Interview guides · Eucloid Data Solutions

Eucloid Data Solutions Data Scientist Interview Questions & Guide 2026

Data scientist interview prep for Eucloid Data Solutions: original practice on experiment design, SQL and metric reasoning, with worked solutions.

The 60-second brief

A Data Scientist at Eucloid Data Solutions plays a pivotal role in shaping the future of multimodal AI systems, particularly through the development of advanced Vision-Language Models (VLMs). This position is essential for architecting and building innovative solutions that integrate complex data types—such as images and text—enabling the company to deliver superior products and services to its users. You will be at the forefront of groundbreaking projects that impact millions, ensuring that the technology not only functions seamlessly but also aligns with user needs and business objectives.

Seniority shifts the scope more than the words in the title do. Earlier-career loops mostly check that you execute a well-posed analysis correctly; senior loops check that you can decide which question is worth answering and defend what you chose not to do.

Focus areas

Separate novelty effects from durable behaviour change
Pick a randomisation unit that respects interference
Turn a vague request into a measurable question

Overview

In this role, you will engage in multifaceted challenges, from designing and implementing Reinforcement Learning from Human Feedback (RLHF) frameworks to deploying large-scale models that serve high volumes of requests. Your work will directly influence product features, enhance user experience, and drive the strategic direction of Eucloid Data Solutions. As a Lead Data Scientist, you will not only contribute your technical expertise but also provide leadership that inspires innovation within your team and across the organization.

The Eucloid Data Solutions interview process

Eucloid Data Solutions candidates report 5 rounds · ≈ 4-6 weeks. The stages below are what candidates describe, not a published process.

Initial Screening

Whoever runs this call is usually not a practitioner. They take notes, and a hiring manager skims those notes later, so the real question is whether your work survives being written down by someone outside the field. Test every project sentence against that: could a non-specialist repeat it correctly without knowing what a propensity score is? Carry a plain-language version of each project and one reason you want this particular role that you could not copy onto another application. Vagueness at this stage reads as inexperience, even when the underlying work was genuinely deep.

What to demonstrate

Whether a non-specialist can restate your projects accurately, since their paraphrase is what reaches the hiring manager
Whether your reason for wanting the role points at the work itself rather than the company's reputation
Whether your language signals the level being screened for: what you decided yourself versus what you were handed

How to prepare

Write a two-sentence, jargon-free version of each major project: the question nobody could answer, and the decision your work changed. Read it to someone outside data and have them repeat it back
Point your 'why this role' answer at something concrete in the job description or the product surface you would be working on, and keep it to two sentences
Have two questions ready about measurement: which metric the team is held to, and who acts on an analysis once it lands

Technical Assessment

A handful of shapes account for most of what gets asked in this format: a ranking or deduplication inside groups, a running or rolling total, a period-over-period comparison, and a cohort tracked forward over time. Recognising the shape quickly is most of the speed here; deriving it from scratch while a clock runs is where the time goes. Know that a window function keeps every row while a GROUP BY collapses them, and know which one the question needs. If the exercise is in Python instead of SQL, the same shapes arrive as groupby with transform, shift and merge, and the same grain mistakes are available.

What to demonstrate

Whether you reach the right construct without a detour, such as ROW_NUMBER over a partition to deduplicate instead of a self-join against a MAX subquery
Whether you know what your window frame actually is, since adding ORDER BY inside OVER changes the default frame and silently changes a running total
Whether the thing runs. A near-miss that throws an error scores below a plainer query that returns the right rows.

How to prepare

Write each of the four shapes once from memory against a small schema and keep the working version somewhere you will reread it: dedupe with ROW_NUMBER, a running total, a month-over-month change with LAG, and a retention table
Compute one running total twice on data with tied timestamps, once on the default frame and once with ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW, and look at where the two disagree
If Python is on the table, rebuild the dedupe and the running total with groupby and cumsum, then assert the two implementations return identical rows

Behavioral Interview

Behavioural answers from data candidates get audited in a way that answers from other roles do not. When you say a model lifted retention, the next question is the denominator, the window, and how you knew the lift was not seasonal. So attach the measurement to each claim while you tell it: what the metric was before, over what period, and against what comparison. Numbers with no baseline read as rounded-up memory, and one unsupported figure tends to make the rest of the story sound rehearsed.

What to demonstrate

Whether each impact number arrives with a baseline, a window and a comparison, or as a bare percentage
Whether you can name the method that attributed the effect to your work (an experiment, a staged rollout, a seasonal control) or concede the link was correlational
Whether the magnitudes stay internally consistent when the interviewer multiplies them against the scale you described earlier

How to prepare

For each story, write the impact line as metric, value before, value after, window, and how attribution was established. Any line missing two of those five is a follow-up you will answer badly.
Re-derive one headline number from the source table rather than the deck that reported it. Resume numbers drift upward across retellings.
Decide in advance which figures you cannot share, and prepare the ratio or relative change you can give instead, so a confidentiality limit does not read as evasion.

Case Studies

Underneath the business framing, this round is usually asking whether you can turn a fuzzy goal into a quantity that could be computed from data such a business would plausibly hold. That means a metric with a stated numerator, denominator, eligibility rule and time window, plus an honest account of the conditions under which it would mislead you. Answers come apart when a candidate names a familiar metric and never defines it, because every follow-up then lands on an ambiguity that was left open and the candidate has to invent the definition under pressure.

What to demonstrate

Whether a named metric arrives with its denominator, eligibility rule and window attached rather than assumed
Whether the measure follows from the mechanism you proposed, or is a recognisable metric retrofitted to it afterwards
Whether you name a guardrail that would reveal the gain came from somewhere you did not want it to come from
Whether you can say what data the plan requires and what you would settle for if that logging were never implemented

How to prepare

Take five metrics you reach for by reflex and write each as one sentence containing numerator, denominator, eligibility rule and time window. The ones you cannot finish are the ones that will fail under follow-up.
For a product you use daily, write the measurement plan you would propose for a change to it: primary metric, one guardrail, the unit of analysis, and the table the numbers would come from.
Practise the substitution question. For three metrics you like, write what you would measure instead if the event you depend on were not being logged.

Final Interviews

A loop is not scored one interview at a time. The people you meet compare notes afterwards, usually in a meeting you are not in, and the outcome turns on what each of them can say about you when asked. That rewards something other than survival: every room needs one specific thing worth repeating, and none of them can contradict another. The common way to lose is to tell the same project four times with different numbers in it, or to be uniformly fine in a way that leaves nobody with anything to argue for.

What to demonstrate

Whether your account of a project survives being told twice, with the same scale, the same metric definition and the same numbers each time
Whether each interviewer leaves with one concrete claim they could make on your behalf later, rather than an absence of complaints
Whether a question you already answered in an earlier room gets the same answer at the same depth, without visible impatience

How to prepare

Write a one-page fact sheet for your two or three main projects that fixes the numbers you will quote: rows of data, the metric as a single sentence, the effect you measured and how long the work took. Say them aloud from the sheet until they come out identical every time
For each kind of room you expect, decide the one sentence you want that interviewer repeating in a debrief, then check during the mock that you said it outright instead of implying it
Rehearse answering the same project question twice in one sitting, the second time as though you had not just answered it, because the thing that needs fixing is the flatness that creeps into a repeated story

Where candidates lose points

Reading a pooled rate that moved because the mix moved, not because any behaviour changed

A pooled conversion rate is a weighted average, and a shift in the weights can move it in the opposite direction to every one of its parts. A paid campaign that brings low-converting traffic drops overall signup conversion even if desktop, mobile web and app conversion each rose that week, which is Simpson's paradox and it is the single most common cause of an inexplicable dashboard move. The discipline is to decompose before explaining: recompute the rate holding last period's segment weights fixed, and compare that counterfactual to the actual, so the mix effect and the rate effect are separated numerically rather than argued about. Segment on the dimensions that actually reweight, which in this domain are almost always device_type, referrer_channel, country and new versus returning.

Counting on an identity key that changes underneath the metric

visitor_id is per browser and per device, and it resets on cookie clearance, private browsing and platform privacy changes, so the distinct-visitor count drifts upward for reasons unrelated to reach. Any rate with visitors in the denominator therefore decays over time even when behaviour is constant, and any rate with visitors in the numerator inflates. The stitching at signup makes it worse in both directions: a user who signed up on mobile and returns on desktop is two visitors and one user, while a shared device is one visitor and several users. Decide which key each metric is counted on, write it into the definition, and when comparing a period before and after a platform privacy change, expect a level shift in every visitor-keyed metric and do not attribute it to the product.

Reading an observational correlation as a causal effect

Name the confounder you are most worried about and the design that would remove it: an experiment, a difference-in-differences with a checked pre-period trend, an instrument, or a regression discontinuity. When none is available, state which direction the bias likely runs and bound the claim accordingly.

Explaining an aggregate move without decomposing the mix shift

Split the change in the aggregate into within-segment movement and movement in segment weights before you explain it. Every segment's rate can fall while the overall rate rises, purely because volume shifted toward segments that already had higher rates.

Questions & practice

What are the best practices for optimizing multimodal model performance?

Medium · machine learning and modelling

Approach

Say how the offline result would be validated online before it is trusted.
Set a baseline first, so any model has something honest to beat.
Check what information would not exist at prediction time, and exclude it.

Follow-up

Where could label leakage enter this setup?
How would you choose the decision threshold, and who owns that choice?

Write a function to preprocess image data for input into a neural network.

Medium · machine learning and modelling

Approach

Pick an evaluation metric that matches the cost of each error type, not a default.
Set a baseline first, so any model has something honest to beat.
Check what information would not exist at prediction time, and exclude it.

Follow-up

How would you choose the decision threshold, and who owns that choice?
What would you monitor after launch to know the model is still valid?

If a deployed model starts to drift, what steps would you take to diagnose and rectify the issue?

Medium · machine learning and modelling

Approach

Say how the offline result would be validated online before it is trusted.
Check what information would not exist at prediction time, and exclude it.
Frame the prediction: the label, the moment of prediction, and the action it triggers.

Follow-up

What would you monitor after launch to know the model is still valid?
How would you choose the decision threshold, and who owns that choice?

Rebuild per-visitor ordering without groupby convenience methods

Easy · pandas · vectorisation · window logic

You have a DataFrame of 2 million fct_event rows with visitor_id, occurred_at_utc and event_id, unsorted and containing duplicate timestamps within a visitor. Produce three new columns: event_rank, the 1-based position of the event within its visitor ordered by occurred_at_utc; seconds_since_prev, the gap to that visitor's previous event, NULL for the first; and is_first_for_visitor. You may use sort_values, shift, cumsum, numpy and boolean masking. You may not use groupby.transform, groupby.apply, groupby.cumcount, groupby.rank or merge_asof. Break timestamp ties on event_id.

Approach

Sort once by ['visitor_id', 'occurred_at_utc', 'event_id'] and reset the index. The whole exercise reduces to row arithmetic on a sorted frame, and the tiebreak on event_id is what makes the result reproducible across runs.
Mark visitor boundaries with is_first = df['visitor_id'].ne(df['visitor_id'].shift()). This is the single fact every other column derives from.
Compute seconds_since_prev as the diff of the timestamp column, then overwrite it with NaT/NaN wherever is_first is True. The shift crosses the boundary between visitors and will otherwise hand the first row of each visitor the last event of the previous one.
Build event_rank from a running counter that resets at boundaries: take a global cumulative position (np.arange(len(df))) and subtract, per row, the global position at which that visitor started. Get the start position by forward-filling the positions where is_first is True, which is a cumsum-free reset and is O(n).
Verify against the forbidden method once, as a test rather than as the implementation, and confirm the two agree on every row.

Worked solution (20 min)

Sort on the three-key tuple and reset_index(drop=True).
Compute is_first via .ne(.shift()), which is True for row 0 because the shifted value is NaN.
pos = np.arange(len(df)); start = pd.Series(np.where(is_first, pos, np.nan)).ffill(); event_rank = (pos - start + 1).astype(int).
gap = df['occurred_at_utc'].diff().dt.total_seconds(); gap[is_first] = np.nan.
Assert event_rank equals df.groupby('visitor_id').cumcount() + 1 on the sorted frame.

Expected result: Three columns on the sorted frame: event_rank starting at 1 for every visitor and increasing by 1 with no gaps, seconds_since_prev null exactly where is_first_for_visitor is True, and is_first_for_visitor summing to df['visitor_id'].nunique().

Verify it yourself

is_first_for_visitor.sum() equals the number of distinct visitor_id values.
seconds_since_prev.isna().sum() equals that same number.
event_rank.max() per visitor equals that visitor's row count, and event_rank is non-negative everywhere.
A visitor with two events at the identical timestamp gets ranks 1 and 2 with a gap of 0.0, ordered by event_id.

Follow-up

The frame does not fit in memory. How does your approach change if you can only process one visitor-partitioned chunk at a time?
occurred_at_utc is client-supplied and sometimes runs backwards within a visitor. Does your seconds_since_prev go negative, and should it?
How would you extend this to reset the counter at every change of surface as well as visitor?

Seven-day activation rate by weekly signup cohort

Easy · cohorts · activation · date-bounds

dim_user holds user_id, account_created_at_utc, is_internal. fct_event holds user_id, occurred_at_utc, is_core_action. A user is activated when core-action events fall on at least two distinct UTC dates inside [account_created_at_utc, account_created_at_utc + 7 days). Return, for the last twelve complete weekly signup cohorts, the cohort week, cohort size, activated users and the activation rate. Exclude is_internal users. Every signup in the cohort week stays in the denominator, including users who never returned.

Approach

Start from dim_user as the denominator spine with is_internal = FALSE and DATE_TRUNC('week', account_created_at_utc) as the cohort key. Driving the query from the event table instead would silently condition on having events and delete the entire non-activating population.
Join fct_event on user_id with is_core_action = TRUE and a per-user bound, occurred_at_utc >= u.account_created_at_utc AND occurred_at_utc < u.account_created_at_utc + interval '7 days'. The bound is correlated to each user's own signup timestamp, not a single global date range.
Aggregate per user with COUNT(DISTINCT occurred_at_utc::date) >= 2, then LEFT JOIN that back onto the spine and COALESCE the flag to FALSE so non-activators contribute a zero rather than vanishing.
Restrict the published cohorts to those whose week ended at least eight days ago. A cohort younger than that has not finished its seven-day window, so its rate is mechanically low and reads as a decline.
Roll up by summing the numerator and denominator per cohort week, and state the two-distinct-days threshold next to the number since it is a choice that re-bases the whole history if changed.

Follow-up

Why two distinct days rather than one event? What happens to the published history if someone changes it to three?
Invited seats and SSO-provisioned users get an account_created_at_utc at provisioning and may never sign in. Should they be in this denominator?
The rate rose 3 points this week. What do you check before believing it?

Rebuild sessions from raw events with a thirty-minute gap

Medium · window-functions · sessionisation · gaps-and-islands

From fct_event (event_id, visitor_id, occurred_at_utc) alone, rebuild sessions: a new session begins when the gap from that visitor's previous event exceeds 30 minutes, and every session is force-closed at UTC midnight so none spans two calendar dates. Return one row per session with visitor_id, session_start, session_end, event_count and session_date. Do not read fct_session; the point is to reproduce it. Assume duplicate occurred_at_utc values exist for the same visitor.

Approach

Get the previous timestamp per visitor with LAG(occurred_at_utc) OVER (PARTITION BY visitor_id ORDER BY occurred_at_utc, event_id). The event_id tiebreaker is required, not stylistic: with duplicate timestamps an unstable ordering makes the boundary flags non-deterministic between runs.
Set a boundary flag when prev IS NULL, or occurred_at_utc - prev > interval '30 minutes', or occurred_at_utc::date <> prev::date. The third disjunct is the midnight rule, expressed as a date change rather than a clock comparison so it holds across any gap length.
Number the islands with SUM(flag::int) OVER (PARTITION BY visitor_id ORDER BY occurred_at_utc, event_id ROWS UNBOUNDED PRECEDING). Because event_id is unique the ordering is total, so no two rows are peers and RANGE UNBOUNDED PRECEDING would compute exactly the same numbers here. Write ROWS anyway: it is the half of the guard that survives someone later simplifying the ORDER BY back to occurred_at_utc alone, at which point the default RANGE frame gives every row sharing a timestamp one shared running total.
GROUP BY visitor_id and the island number, then MIN(occurred_at_utc) AS session_start, MAX(...) AS session_end, COUNT(*) AS event_count, session_start::date AS session_date.
Reconcile against fct_session on one sample day. The counts should agree except for server-emitted events carrying no client session, so a systematic difference beyond those is a bug in the gap rule or in the ordering.

Worked solution (30 min)

Pick one high-volume visitor and dump their ordered event timestamps for a day to trace by hand.
Add LAG with the tiebreaker and eyeball the computed gaps.
Add the three-part boundary flag and confirm the first event of each date is flagged.
Add the running SUM with an explicit ROWS frame, then group and aggregate.
Compare total event_count against the raw input count, and compare session counts to fct_session for the sample day.

Expected result: One row per (visitor_id, island). SUM(event_count) equals the input row count exactly, with no events lost or duplicated. No session_end falls on a different date from its session_start.

Verify it yourself

Total events in equals total events out.
MAX(session_end::date - session_start::date) is 0 across all rows.
For a visitor ordered 09:00, 09:10, 09:55, 23:58, 00:02, the result is four sessions, not three.
No two sessions for the same visitor have overlapping [session_start, session_end] ranges.
Swapping ROWS for RANGE while event_id stays in the ORDER BY changes nothing; dropping event_id from both ORDER BY clauses does change the boundaries for a visitor with duplicate timestamps, which locates the guard in the tiebreaker rather than in the frame keyword.

Follow-up

Why 30 minutes? What does a 5-minute rule do to sessions-per-visitor and to any per-session conversion rate?
The same person uses phone then laptop. Two visitor_ids, two sessions. What breaks if you sessionise on user_id instead?
The midnight rule splits an overnight session. Which metrics does that bias, and in which direction?

What metrics would you use to evaluate the performance of a multimodal AI system?

Medium · product sense and metrics

Approach

State what result would change your recommendation, so the answer is falsifiable.
Decompose the metric into the rates that drive it, and say which one you would check first.
Name one primary metric, then the guardrail that stops it being gamed.

Follow-up

Which segment would you cut first, and what would that rule out?
How would you detect that the metric is being gamed rather than genuinely improving?

How would you architect a distributed inference pipeline for real-time processing?

Medium

Approach

Say what you would check first and why it is the highest-information step.
Clarify what is being asked and what a complete answer would contain.
State your assumptions explicitly before working the problem.

Follow-up

What assumption would you test first?
How would you know your answer was wrong?

Describe how you would implement a preference modeling system for RLHF.

Medium

Approach

State your assumptions explicitly before working the problem.
Work from the decision backwards to the evidence you would need.
Say what you would check first and why it is the highest-information step.

Follow-up

How would you know your answer was wrong?
What assumption would you test first?

A test that won on day four and lost by day twelve

Medium · peeking · sequential testing · multiple comparisons · winner's curse

A two-week test was checked every morning. On day four the primary metric crossed p = 0.03 and the team shipped. By day twelve, with logging still running, the estimate had fallen to a 0.2% lift at p = 0.61. The day-four deck also reported a significant 9% lift among paid_search visitors on mobile_web, one of twenty segments inspected. Explain both patterns quantitatively, say what the day-four evidence was actually worth, and specify the monitoring rule that prevents a repeat.

Approach

Price the peeking. A fixed-sample test controls type I error at one pre-declared look. Ten daily looks at a nominal 5% raise the false positive rate to roughly 0.15 to 0.20, because the running test statistic takes a random walk that will eventually cross the boundary under the null.
Price the winner's curse separately, because it is a different error. Conditioning an estimate on having crossed the threshold biases it away from zero, by a factor of roughly 3 when true power is 20% and only about 1.1 at 80% power. Day four sits at roughly 29% of planned information, which is exactly the low-power case.
Read day twelve as the better estimate rather than as a contradiction. Nothing regressed; the day-four value was an extreme draw that was selected precisely for being extreme.
Price the segment claim. Across twenty segments at a nominal 5%, at least one crosses about 64% of the time under a global null, since 1 - 0.95^20 = 0.64, and the slice that surfaces is by construction the one with the most favourable noise.
Specify the rule instead of scolding. Either fix the horizon and look once, or use group-sequential boundaries such as O'Brien-Fleming that spend almost no alpha early, or use always-valid confidence sequences that stay correct under continuous monitoring. Pre-register the small set of segments, correct across the ones tested, and treat anything found afterwards as a hypothesis needing its own powered test.

Worked solution (25 min)

Count the looks actually taken, twelve daily, and state the inflated alpha band of 0.15 to 0.20 for ten looks, rising with more.
Place day four on the information fraction, about 4/14 = 29% of planned sample, and apply the exaggeration factor for low power.
Compute 1 - 0.95^k for the number of segments actually inspected; with k = 20 this is 0.64.
Report the day-twelve interval as the estimate and say plainly that the experiment supports no effect at any size the team would ship for.
Write the rule into the experiment template: horizon and segments declared at launch, sequential boundaries if interim looks are needed at all.

Expected result: The day-four result is consistent with pure noise: ten looks inflate the false positive rate to roughly 0.15 to 0.20, and an estimate conditioned on crossing at about 29% information is exaggerated by roughly a factor of three at low power. The segment finding appears about 64% of the time across twenty slices under a global null. The supportable conclusion is a 0.2% lift whose interval covers zero.

Verify it yourself

1 - 0.95^20 = 0.6415. If your family-wise number lands near 0.05 you have computed the per-test rate instead.
The day-twelve standard error should be roughly sqrt(12/4) = 1.7 times smaller than day four's. If the interval did not narrow, sample was not accumulating and there is a second problem.
A Bonferroni threshold for twenty segments is 0.0025; check whether the mobile_web result would have survived it.

Follow-up

Under O'Brien-Fleming with five planned looks, roughly what nominal p-value would the first look have needed to stop?
The feature already shipped. What analysis can you still run, and what can it not tell you?
If mobile_web paid_search were genuinely the only affected segment, how would you design the confirmatory test and how large would it have to be?

Tell a pipeline outage from a collapse in usage

Medium · pipeline-failure · instrumentation · event-volume

Weekly active accounts completing a core action fell 9%, and almost the entire fall sits in accounts whose events carry surface = 'ios'. App crash rates and store reviews are unchanged. You have fct_event with occurred_at_utc, received_at_utc, event_name, is_core_action, app_version and surface, plus fct_session and the ingestion job run log. Establish within the hour whether iOS engagement fell or iOS events stopped arriving, name the evidence that distinguishes them, and say what you would publish on the dashboard in the meantime.

Approach

Compare the event-name composition inside surface = 'ios' against the prior four weeks as shares, not counts. A behaviour collapse scales most event names together; a dropped event definition or a broken downstream filter hits specific event_name values while page_view and session-opening events hold steady. That shape difference is the fastest discriminator available.
Profile the received_at_utc minus occurred_at_utc distribution per day for surface = 'ios'. A stalled-then-backfilling pipeline shows a fat upper tail and a recovering p99; a silently dropped stream shows an unchanged lag distribution over a smaller volume. The two failure modes have different remedies and different histories.
Cut by app_version. A logging SDK change arrives with one build and ramps with its adoption curve; an infrastructure fault arrives across every build within the same hour. Checking this costs one group-by and rules out half the hypothesis space.
Cross-check against a signal that does not travel the suspect path: server-emitted events with session_id NULL, and subscription or billing activity for the same accounts. If those accounts are still transacting, the users did not leave.
Publish an ex-iOS total with an explicit annotated break rather than a blended total. A blended number during a known ingestion gap is wrong in a direction you can already name, and republishing it daily spreads the artefact into every downstream report.

Follow-up

Suppose the events do eventually backfill. What is your policy for restating the published weekly numbers, and who needs to be told?
What monitor would have caught this before a human noticed the weekly metric, and what would it alert on?
If is_core_action is maintained in the tracking plan, what governance would stop a change to that list from silently moving a north-star metric?

Suggested practice checklist

Four days spend equal time on query work, statistics, modelling and product judgement at deliberately shallow depth, which produces a scored map of where you actually stand. The last three days spend everything on the two areas the role weights most, and close by re-running day one to measure movement.

Day 1 — Breadth pass: query fluency

Solve six prompts spanning aggregation, joins, window functions and date arithmetic in 60 minutes total, stopping at 10 minutes each whether or not it works, and mark every prompt as solved, solved slowly, or stuck.
For each unsolved prompt write the single blocking sentence (I lost the grain, I did not know the frame clause, I could not express the date boundary) instead of reading the solution.
Translate one pandas transformation you know well into SQL and one SQL query into pandas, checking that both return the same row count and the same totals.

Deliverable: A scored six-row table, one line per prompt, saved for the day-seven re-run.

Day 2 — Breadth pass: statistics and inference

Answer ten short questions in writing with nothing open: what a p-value is conditional on, what a 95 percent interval covers across repeated samples, when a paired test is the right one, what the bootstrap estimates, why multiple comparisons inflate false positives, how controlling the family-wise error rate differs from controlling the false discovery rate, what power depends on, what a missed real effect costs a product, the three situations where the central limit theorem does not rescue you (small n, very heavy tails, dependent observations), and what a standard error is the standard deviation of.
Grade yourself against a reference and count only the answers that were exactly right, not the ones that were nearly right.
Rewrite the two weakest answers the following morning from memory in full sentences.

Deliverable: Ten graded answers with an honest count of exact hits.

Day 3 — Breadth pass: modelling

Take one tabular dataset end to end in 90 minutes: a leakage-safe split, a baseline that is not a model (majority class or historical mean), one regularized linear model, one gradient-boosted tree, and a single evaluation metric chosen before you look at any result.
Write why that metric fits the cost structure: precision at a fixed recall for alerting, calibration for anything feeding a price or a threshold, ranking metrics for retrieval, and note that area under the ROC curve is insensitive to class balance in a way that can flatter a rare-positive problem.
Name the leak you were most likely to introduce (an encoding fit on all rows before splitting, or a feature computed after the label's timestamp) and write the check that would have caught it.

Deliverable: A notebook whose first cell states the metric and the baseline, plus two lines on what beat what and by how much.

Day 4 — Breadth pass: product judgement

Answer three case prompts aloud at 15 minutes each, timing how long passes before you state a success metric.
For one case write the first segmentation you would run and the row counts you expect per segment, so that a tiny segment cannot quietly drive the conclusion.
Take a metric definition you did not write, from a public dashboard, a textbook, or documentation you already have open, and list every place two analysts implementing it would diverge: which rows the denominator admits, whether the unit is an account or a person, what the time window is anchored to, and what happens to data that arrives late. Then write the one question that would close the largest of those gaps.

Deliverable: Three recorded case answers plus an ambiguity list for a metric someone else defined, ending in the single question you would ask about it.

Day 5 — Depth, first area

Rank the four areas by how many bullet points in the role description each one covers, pick the top one, and spend the entire day inside it.
Work the six hardest problems you can find in that area and for each write the generalizable move you should have reached for first, rather than the answer.
Re-solve the two you failed the same evening with notes closed.

Deliverable: Six generalizable moves written as instructions to yourself, not as solutions.

Day 6 — Depth, second area, and the seam between them

Repeat the depth protocol on the second-ranked area with the same six-problem structure.
Construct one problem that requires both areas at once, for example a metric redefinition whose effect you must validate with a test whose readout you then have to query.
Solve your own combined problem end to end and note where the handoff between the two areas cost you time.

Deliverable: One combined problem, solved end to end, with the handoff failure written down.

Day 7 — Integration and re-measurement

Re-run the six prompts from day one under the same clock and compare both correctness and time.
Run a 60-minute mixed mock that moves between areas without warning, since switching cost is what breadth passes do not train.
Write the two areas you would still fail on, and the sentence you will use in the interview when you hit one of them.

Deliverable: A before-and-after score table plus a written plan for the two remaining gaps.

Stories where someone disagreed with you

Have two ready. In one, the data was on your side and you had to move someone who outranked you. In the other, the pushback was correct and you changed position. The second is the harder story and it lands better, because it shows you separate being right from being attached to an answer. Name the person's actual objection.

How do you ensure alignment between technical teams and product management?

Medium · behavioural and stakeholder questions

Approach

Quantify the outcome, including what you would not claim credit for.
Close with what you would do differently, concretely.
Name the disagreement or constraint, and how you resolved it with evidence.

Follow-up

How did you know the outcome was caused by your change?
What did you decide not to do, and why?

Discuss your experience with fine-tuning large language models.

Medium · behavioural and stakeholder questions

Approach

Pick a story where you drove the decision, not one where you observed it.
Quantify the outcome, including what you would not claim credit for.
Close with what you would do differently, concretely.

Follow-up

What did you decide not to do, and why?
What would you do differently if you ran that project again?

Choose between three teams' requests with one analyst-week

Medium · prioritisation · stakeholder · judgement

You have one analyst-week. Three requests land the same morning. A growth team wants a paid-channel readout before a Friday spend decision. A billing team wants gross monthly revenue churn rebuilt, because the current figure recognises cancellation at canceled_at_utc rather than period_end_utc and is therefore wrong. A product team wants a dashboard for a feature launching in six weeks. All three sponsors are peers of your manager. Deliver your ranking, the explicit rule that produced it, and the message you send to the two teams you defer.

Approach

Recognise what is being probed: whether you prioritise on decision value and reversibility or on who asked most recently and most loudly. The generic answer sorts by importance; the strong one states a rule, applies it, and accepts the ranking it produces even where that is uncomfortable.
Score each request on three statable things: the decision it unblocks and the date that decision is made, the cost of being wrong in the meantime, and whether the work is one-off or compounding. A wrong published churn figure compounds, because it is quoted downstream and enters forecasts; the channel readout has a fixed date that cannot move; the dashboard has six weeks of slack.
Notice the tension between value and urgency rather than resolving it by feel. The churn defect is the most valuable item and the least urgent one, which is exactly the shape of work that never gets done.
Break the churn item in two. A one-hour severity check, sizing the gap between the two recognition points in MRR, is cheap enough to do before ranking anything and may promote the item outright. Do that first, then rank.
Make the deferrals concrete. Each deferred team gets a date, a reason expressed as another team's decision deadline rather than as relative importance, and the smallest thing you can hand them immediately.

Follow-up

The dashboard team escalates to your manager. What do you say in that conversation?
Your severity check shows churn is overstated by 15%. Does the ranking change, and does anybody need to be told today regardless of the ranking?
A fourth request arrives Wednesday with a Thursday deadline. What comes off the list, and who do you tell first?