Glossary

Statistics and business-metric terms in one place.

Statistics

Mean→ covered in a lesson: The sum of all values divided by their count. It marks the centre of gravity of the data: if every observation were identical, each one would equal the mean.; $\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$
Median→ covered in a lesson: The value that splits the ordered list in half: half the observations fall below it, half above. With an even count you take the midpoint of the two central values.
Mode→ covered in a lesson: The value that occurs most often. It is the only measure of centre that works for categories — the best-selling product, the most common payment method.
Variance→ covered in a lesson: The average squared deviation of values from their mean: the more spread out the data, the larger it gets. It is measured in squared original units — dollars², minutes².; $\sigma^2 = \frac{1}{n}\sum (x_i - \bar{x})^2$
Standard deviation (σ)→ covered in a lesson: The square root of the variance: the typical distance from the mean to a single observation, in the same units as the data. For a normal distribution about 68% of values lie within ±1σ of the mean and 95% within ±2σ.; $\sigma = \sqrt{\frac{1}{n}\sum (x_i - \bar{x})^2}$
Percentile / quartile→ covered in a lesson: The value below which a given share of the data lies: p95 is the threshold that 95% of observations do not exceed. Quartiles are the 25th, 50th and 75th percentiles (Q1, median, Q3).
Normal distribution→ covered in a lesson: A symmetric bell-shaped distribution fully described by two numbers: the mean μ (where the peak sits) and the standard deviation σ (how wide the bell is). The 68-95-99.7 rule: ±1σ, ±2σ and ±3σ contain 68%, 95% and 99.7% of values.
Skewness→ covered in a lesson: A measure of asymmetry in a distribution: one tail stretches further than the other. Under right skew, rare large values pull the mean up above the median.
Probability→ covered in a lesson: A number from 0 to 1 saying how expected an event is: 0 means impossible, 1 means certain. Under the frequentist reading it is the share of cases in which the event occurs if the trial is repeated many times.
Law of large numbers→ covered in a lesson: As trials accumulate, the observed share converges to the true probability. The law describes the behaviour of the average over a long run and says nothing about any individual trial.
Conditional probability→ covered in a lesson: The probability of event A given that event B has already happened, written P(A|B). It differs from the reverse quantity P(B|A) — these are different numbers.; $P(A|B) = \frac{P(A \cap B)}{P(B)}$
Bayes’ theorem→ covered in a lesson: The rule for updating a probability once new data arrives: P(A|B) = P(B|A)·P(A) / P(B). It accounts for the base rate P(A) — how common the event is before any evidence.; $P(A|B) = \frac{P(B|A)\cdot P(A)}{P(B)}$
CLT→ covered in a lesson: The central limit theorem: take samples from almost any distribution and compute the mean of each, and the distribution of those means tends toward normal while its spread shrinks as σ/√n.; $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$
Standard error→ covered in a lesson: The standard deviation of the estimate itself rather than of the data: how much the mean varies from one sample to another. For a mean, SE = σ/√n.; $SE = \frac{\sigma}{\sqrt{n}}$
Confidence interval→ covered in a lesson: A range of plausible values for the quantity being estimated. The interpretation applies to the method: repeat the experiment many times, build a 95% interval each time, and about 95% of those intervals will cover the true value.; $\bar{x} \pm z \cdot SE$
Bootstrap→ covered in a lesson: Estimating uncertainty without formulas: from the sample you have, repeatedly draw a new sample of the same size with replacement and observe how the statistic of interest varies.
Null hypothesis (H0)→ covered in a lesson: The claim that there is no effect and the observed difference is chance. Testing proceeds by contradiction: you compute how implausible the observed data would be in a world without the effect.
p-value→ covered in a lesson: The probability of seeing a result at least this extreme if there is genuinely no effect. It is not the probability that the hypothesis is true, and it is not the size of the effect.
Type I error (α)→ covered in a lesson: A false positive: the test rejected a true null hypothesis, declaring an effect that does not exist. The level α is chosen in advance and is the share of such errors accepted (usually 0.05).
Type II error (β)→ covered in a lesson: A false negative: the effect is genuinely there but the test failed to detect it. The converse — detecting an effect that exists — is called power and equals 1−β.; $\text{power} = 1 - \beta$
Power→ covered in a lesson: The probability of detecting an effect of a given size, assuming it is genuinely there. It depends on the effect size, the spread of the data, the sample size and the chosen α.; $1 - \beta$
t-test→ covered in a lesson: A test comparing the means of two groups: it measures the observed difference against the standard error of that difference. It assumes independent observations and roughly normal sample means.; $t = \frac{\bar{x}_1 - \bar{x}_2}{SE_{\text{diff}}}$
Multiple comparisons→ covered in a lesson: Testing many hypotheses at once — several metrics, segments or variants. The risk of a false positive accumulates: with 20 independent tests at α=0.05, at least one false "significant" appears about 64% of the time.; $P(\text{at least one error}) = 1 - (1-\alpha)^m$
Correlation (r)→ covered in a lesson: A number from −1 to +1 describing the strength and direction of a linear relationship. Zero means no linear relationship, not the absence of any relationship.
Regression / OLS→ covered in a lesson: A method that fits a line (or a more complex shape) so the sum of squared deviations of the points from it is as small as possible. The slope shows how much y changes on average when x rises by one.; $y = b_0 + b_1 x$
Simpson’s paradox→ covered in a lesson: A relationship visible in the aggregate reverses inside every subgroup. The cause is a hidden factor distributed unevenly across the groups.
Overfitting→ covered in a lesson: The model learned the random noise of the training data rather than the pattern: excellent results there, poor results on new data. It shows up as a gap between training and hold-out performance.
Precision / Recall→ covered in a lesson: Precision — of the items the model assigned to a class, what share was assigned correctly. Recall — what share of the items actually in that class the model found.; $\text{precision} = \frac{TP}{TP+FP},\quad \text{recall} = \frac{TP}{TP+FN}$
ROC / AUC→ covered in a lesson: The ROC curve shows how the shares of true positives and false positives relate as the classifier threshold is swept across its whole range. AUC is the area under that curve: 1.0 is perfect, 0.5 is coin-flip guessing.
Survivorship bias→ covered in a lesson: A distortion where conclusions are drawn only from the cases that survived into the data, while those that dropped out are invisible.
Goodhart’s law→ covered in a lesson: Once a measure becomes a target, it starts being optimized directly and stops reflecting whatever it was introduced to capture.

Business metrics

North Star Metric: The metric a team picks as its main one: it reflects the value users receive and leads revenue. It sits at the top of the metric tree, with the rest broken out as its drivers.
DAU / MAU→ formula and SQL: The count of unique users who took a target action in a day (DAU) and in a month (MAU). Their ratio is called stickiness and reads as "how many days a month a user shows up": 0.2 is roughly 6 days out of 30.; stickiness = DAU / MAU
Retention→ formula and SQL: The share of a cohort that returns to the product after a given amount of time from first contact. It is computed by cohorts — groups that arrived in the same period.; retention = returning cohort members / cohort size
Churn→ formula and SQL: The share of customers or revenue lost over a period. At 5% monthly churn the average customer life is about 20 months (1 / 0.05).; churn = customers lost in period / customers at period start
ARPU / ARPPU→ formula and SQL: Average revenue per user (ARPU) and, separately, per paying user (ARPPU). The gap between them shows what share of the audience pays.; ARPU = revenue / all users; ARPPU = revenue / paying users
LTV→ formula and SQL: The total profit a customer brings over their whole life with the product. A rough subscription estimate: average revenue × margin / churn.; LTV = average revenue × margin / churn
CAC→ formula and SQL: The full cost of acquiring one new customer: marketing and sales budget divided by the number acquired. Computed over paid channels.; CAC = acquisition spend / new customers acquired
GMV→ formula and SQL: The total value of all goods sold through the platform in a period, before commissions, discounts, cancellations and returns. This is turnover, not revenue: the platform earns only its cut of GMV.
Take Rate→ formula and SQL: The share of GMV the platform keeps as commissions and paid services. GMV of 10bn at a 5% take rate is 500m of revenue.; take rate = platform revenue / GMV
Conversion Rate (CR)→ formula and SQL: The share of users who reached a target action, out of those who had the chance to take it. It needs its base spelled out: "visit to order" and "cart to order" are different quantities.; CR = target actions / users who could take them
AOV→ formula and SQL: Average order value: revenue divided by the number of orders. Like any average, it is sensitive to outliers.; AOV = revenue / number of orders
NRR→ formula and SQL: Net revenue retention — what the revenue from a cohort of customers became a year later, counting expansions, downgrades and churn but excluding new customers. Above 100% means growth without new sales.; NRR = (starting MRR + expansion − contraction − churn) / starting MRR
MRR→ formula and SQL: Recurring monthly subscription revenue, normalized to a month: an annual contract is divided by 12 and one-off payments are excluded. It decomposes into new, expansion, contraction and churn.
Fulfillment / Match Rate: The share of requests that reached a successful outcome: the order delivered, the ride taken, demand matched to supply. A measure of the balance between supply and demand on the platform.; match rate = successfully closed requests / all requests
Same-store sales→ formula and SQL: Sales of comparable locations: only the stores or restaurants open in both periods being compared. It strips out the effect of new openings. Reported as LFL (like-for-like).
Guardrail metrics→ covered in a lesson: Limit metrics that watch whether a gain in the target number is being bought with damage elsewhere. They are fixed before the experiment starts and reviewed together with the target metric.
ACV: Annual contract value — the value of a contract expressed per year: a three-year deal worth 300k has an ACV of 100k. Unlike TCV, which counts the whole sum across the contract term.; ACV = total contract value / term in years
ARR: Annual recurring revenue from active subscriptions, usually MRR × 12. It describes the current run rate: what the business will earn over the next 12 months if nothing changes.; ARR = MRR × 12
KYC: Know Your Customer — the mandatory identity check before opening an account or processing transactions, required by regulators to fight money laundering.
Interchange: An interbank fee: the acquiring bank pays it to the issuing bank on every card transaction. The card network sets the rate, while the issuer collects it.
TPV→ formula and SQL: Total payment volume — the total value of payments processed through the platform in a period. For fintech it plays the role GMV plays for a marketplace: it is flow, not income.
SKU: Stock keeping unit — one distinct product variant with a unique set of attributes: a red T-shirt in size M and the same shirt in size L are two different SKUs. The SKU count describes assortment breadth.
FBO: A fulfillment model where stock sits in the marketplace warehouse ahead of time and the platform itself stores, picks and delivers it. The opposite model is FBS, where goods stay with the seller and ship per order.
GBV: Gross booking value — the total value of services booked in a period: flights, hotels, tours. For travel it is what GMV is for a marketplace.
TAC: Traffic acquisition cost — what a platform pays for incoming traffic: to partners for being the default search and to network partners for showing its ads.
ROAS→ formula and SQL: Return on ad spend — how much revenue each unit of ad budget brings back: ROAS of 4 means four in revenue per one spent. Its inverse is the ad-cost share of revenue.; ROAS = revenue from ads / ad spend
NPS→ formula and SQL: Net promoter score — a loyalty index based on the question "how likely are you to recommend us" on a 0–10 scale. The share of detractors (0–6) is subtracted from the share of promoters (9–10); passives at 7–8 are excluded. The result runs from −100 to +100.; NPS = %promoters (9–10) − %detractors (0–6)
CPI: Cost per install — the cost of a single app install. The base metric of paid traffic in mobile products.; CPI = acquisition spend / installs
UA: User acquisition — the function responsible for paid growth: budgets, channels, creatives and media buying.
F2P: Free-to-play — a model where the product is free for everyone and revenue comes from a small share of payers, typically 1–5%.
D1 / D7 / D30→ formula and SQL: Retention on day 1, 7 and 30 after install: the share of a cohort that returns to the product on that day. The standard checkpoints of mobile analytics.; Dn = users returning on day n / cohort size
ETA: Estimated time of arrival — the forecast for when a courier, driver or order will arrive. What is measured is not only the duration but the accuracy of the forecast.
LMS: Learning management system — the platform that hosts courses, tracks learners and collects completion statistics.
RPM: Revenue per mille — what a creator or platform earns per thousand views, after the platform has taken its cut. Unlike CPM, which is what the advertiser pays per thousand impressions.; RPM = revenue / views × 1000
CPC→ formula and SQL: Cost per click — the price of a single click on an ad. It is set in an auction and depends not only on the bid but on ad quality.; CPC = spend / clicks
SEM: Search engine marketing — paid promotion in search results, i.e. keyword advertising. Unlike SEO, it works only while the budget lasts.
Look-to-Book: The ratio of bookings to search sessions in travel services. Low values are normal for the industry: people compare options, dates and prices at length before buying.; look-to-book = bookings / search sessions
Contribution margin→ formula and SQL: Revenue minus the variable costs tied directly to one unit — an order, a ride, a subscription. It shows how much is left to cover fixed costs.; contribution margin = revenue − variable costs
Bookings→ formula and SQL: The total users actually paid during a period, before revenue is recognized under accounting rules. In games it diverges from revenue because in-game currency is recognized as it gets spent.
Trial → Paid: Conversion from a free trial into a paying subscription. It depends heavily on the entry terms: a card-required trial converts better but brings fewer people in.; conversion = paid subscriptions / trials started
CTR→ formula and SQL: Click-through rate — clicks as a share of impressions of an ad, email or link. It measures appeal, not outcome.; CTR = clicks / impressions
SEO→ formula and SQL: Search engine optimization — the work of getting pages to rank higher in unpaid search results, through content, technical health and links.
B2B / B2C: Business-to-business and business-to-consumer — selling to companies or directly to end users. B2B has few deals and a long cycle with group decision-making; B2C has many fast transactions.

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