committed, or comment_posted; logins, views, notification opens, and failed writes do not count. - The window is [00:00 UTC on day 1, 00:00 UTC on day 1 of the next month), uses event time, and closes after a 48-hour late-arrival allowance. - Identity resolution counts 1 canonical user across web and mobile, excludes anonymous activity until linked, and removes employee, test, bot, and suspended accounts. - I would rename the old 1.2 million figure visited MAU, backfill both definitions for 12 months, and make 430,000 the governed baseline for the new contract.

A learning app gets 2 million new signups per month, and growth wants reminders to raise activation from 32% to 40%. Define the KPI and guardrails.

I would optimize 7-day qualified activation, not reminder clicks or raw lesson starts. - A signup activates only after completing 3 lessons on at least 2 distinct days within 168 hours; moving from 32% to 40% means 160,000 additional activated users per monthly cohort. - Keep the denominator to eligible new human accounts assigned before their first reminder, and report channel segments only when they contain at least 10,000 signups. - Require 30-day retention among activated users to decline by no more than 1 percentage point and push opt-outs to increase by no more than 0.5 percentage points. - Cap reminder complaints at 2 per 10,000 sends and variable delivery cost at $0.30 per incremental activated user.

Market A has 9,000 eligible checkout sessions and 1,800 purchases, while market B has 1,000 sessions and 400 purchases. How should monthly checkout conversion be aggregated?

The global conversion is the ratio of summed purchases to summed eligible sessions, so it is 2,200 divided by 10,000, or 22%. - Market A converts at 20% and market B at 40%; their unweighted average of 30% gives a 10-point overstatement. - Weighting each market rate by its denominator gives 90% times 20% plus 10% times 40%, which reconciles to 22%. - If the mix moves to 50% per market with both rates unchanged, raw conversion rises to 30%, so I also publish a mix-standardized series using the original 90/10 weights. - The contract counts at most 1 purchase per eligible checkout session and shows the 2,200 numerator and 10,000 denominator beside every reported ratio.

A lending funnel has 100,000 visitors, 60,000 application starts, 30,000 completed eligibility-qualified applications, 12,000 approvals, and 8,000 funded loans. Growth reports 8% conversion while risk reports 26.7%. How do you define the funnel?

Both rates are valid for different questions, so I would name every transition and its eligible denominator rather than publish one ambiguous conversion. - Visitor-to-start is 60,000 divided by 100,000, or 60%, and start-to-qualified-completion is 30,000 divided by 60,000, or 50%. - Underwriting approval is 12,000 divided by 30,000 eligible completed applications, or 40%; ineligible and incomplete applications never enter that denominator. - Qualified-to-funded is 8,000 divided by 30,000, or 26.7%, which decomposes into 40% approval and 66.7% funding after approval; end-to-end conversion is 8%. - Freeze eligibility at application submission, deduplicate repeat applications from the same person within 30 days, and display all 5 stage counts beside the conditional rates.

A food-delivery marketplace processes 50,000 weekly orders with a $32 basket, a 22% take rate, a $2.20 customer fee, $5.50 courier cost, 2.9% payment fees, $0.80 support and refunds, and a $1.50 promotion. What is the unit economics view?

Contribution margin is only about $0.51 per order, so the apparently healthy 22% take rate leaves little room for more discounting. - Variable revenue is $7.04 of commission plus the $2.20 customer fee, totaling $9.24 per order. - Variable cost is $5.50 plus $0.93 payment processing, $0.80 support and refunds, and $1.50 promotion, totaling about $8.73. - Contribution is therefore $0.51 per order, 1.6% of GMV, or roughly $25,600 across 50,000 weekly orders before fixed costs. - Raising the promotion from $1.50 to $3.00 makes contribution about negative $0.99 per order, so I would require at least $1.50 of measured future cohort margin to justify it.

A search team wants to use click-through rate as a proxy for 28-day repeat purchase because experiments run for 2 weeks, and user-level correlation is 0.65. How would you validate the proxy using 24 past experiments?

I would validate click-through at the experiment-effect level because a 0.65 user correlation does not show that changing clicks changes repeat purchase. - For all 24 mature tests, estimate treatment effects on both metrics at the randomized unit and fit a precision-weighted relationship with leave-one-experiment-out validation. - I would require matching effect direction in at least 20 of 24 tests, out-of-sample R-squared above 0.50, and a calibration slope between 0.8 and 1.2. - Check that a 1-point CTR lift does not systematically raise 5-second return-to-search by more than 0.3 points, which would reveal low-quality click optimization. - Shadow the proxy for the next 6 experiments that reach day 28 and suspend it after 2 direction reversals or when quarterly calibration leaves the 0.8 to 1.2 range.

A home-services marketplace has 90,000 requested service hours and 100,000 provider-available hours per week, yet only 72% of requests are filled and provider utilization is 55%. What balance metric would you build?

I would use balanced-liquidity coverage: the share of eligible requests occurring in local cells where requested hours divided by available provider hours is between 0.8 and 1.0. - Compute load by city, service category, and day using expected job duration; the global ratio of 90,000 to 100,000, or 0.9, hides local shortages and idle supply. - Treat load below 0.6 as excess supply and above 1.2 as shortage, and roll cells with fewer than 100 weekly requests into a broader regional cell. - If only 58% of requests currently fall in the 0.8 to 1.0 band, set a target of 75% rather than trying to maximize either provider count or request volume alone. - Validate the band by requiring fill rate to rise above 80%, provider utilization to stay between 55% and 70%, and median first response to remain below 4 hours.

Weekly paid orders are 1.02 million versus a 1.08 million plan, and quarter-over-quarter growth slowed from 8% to 2%. The entire brief is: why is growth slowing? Turn it into a bounded analysis.

I would bound the question to explaining the 60,000 weekly order shortfall over the latest 13 weeks versus the prior 13-week plan for the 5 established markets. - Define paid orders as eligible visitors times buyer conversion times orders per buyer, and require the components to reconcile from the 1.02 million actual to the 1.08 million plan. - Allocate the 60,000 gap across those 3 components with a log-change or Shapley decomposition, then separate new and returning buyers so acquisition mix is not mislabeled as retention. - Cut the gap by the top 5 markets, top 5 channels, platform, and cohort age, but drill deeper only when a segment explains at least 5,000 orders or 10% of the shortfall. - Deliver the diagnostic in 5 business days, compare with the same 13 weeks last year for seasonality, and leave causal claims to follow-up tests on the 2 largest contributors.

Data Analyst interview questions

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Questions

activationsqlonboarding

I would sessionize in SQL with a deterministic window sequence, then aggregate at the generated session grain.

Use LAG over each user ordered by event_ts and event_id, and mark a new session when the prior event is absent or the gap exceeds 30 minutes.
Cumulatively sum that marker over the same partition to create a stable session number, keeping event_id as the tie-breaker for equal timestamps.
Group by user_id and session number to return session start, session end, event count, and the first activation timestamp.
Filter event_date before the windows so only 90 partitions scan, then compare median activation duration for the old and new onboarding variants.

Why interviewers ask this: The interviewer is checking whether the candidate can turn window functions into a deterministic, scalable session-level dataset tied to a product threshold.

sqlwarehousequeries

I would select one canonical row per event before any joins or purchase aggregation.

Apply ROW_NUMBER partitioned by event_id and ordered by source_updated_at descending, ingestion_ts descending, then keep row number 1.
If legacy clients lack event_id, build a documented fingerprint from user_id, event_name, client_ts, order_id, and payload hash, while reporting its collision rate separately.
Restrict the scan to the report date plus the three-day retry window, but allow a scheduled seven-day restatement for late events.
Reconcile distinct order_id and summed revenue against the payment table, and block the 09:00 report if either differs by more than 0.1 percent.

Why interviewers ask this: A strong answer defines deterministic survivorship, handles imperfect keys and late arrivals, and validates the financial output rather than merely using DISTINCT.

retentioncohortssql

I would fix each user's cohort and denominator once, then join activity to an explicit week spine.

Assign each user their earliest valid signup timestamp, signup month, and acquisition channel before joining the 6 billion activity rows.
Reduce activity to distinct user_id and activity_date, then calculate week_number from the user's signup date and keep weeks 1 through 12.
Cross join every cohort and channel to a 1-to-12 week spine so weeks with zero retained users remain visible instead of disappearing.
Divide distinct active users by the original cohort size, exclude incomplete week-4 cohorts from the decision table, and output channels below the 18 percent threshold.

Why interviewers ask this: The interviewer evaluates grain control, stable cohort denominators, zero-filled periods, and protection against right-censoring.

funnelqueries

I would chain each funnel step to the earliest qualifying event after the prior step at a defined attempt grain.

Start from one view_item per user and checkout attempt, retaining item_id, variant, and its timestamp as the denominator row.
For each next step, take the minimum timestamp greater than the previous step and no later than 24 hours after the initial view, using order_id or attempt_id to prevent cross-purchase matching.
Left join the chained steps so abandoners stay in the denominator, and count a stage only when every preceding timestamp is present.
Return stage conversion and step-to-step drop-off by device and variant, with the rollout table flagging variants whose purchase conversion improves by at least 2 percent.

Why interviewers ask this: The interviewer is testing whether the candidate enforces order, time bounds, attempt grain, and denominator preservation in a multi-step funnel.

sqltransactionsjoins

I would join each transaction to the single risk-tier version whose validity interval contains the purchase timestamp.

Represent tier history with valid_from inclusive and valid_to exclusive, using a far-future value only for the current version.
Join on customer_id with valid_from less than or equal to purchased_at and purchased_at less than valid_to, or use the warehouse's native ASOF join with the same semantics.
Assert that intervals never overlap and use version_id as a deterministic tie-breaker while routing unmatched transactions to an explicit unknown tier.
Prune transactions to the planning quarter and prefilter tier versions to intersect that period, then output default rate and exposure by the historical tier for limit setting.

Why interviewers ask this: A strong answer prevents future information leakage and proves that every fact receives at most one historically valid dimension row.

sqlsnapshot

I would create a complete daily series, classify data gaps explicitly, and form islands only from confirmed out-of-stock days.

Cross join active seller-SKU ranges to a calendar for the 60-day review window, then left join snapshots so a missing row becomes unknown rather than zero inventory.
Mark an island boundary when the status changes, the prior calendar date is not yesterday, or either day is unknown, using LAG within each seller_id and sku_id.
Cumulatively sum the boundary marker to assign an island id, then group confirmed out-of-stock islands to get start_date, end_date, and day_count.
Return islands with day_count at least 14 for suppression and send unknown runs longer than two days to a separate data-quality queue.

Why interviewers ask this: The interviewer checks whether the candidate can apply gaps-and-islands without converting missing telemetry into a false business state.

percentilessqllatency

I would use approximate percentiles for the broad gate scan, then calculate exact percentiles only for groups near the 2.5-second boundary.

Exact PERCENTILE_CONT requires large per-group sorts and gives interpolated quantiles suitable for audited final numbers, but it is unlikely to meet the 10-minute scan target on 12 billion rows.
APPROX_PERCENTILE or APPROX_QUANTILES uses bounded-memory sketches and should return p50, p95, and p99 for all 500 groups within the dashboard SLA.
Calibrate the approximation monthly against exact results on representative partitions and record absolute p95 error, requiring it to stay below 50 milliseconds.
Recompute exact p95 for groups whose approximate result is between 2.4 and 2.6 seconds, then block the release only from that exact boundary table.

Why interviewers ask this: The interviewer wants a cost-aware percentile strategy that quantifies approximation error and preserves exactness where it can change the release decision.

sql

I would aggregate to one row per category and product, then use DENSE_RANK within each category.

Sum line revenue minus refunds at category_id and product_id grain before applying any window function, with revenue rounded to accounting cents.
Compute DENSE_RANK partitioned by category_id and ordered by net_revenue descending, then keep ranks 1 through 5.
Do not use ROW_NUMBER because it would arbitrarily discard fifth-place ties, and do not use RANK because gaps can return fewer than five distinct revenue levels.
Return rank, net revenue, and category revenue share, warning merchandising that a category may contain more than five output products when rank 5 is tied.

Why interviewers ask this: The interviewer evaluates whether the candidate controls aggregation grain and deliberately chooses ranking semantics that match the requested tie policy.

sqlqueriesrecursion

I would build an ancestor-descendant closure with a recursive CTE, then aggregate descendant ARR to each ancestor.

Seed every account as both ancestor and descendant at depth 0, then recursively follow parent_account_id while carrying ancestor_id, descendant_id, depth, and a visited-id path.
Stop a branch when an id repeats or depth reaches 50, and output cycles and missing parents separately instead of silently dropping them.
Sum each descendant's ARR once by ancestor_id from the closure, and calculate maximum depth without adding parent ARR repeatedly at intermediate levels.
Materialize the validated closure incrementally for 8 million nodes, then provide rolled-up ARR and ancestors with maximum depth above eight for territory redesign.

Why interviewers ask this: A strong answer uses recursive SQL with correct rollup grain, cycle protection, depth controls, and an output tied to the hierarchy decision.

sqlqueriesjoins

I would use the query profile to remove scanned and shuffled data before changing warehouse size.

Inspect bytes scanned, join cardinalities, spill, and stage timing, then push event_date and valid campaign predicates into the earliest clickstream scan so partition pruning still works.
Reduce clicks to the required user-session-campaign grain before joining orders, and join small campaign dimensions only after that reduction to prevent fan-out and network shuffle.
Cluster or sort the large intermediate by event_date and user_id, and incrementally materialize daily attribution inputs if the same 15 TB history is reread every week.
Compare row counts, attributed order ids, and revenue checksums with the original query, accepting the rewrite only if it runs under 10 minutes with identical business totals.

Why interviewers ask this: The interviewer is looking for evidence-driven warehouse optimization that attacks scan, shuffle, and join grain while preserving a verifiable analytical result.

north-starmonitoring

I would use weekly successfully completed jobs because it records value delivered to both customers and providers.

Count a job once when payment settles and it has neither a cancellation nor a refund within 7 days; the current baseline is 40,000.
Decompose it as 500,000 eligible visitors times 12% request creation, 80% matching, and 83% completion, which yields about 39,840 jobs.
Protect quality with a 7-day dispute rate below 3%, median provider earnings of at least $24 per hour, and p90 time to match below 48 hours.
Publish the count by city and service category, and flag any segment contributing over 20% of growth while its repeat-booking rate falls by more than 2 percentage points.

Why interviewers ask this: A strong answer defines delivered marketplace value, supplies an arithmetic decomposition, and prevents low-quality volume from masquerading as growth.

metric-treesmonitoring

I would root the tree in ending MRR and connect every branch through identities that reconcile to the $2.4 million target.

The stock branch starts at $2 million, equal to 100,000 paid seats times $20 realized MRR per seat, and ends at the $2.4 million goal.
The monthly bridge is opening MRR plus $50,000 new and $30,000 expansion, minus $20,000 contraction and $25,000 churn, for a current net gain of $35,000.
Acquisition owns the $50,000 new-MRR branch as 1,000 new accounts times $50 first-month MRR, with trial volume and paid conversion beneath it.
Retention owns gross MRR churn of 1.25%, while expansion owns the $30,000 branch; keeping current flows adds only $210,000 in 6 months, leaving a $190,000 gap to assign.

Why interviewers ask this: The interviewer is checking whether the tree is mathematically reconcilable, actionable by teams, and explicit about the gap to target.

active-usersdecision-making

I would define MAU as distinct canonical human users who create at least 1 persisted content change during a UTC calendar month.

Qualifying actions are exactly 3 successful events: document_created, edit_committed, or comment_posted; logins, views, notification opens, and failed writes do not count.
The window is [00:00 UTC on day 1, 00:00 UTC on day 1 of the next month), uses event time, and closes after a 48-hour late-arrival allowance.
Identity resolution counts 1 canonical user across web and mobile, excludes anonymous activity until linked, and removes employee, test, bot, and suspended accounts.
I would rename the old 1.2 million figure visited MAU, backfill both definitions for 12 months, and make 430,000 the governed baseline for the new contract.

Why interviewers ask this: A strong answer removes ambiguity from behavior, identity, time, and eligibility rather than merely choosing a stricter adjective for active.

activationguardrails

I would optimize 7-day qualified activation, not reminder clicks or raw lesson starts.

A signup activates only after completing 3 lessons on at least 2 distinct days within 168 hours; moving from 32% to 40% means 160,000 additional activated users per monthly cohort.
Keep the denominator to eligible new human accounts assigned before their first reminder, and report channel segments only when they contain at least 10,000 signups.
Require 30-day retention among activated users to decline by no more than 1 percentage point and push opt-outs to increase by no more than 0.5 percentage points.
Cap reminder complaints at 2 per 10,000 sends and variable delivery cost at $0.30 per incremental activated user.

Why interviewers ask this: The interviewer wants a value-based growth KPI with a precise contract and numerical limits on downstream quality, user harm, and cost.

aggregationsessions

The global conversion is the ratio of summed purchases to summed eligible sessions, so it is 2,200 divided by 10,000, or 22%.

Market A converts at 20% and market B at 40%; their unweighted average of 30% gives a 10-point overstatement.
Weighting each market rate by its denominator gives 90% times 20% plus 10% times 40%, which reconciles to 22%.
If the mix moves to 50% per market with both rates unchanged, raw conversion rises to 30%, so I also publish a mix-standardized series using the original 90/10 weights.
The contract counts at most 1 purchase per eligible checkout session and shows the 2,200 numerator and 10,000 denominator beside every reported ratio.

Why interviewers ask this: A strong answer computes a ratio of sums, exposes mix effects, and fixes the counting grain instead of averaging percentages.

funnel

Both rates are valid for different questions, so I would name every transition and its eligible denominator rather than publish one ambiguous conversion.

Visitor-to-start is 60,000 divided by 100,000, or 60%, and start-to-qualified-completion is 30,000 divided by 60,000, or 50%.
Underwriting approval is 12,000 divided by 30,000 eligible completed applications, or 40%; ineligible and incomplete applications never enter that denominator.
Qualified-to-funded is 8,000 divided by 30,000, or 26.7%, which decomposes into 40% approval and 66.7% funding after approval; end-to-end conversion is 8%.
Freeze eligibility at application submission, deduplicate repeat applications from the same person within 30 days, and display all 5 stage counts beside the conditional rates.

Why interviewers ask this: The interviewer is evaluating whether the candidate can separate acquisition, eligibility, underwriting, and fulfillment denominators without hiding volume.

concurrency

Contribution margin is only about $0.51 per order, so the apparently healthy 22% take rate leaves little room for more discounting.

Variable revenue is $7.04 of commission plus the $2.20 customer fee, totaling $9.24 per order.
Variable cost is $5.50 plus $0.93 payment processing, $0.80 support and refunds, and $1.50 promotion, totaling about $8.73.
Contribution is therefore $0.51 per order, 1.6% of GMV, or roughly $25,600 across 50,000 weekly orders before fixed costs.
Raising the promotion from $1.50 to $3.00 makes contribution about negative $0.99 per order, so I would require at least $1.50 of measured future cohort margin to justify it.

Why interviewers ask this: A strong answer reconstructs contribution margin from auditable revenue and variable-cost components and tests the proposed economic lever.

experimentsproxyvalidation

I would validate click-through at the experiment-effect level because a 0.65 user correlation does not show that changing clicks changes repeat purchase.

For all 24 mature tests, estimate treatment effects on both metrics at the randomized unit and fit a precision-weighted relationship with leave-one-experiment-out validation.
I would require matching effect direction in at least 20 of 24 tests, out-of-sample R-squared above 0.50, and a calibration slope between 0.8 and 1.2.
Check that a 1-point CTR lift does not systematically raise 5-second return-to-search by more than 0.3 points, which would reveal low-quality click optimization.
Shadow the proxy for the next 6 experiments that reach day 28 and suspend it after 2 direction reversals or when quarterly calibration leaves the 0.8 to 1.2 range.

Why interviewers ask this: The interviewer checks whether the candidate distinguishes predictive user correlation from intervention-level surrogacy and sets falsifiable acceptance criteria.

monitoring

I would use balanced-liquidity coverage: the share of eligible requests occurring in local cells where requested hours divided by available provider hours is between 0.8 and 1.0.

Compute load by city, service category, and day using expected job duration; the global ratio of 90,000 to 100,000, or 0.9, hides local shortages and idle supply.
Treat load below 0.6 as excess supply and above 1.2 as shortage, and roll cells with fewer than 100 weekly requests into a broader regional cell.
If only 58% of requests currently fall in the 0.8 to 1.0 band, set a target of 75% rather than trying to maximize either provider count or request volume alone.
Validate the band by requiring fill rate to rise above 80%, provider utilization to stay between 55% and 70%, and median first response to remain below 4 hours.

Why interviewers ask this: A strong answer measures balance at the market cell where matching happens and proves that the chosen band benefits both sides.

I would bound the question to explaining the 60,000 weekly order shortfall over the latest 13 weeks versus the prior 13-week plan for the 5 established markets.

Define paid orders as eligible visitors times buyer conversion times orders per buyer, and require the components to reconcile from the 1.02 million actual to the 1.08 million plan.
Allocate the 60,000 gap across those 3 components with a log-change or Shapley decomposition, then separate new and returning buyers so acquisition mix is not mislabeled as retention.
Cut the gap by the top 5 markets, top 5 channels, platform, and cohort age, but drill deeper only when a segment explains at least 5,000 orders or 10% of the shortfall.
Deliver the diagnostic in 5 business days, compare with the same 13 weeks last year for seasonality, and leave causal claims to follow-up tests on the 2 largest contributors.

Why interviewers ask this: The interviewer wants a vague growth question converted into a reconciled quantity, fixed scope, controlled segmentation, and a decision-ready deadline.

Locked questions

21
A checkout experiment has a 12% baseline conversion rate, and a 0.8 percentage-point lift is the smallest effect worth $120,000 annually. With 5% two-sided alpha, 80% power, and 15,000 eligible users per day, how do you size and schedule it?
experimentsconversion
22
A pricing test raises conversion from 18.00% to 18.18%, with a 95% confidence interval of 0.05 to 0.31 percentage points, but finance says at least 0.30 points are needed to cover a $250,000 implementation. What do you recommend?
confidence-intervalspricing
23
A nominally 50/50 experiment assigns 100,000 users but records 54,000 in treatment and 46,000 in control. The treatment metric is up 4%. How do you analyze and decide?
experimentsmonitoring
24
Before launch, a team preregisters checkout completion as primary, two non-inferiority guardrails, and 24 secondary metrics. Results show primary lift of 1.4% at p = 0.03 and one secondary metric at p = 0.02. How do you decide?
guardrailsmonitoring
25
In an 80,000-user subscription test, mean revenue per user is up 6%, but one treatment account contributes $180,000 and removing it changes the estimate to negative 1%. What do you report and decide?
estimation
26
A redesigned home feed lifts sessions by 12% in week one, 6% in week two, and 3% in week four, while day-30 retention is not yet mature. How do you distinguish novelty from durable value?
retentionsessions
27
A collaboration feature will be tested on 120,000 users in 6,000 workspaces averaging 20 members, but treated members can invite and influence control members. With an intracluster correlation of 0.08, how do you design the test?
correlationdesign
28
You need to test a new dispatch ranking across eight cities where each driver's treatment changes wait times for other drivers. How would you design the switchback and decide from a 2.4% trip lift with pickup p90 worsening by 0.7 minutes against a 0.5-minute guardrail?
designguardrails
29
An experiment has 200,000 existing users, and the pre-period version of its primary metric correlates 0.65 with the outcome. How would CUPED change precision, and what checks precede using its positive result?
variance-reductionexperimentsmonitoring
30
A legal requirement forces a compliance flow to launch in all eight EU markets on July 1, with no holdout. You have 12 weeks before and after plus 14 unaffected markets. How do you estimate the causal effect on activation?
causaldesignestimation
31
A 60-person analytics team has 400 dbt models and seven Looker definitions of bookings. How would you structure the semantic metrics layer?
monitoringbidbt
32
A 25-tile dashboard scans a two-billion-row fact table and 400 users open it at 9 a.m.; p95 load time must stay below five seconds. What query architecture would you use?
queriesmodelingarchitecture
33
An eight-billion-row sales fact powers a daily country-by-category dashboard, but net revenue includes returns arriving up to 30 days late. Would you use an aggregate table or a materialized view?
materialized-viewsaggregation
34
A Tableau sales dashboard has 200 viewers, 120 million order lines, a 30-minute freshness SLA, and a two-second interaction target. Would you use a live connection or an extract?
bi
35
How would you enforce row-level security for 8,000 BI users, 30,000 customer accounts, and four million user-to-account entitlements without making every dashboard slow?
36
Design a commerce star schema for 500 million order lines per year with partial returns, split shipments, and multiple payment attempts.
schemamodelingdesign
37
You receive 150 million product events per day and need DAU, funnels, and session analysis. What grain would you choose for the base fact and why?
funnelactive-userssessions
38
Customer segment and sales territory change over time, but finance must report 80 million invoice lines using the attributes valid when each invoice was booked. How would you model this with SCD Type 2?
39
A lender processes 2 million applications per year and needs both daily pipeline balances and time from submission through approval and funding. Would you use a periodic or accumulating snapshot?
snapshotconcurrencyci-cd
40
Design a self-service executive dashboard for bookings and margin with 15-minute freshness, p95 under three seconds at 9 a.m., and drill-down from region to account to order.
cssdesign
41
Overall conversion rose from 7.8% to 8.75%, while mobile fell from 6.0% to 5.8% and desktop fell from 12.0% to 11.7%; how would you test whether this is Simpson's paradox?
paradoxes
42
Users who open recommendations at least 3 times a week have 68% eight-week retention versus 42% for other users; how would you determine whether recommendations cause the 26-point gap?
retention
43
In 18 months of daily data, a regression says each extra $1 of campaign spend is associated with $2.40 of revenue, but spend rises on weekends and holidays; how would you assess confounding?
44
An A/B test with 120,000 users reports a +2.1% relative lift and a 95% confidence interval from -0.4% to +4.6%, while launch requires at least +1.5%; what do you conclude?
ab-testingconfidence-intervals
45
For 1,800 delivery orders, median time fell from 42 to 39 minutes but the 99th percentile is 310 minutes; how would you use a bootstrap for this non-normal metric?
percentilesmonitoring
46
You have 3 years of weekly orders, a recurring 30% December spike, and a plan to forecast the next 13 weeks under a 15% campaign-spend increase; what is your analytical plan?
47
A subscription product has only 6 months of history, 45% of customers joined in the last 60 days, and the business asks for 180-day churn; how do you handle censoring?
churnsoft-skills
48
Monthly churn increased from 4.8% to 6.1% over 3 months; how would you decompose that business question into testable analytical questions?
churn
49
After adding a $19 plan below a $39 premium plan, total signups rose 24% but premium starts fell 18%; how would you estimate pricing cannibalization and net value?
pricingestimation
50
A new country has 25 million adults, a survey of 1,200 reports 14% need for the product, and a paid pilot of 800 visitors converts 3.5%; how would you size expansion with uncertainty?
51
At 08:30, the executive bookings KPI for yesterday is 12% high because retries duplicated 84,000 order rows, and the CEO review starts in 90 minutes. What do you do now, and how do you prove the replacement number is safe?
52
Three hours before a board meeting, the CFO finds that monthly revenue in the analytics report is 4.6%, or $3.2 million, below the general ledger. How do you handle the report and reconcile the gap?
soft-skills
53
A sales dashboard with a 30-minute freshness SLA is suddenly 9 hours stale, 700 employees use it, and the daily forecast meeting begins in 40 minutes. Describe your immediate response and recovery check.
54
A daily-orders metric shifts by 6.8% every midnight because events are grouped by UTC instead of each market's local date across 14 countries, and tomorrow's report is due in 2 hours. What do you change and restate?
monitoring
55
Refunds arrived up to 18 days late, leaving last month's net revenue overstated by 2.7%, or $740,000, and Finance requires a restatement before an earnings call in 6 hours. How do you execute it?
56
A BI export exposed 420 sensitive customer rows, and audit logs show that 17 employees downloaded the file during the last 36 hours. What are your first actions, impact assessment, and proof of containment?
57
A source release renamed checkout_status, causing 38% NULLs for 6 hours and making reported checkout conversion fall by 11 percentage points. The product review starts in 45 minutes. How do you respond?
58
A corrective six-month backfill stops at 61%, so the executive dashboard now mixes corrected and corrupted months and shows a 3.4% KPI jump. What do you do before resuming it?
backfill
59
For 2 hours, an EMEA sales dashboard intermittently showed the APAC slice because a shared cache key omitted the region filter, and logs record 63 executive views. How do you contain and investigate the incident?
incidentscaching
60
The dashboard shows $48.27 million while its 18,400-row CSV export sums to $49.01 million, a 1.53% gap, and Finance needs one answer in 60 minutes. You find $620,000 of test orders plus $120,000 from scope and row-level rounding. What do you publish?
61
Product reports 1.2 million MAU while the governed customer dashboard reports 780,000, and the board pack is due in 3 hours. What do you publish and how do you settle the dispute?
active-users
62
Sales says quarterly revenue is $84 million, Finance says it is $71 million, and executive bonuses close tomorrow. How do you resolve gross versus net revenue?
63
The commerce dashboard shows 2.46 million orders for June, but the payment system has 1.82 million settled order IDs. A promotion decision depends on the count today. What do you do?
system-design
64
Marketing attribution assigns 52% of conversions to paid search, 38% to paid social, 27% to email, and 18% to direct, totaling 135%, while the CMO wants to move $4 million tomorrow. How do you handle it?
soft-skills
65
Customer Success reports monthly logo churn of 4.8%, Finance reports 6.0%, and both use the same 12,000 cancellations. Which number do you use for the renewal plan?
churnresilience
66
Product counts 4.08 million April orders using a UTC calendar month, while Finance counts 3.92 million in fiscal April under a 4-4-5 calendar that closed on April 28. What goes into the quarterly review?
67
A marketplace dashboard reports $96 million monthly GMV, but $14 million comes from canceled or failed orders and Finance expects $82 million. Which figure do you keep?
68
Product reports $14.8 million MRR, Finance reports $13.9 million, and the gap comes from foreign exchange and upgrade timing across 22 currencies. What do you report at month-end?
69
Support reports median first response of 2.1 hours across 80,000 tickets, while Customer Success reports 11.4 hours and contracts impose penalties above 8 hours. Support pauses time outside staffed hours and counts bot acknowledgments; Customer Success uses elapsed time to the first human reply. What becomes official?
70
Leadership wants to change weekly active teams from any login to at least 3 collaborative actions, but the existing metric has 18 months of history, a current value of 640,000, and a year-end target of 750,000. How do you migrate the contract?
monitoring
71
A team planned a 14-day, 60,000-user checkout test but checked it 12 times and stopped on day 4 at 18,000 users when lift reached 3.2% with p = 0.041. The VP has approved launch. What do you correct immediately?
72
A feed redesign lifted sessions by 14% in week 1 and 7% in week 2, so product began a full rollout based on the 10.5% early average; by week 6 the effect is negative 1%. How do you correct the decision?
sessions
73
An executive slide says a redesign raised conversion from 14.0% to 20.4%, but enterprise conversion fell from 30% to 28%, SMB fell from 10% to 9%, and enterprise traffic grew from 20% to 60%. What do you tell the executive team?
74
A survey of 2,000 customers says 62% want a new workflow, and leadership is ready to fund a $2 million build; 70% of respondents are enterprise customers although enterprise represents 15% of the customer base, with 75% support in enterprise and 32% in SMB. What is your correction?
75
In a 100,000-user notification experiment, an analyst removes 30,000 treatment users and 20,000 control users who did not open the app after assignment; the remaining users purchase at 12% versus 10%, while intent-to-treat rates are 8.4% versus 8.2%. The team wants to ship. How do you respond?
experiments
76
A test reports 30 outcome metrics: the registered primary metric is negative 0.4% with p = 0.62, but one unregistered sharing metric is positive 6% with p = 0.03, and the launch memo calls the experiment a win. What do you change?
experimentsmonitoring
77
A 12,000-user test estimates a 1.0 percentage-point conversion lift with p = 0.57 and a 95% confidence interval from negative 2.5 to positive 4.5 points; the team says the feature has no effect and wants to roll it out because it is already built. What do you decide?
confidence-intervalsestimation
78
A search experiment randomizes 40,000 users but analyzes 3.2 million searches as independent rows, reporting a 1.8% lift with p = 0.004. Reanalysis at the user level gives a 95% interval from -0.6% to +4.2%, launch requires at least +2.5%, and the CMO wants to proceed. What do you do?
experiments
79
Operations targeted the 20 worst regions after an 8-week dip to 72 orders per day; after coaching they rose to 88, and the team claims a 22% lift. A randomized 20-region waitlist rose from 73 to 87 over the same period, while rollout requires 10 incremental orders per day. How do you correct the claim?
design
80
A customer-health review surveys only the 18,000 accounts still active from a 30,000-account cohort and reports 84% satisfaction after 12 months; 12,000 churned accounts were excluded, and leadership cites the result to renew a $3 million success program. What do you do?
churncohorts
81
The COO asks within 4 hours whether to approve $3 million of emergency freight because fill rate fell from 96% to 89% across 12 warehouses, but one warehouse representing 8% of orders has not loaded today. What do you deliver?
warehouse
82
A board deck is due in 3 hours, but the warehouse is missing a source that represents 8% of quarterly bookings. How do you present the number?
warehouse
83
A product launch is scheduled in 12 hours, but the payment-quality table used for its 1.0% failure-rate gate is 2 days stale. What do you recommend?
84
The CFO demands one annual revenue forecast in 6 hours for the budget, although the current models span $116 million to $141 million. What do you provide?
85
A VP asks you to remove a customer segment covering 14% of accounts because its retention fell 11 percentage points and hides the other segments' 3% gain. What do you do?
retention
86
Marketing spends $4.2 million per quarter and demands causal ROI from observational attribution data in 3 hours; the dashboard reports 3.1x ROAS. How do you answer?
causal
87
Communications needs a public customer count in 24 hours and wants to say 2 million, but identity rules produce estimates from 1.84 million to 2.07 million. What number do you approve?
estimation
88
A regulator requests a transaction report in 36 hours, but the warehouse total is $138.6 million versus $141.0 million in the ledger, a 1.7% reconciliation gap. What do you submit?
transactionswarehousereact
89
Leadership proposes laying off 15% of a 240-person operations team because a productivity dashboard ranks them lowest, but 22% of completed work is missing from the feed. What is your response?
90
Acquisition due diligence closes in 48 hours, while the target reports $62 million revenue, its general ledger shows $57 million, and CRM shows $65 million. How do you advise the deal team?
91
Two hours before an executive review, a junior presents complaints as tripling from 0.2% to 0.6% on a chart whose y-axis starts at 0.18%; the samples are 22,000 and 1,900 users. How do you correct the decision view and coach them without taking over?
92
A junior allocates a $5 million campaign budget from a spreadsheet with 6 manual filters, and rerunning it changes channel totals by 3.2%; the recommendation is due at 10:00 tomorrow. What do you do?
spreadsheetsspread
93
A mid-level analyst tells the quarterly review that revenue grew 18%, from $100 million to $118 million, but prices rose 12% and customer count fell 4%. How do you correct the conclusion and turn it into a mentoring case?
mentoring
94
A junior has built a 47-chart executive dashboard due at 09:00 tomorrow for 12 leaders, but the meeting needs decisions on only three business questions. How do you rescue the delivery and coach them?
95
Customers who opt into coaching have 68% 90-day retention versus 42% for non-users, but adopters were already 2.3 times more active before signup; an analyst writes that coaching raises retention by 26 points in a deck going to the VP today. What do you do?
retentiondecision-making
96
A mid-level analyst promised a five-day churn diagnosis, but on day 5 has no readout after expanding from four hypotheses to 34 segment cuts, and the executive decision is tomorrow. How do you handle it?
churnpromisessoft-skills
97
An analyst wants promotion to senior within six months, while three teams currently log 18 conversion-metric disputes per quarter and spend six hours a week reconciling them. What ownership project would you give them?
ownershipmonitoring
98
Two analysts publish Q3 support staffing needs of 120 and 165 FTE for 4.2 million forecast contacts, 30 minutes before the operating plan is locked. How do you resolve it without assigning blame?
99
At 14:00 before a 16:00 regional report deadline, a junior discovers that 9% of orders lack region, assigns them to the largest region, and omits the gap from the notes. How do you respond?
estimation
100
Your team recommended a new onboarding flow, but after a 10% rollout activation falls from 35.0% to 33.2% and support contacts rise 18%. What do you do with the rollout and the team?
activationonboarding

Questions

1A clickstream table receives 2 billion events per day, and product needs user sessions split after 30 minutes of inactivity to decide whether a new onboarding flow reduced median time to activation by at least 10 percent. How would you build the SQL output for the last 90 days?

2Your warehouse ingests 800 million mobile events per day, and network retries duplicate about 0.7 percent of them before the daily purchase report is produced at 09:00. How would you deduplicate the events in SQL so finance can trust the reported order count?

3A subscription product has 20 million signups across 18 months, and growth will pause channels whose week-4 retention is below 18 percent. How would you write the SQL for signup-month cohorts with week 1 through week 12 retention by acquisition channel?

5You have 400 million historical transactions and a customer-risk table whose tier changes over time, and credit operations needs each transaction labeled with the tier valid at purchase time to set next quarter's limits. How would you implement the point-in-time join in SQL?

7A latency table contains 12 billion rows per month and 500 country-device groups, but the release gate needs p50, p95, and p99 within 10 minutes and blocks any group whose p95 exceeds 2.5 seconds. When would you use exact versus approximate percentiles in SQL?

8Merchandising needs the top five products by net revenue within each of 120 categories from 250 million order lines, with all fifth-place ties included for an assortment decision. How would you write the SQL and make tie behavior explicit?

9A B2B company has an 8 million-node account hierarchy with parent_account_id and annual recurring revenue, and sales needs ARR rolled up to every ancestor plus a list of structures deeper than eight levels before redesigning territories. How would you query it with recursive SQL?

10A weekly attribution query scans 15 TB of clickstream data, joins orders and campaign history, runs for 70 minutes, and costs $180, but marketing needs it under 10 minutes before reallocating $5 million of spend. How would you optimize the analytical SQL without changing its result?

11A local-services marketplace has 500,000 weekly visitors, 40,000 completed jobs, and $8 million in weekly GMV. What north star metric would you choose?

12A subscription product has 100,000 paid seats and $2 million in MRR, with a target to grow MRR by 20% in 6 months. Build the metric tree you would use.

13A web and mobile collaboration product reports 1.2 million MAU, but only 430,000 users meaningfully edit content. Write the exact active-user contract you would adopt.

14A learning app gets 2 million new signups per month, and growth wants reminders to raise activation from 32% to 40%. Define the KPI and guardrails.

15Market A has 9,000 eligible checkout sessions and 1,800 purchases, while market B has 1,000 sessions and 400 purchases. How should monthly checkout conversion be aggregated?

16A lending funnel has 100,000 visitors, 60,000 application starts, 30,000 completed eligibility-qualified applications, 12,000 approvals, and 8,000 funded loans. Growth reports 8% conversion while risk reports 26.7%. How do you define the funnel?

17A food-delivery marketplace processes 50,000 weekly orders with a $32 basket, a 22% take rate, a $2.20 customer fee, $5.50 courier cost, 2.9% payment fees, $0.80 support and refunds, and a $1.50 promotion. What is the unit economics view?

18A search team wants to use click-through rate as a proxy for 28-day repeat purchase because experiments run for 2 weeks, and user-level correlation is 0.65. How would you validate the proxy using 24 past experiments?

19A home-services marketplace has 90,000 requested service hours and 100,000 provider-available hours per week, yet only 72% of requests are filled and provider utilization is 55%. What balance metric would you build?

20Weekly paid orders are 1.02 million versus a 1.08 million plan, and quarter-over-quarter growth slowed from 8% to 2%. The entire brief is: why is growth slowing? Turn it into a bounded analysis.

Locked questions