- Trainer
- Product managers
- Marketers
Math for Statistics and Unit Economics
The school math behind every formula in our statistics, finance and product-analytics courses, explained for people who forgot it. Percent and percentage points, rounding and quick estimates, the sum sign, averages and weights, squares and roots, lines, compounding and discounting, probability and the normal curve, then unit economics from scratch. No proofs and no calculus: read a formula, say what each part does and compute it by hand or in a spreadsheet.
Free36 lessons~17 h 17 min of learning
Module 1: Numbers and shares
Fractions, ratios and the order of operations; percent vs percentage points and relative change; rounding at the end and rounding up; quick estimates and orders of magnitude.
- 1.1Order of operations, ratios and multiplesRead a business formula in the right order, tell a share from a ratio, and turn a multiple into a value.~28 min
- 1.2Percent vs percentage pointsAbsolute and relative change, new ÷ old − 1, lift in an A/B test, and why "+1%" can mean two different things.~24 min
- 1.3Rounding: at the end, and sometimes upCompute from unrounded values, round once at the end, and round up whenever you need enough: break-even, staff, test length.~28 min
- 1.4Back-of-the-envelope estimatesCheck any number in ten seconds: round to one significant figure, count the zeros, and give a range instead of false precision.~32 min
Module examComplete 4 more lessons to unlockModule 2: The language of formulas
Notation and Greek letters, the sum sign with its limits and double indices, rearranging a formula to find the unknown, inequalities, intervals and formulas with cases.
- 2.1Notation: indices, bars, hats and Greek lettersHow to read x_i, sorted values, x̄ and ŷ, the Greek letters μ, σ, α, β and λ, Δ for a change, and sample vs population.~23 min
- 2.2The Σ sign: sums, limits and running totalsRead Σ with its limits, see why deviations from the mean add up to zero, use sums of products, running totals and double indices, and two shortcuts: n(n + 1)/2 and k(k − 1)/2.~26 min
- 2.3Rearranging a formula: solve for what you needDo the same to both sides and undo in reverse order: break-even Q = F/c, runway, the regression intercept, sample size, a fraction inside a denominator, and why a gross-up divides by (1 − f).~25 min
- 2.4Inequalities, intervals and formulas with cases<, ≤, ± and intervals, "if and only if", min and max, formulas with cases, fences, payback as the first month that clears a bar, and tiered rates with effective vs marginal.~34 min
Module examComplete 4 more lessons to unlockModule 3: Averages and shares of shares
Mean, median and trimmed mean; weighted means and mix; products of shares in funnels and metric trees; choosing the right denominator.
- 3.1Typical value and position: mean, median, quartilesMean, median, mode and trimmed mean, quartiles, percentiles and the IQR (two ways to compute them), a seasonal index, and the cumulative share curve.~27 min
- 3.2Weighted mean and mixΣwx/Σw, why a pooled rate is not the mean of rates, mix-adjusted rates, pooled variance and pooled p̄, the cost of capital, PERT estimates and weighted scoring.~27 min
- 3.3Products of shares: funnels and metric treesOverall conversion as a product of step rates, working a funnel backwards from a goal, ARPU = paying share × ARPPU, revenue per visitor, stickiness, diluted effects, ownership dilution and RICE.~25 min
- 3.4What do we divide by? Denominator trapsARPU vs ARPPU, LTV per cohort user vs per survivor, win rate with or without "no decision", gross vs net margin, concentration with the item in the total, and incremental results against a control group.~34 min
Module examComplete 4 more lessons to unlockModule 4: Squares, roots and distances
Why statistics squares deviations, the square root and √n, errors that add like the sides of a right triangle, and standardizing with z.
- 4.1Why we square: variance, sums of squares and n − 1Why spread formulas square deviations, variance s² and σ², sums of squares split into between and within, λ as a sum of squared loadings, and the idea behind n − 1 and degrees of freedom.~28 min
- 4.2Square roots and √n: SD and the standard errorThe standard deviation as √s², the standard error s/√n and why 4× the data halves it, the standard error of a proportion, the minimum detectable effect, the paired t and the finite-population correction.~25 min
- 4.3Pythagoras in statistics: distances and errors in quadratureEuclidean and Manhattan distance, why independent errors add as squares, the pooled SE of a z-test vs the unpooled SE of an interval, and how to read the Wilson and Newcombe interval formulas.~28 min
- 4.4Standardizing: z, CV, effect size and rPut different scales side by side: z-scores, the coefficient of variation, t as signal over noise, Cohen's d as an effect in SD units, and correlation as a covariance scaled to between −1 and 1.~35 min
Module examComplete 4 more lessons to unlockModule 5: Lines and models
The linear function, slope as a marginal quantity, models with several variables, and splitting a total into parts.
- 5.1The linear functionRead y = a + bx in business formulas: profit = c·n − F, trend lines, a tax with a fixed part, the design effect, where two lines cross, and two relations that are not lines.~26 min
- 5.2Slope as a marginal quantityWhat one more unit adds: marginal vs average CAC and cost, operating leverage as 1 ÷ margin of safety, and price elasticity as a ratio of relative changes.~28 min
- 5.3Several variablesFormulas with several inputs: ŷ = b₀ + Σ bⱼxⱼ, 0/1 variables and interactions, a driver-based forecast, ±10% sensitivity and scenarios.~28 min
- 5.4Splitting a totalSplit a total into parts that add up exactly: sums of squares and R², plan vs actual as volume + mix + price, and a change in savings as contributions + growth.~35 min
Module examComplete 4 more lessons to unlockModule 6: Growth and time
Compounding and average growth rates, discounting and NPV, geometric series behind virality and LTV, and e, ln, odds and the S-curve.
- 6.1CompoundingGrowth factors, why −50% then +50% loses a quarter, (1 + r)ⁿ, simple vs compound interest, CAGR with a fractional power, and monthly ↔ yearly rates and churn.~27 min
- 6.2DiscountingCompounding in reverse: PV = FV ÷ (1 + r)ᵗ, NPV as a sum of discounted cash flows, IRR found by trial, the hurdle rate, and payback with linear interpolation.~27 min
- 6.3Geometric seriesSums that shrink by the same factor: seed ÷ (1 − k) for referrals, LTV ≈ margin ÷ churn and lifetime 1 ÷ churn, the finite sum for annuities, capped LTV and a savings pot.~30 min
- 6.4e, ln, odds and the sigmoidln undoes a power, so it solves for time; odds = p ÷ (1 − p), log-odds and the sigmoid p = 1 ÷ (1 + e⁻ᶻ), eᵇ as an odds multiplier, and payback with churn.~35 min
Module examComplete 4 more lessons to unlockModule 7: Probability and distributions
p and 1 − p, conditional probability and the 2×2 table, expected value, many tests at once, the normal curve, and the other curves with power.
- 7.1p and 1 − pProbability as a share, its complement 1 − p, retention as 1 − churn, and why p(1 − p) peaks at 0.5.~26 min
- 7.2Conditional probability and the 2×2 tableP(A | B) as a share inside a row, precision, recall and accuracy, relative risk and the odds ratio, and why the direction of a condition matters.~26 min
- 7.3Expected value and scenariosWeighting outcomes by their probabilities, deal pipelines and earn-outs, expected loss against an insurance premium, and risk exposure in matching units.~26 min
- 7.4Many tests at onceThe complement rule, multiplying independent chances, the chance of at least one false alarm, counting pairs and the Bonferroni split.~26 min
- 7.5The normal curveArea as probability, the 68–95–99.7 rule, where 1.96 comes from, one- and two-tailed p-values, and the z-values for α and power.~25 min
- 7.6Other curves and powert, chi-square and F as the same idea with another table, degrees of freedom, expected counts and Σ(O − E)²/E, and computing the power of a test.~36 min
Module examComplete 6 more lessons to unlockModule 8: Unit economics, the bridge
Contribution margin, break-even and the discount break-even; flows of customers and cash, runway, CAC payback and incrementality. The business reading lives in the finance and product-analytics courses.
- 8.1Contribution margin and break-evenThe unit-economics formulas as pure math: CM = P(1 − f) − T − V, CM%, break-even ⌈F ÷ c⌉, margin of safety, step costs, the volume a discount needs, gross-up and ROI.~29 min
- 8.2Flows: customers and cashOne rule for every stock, end = start + in − out: MRR, churn, NRR and GRR; profit vs cash, working capital, DSO and runway; CAC payback and incrementality against a holdout.~39 min
Module examComplete 2 more lessons to unlockModule 9: Money over time
Simple interest and day counts, loans and amortisation, real and nominal rates, taxes and fees.
- 9.1Simple interest, days and annualizingInterest on the original amount, counting days, the cost of paying late or skipping an early-payment discount, and turning a period rate into a yearly one.~28 min
- 9.2Loans and amortizationHow a payment splits into interest and principal, months to repay, a flat fee against interest on the balance, and the real annual cost of a loan as its internal rate.~27 min
- 9.3Real and nominal ratesInflation and purchasing power, the real rate as a ratio of growth factors, why n − i is only a shortcut, deflating a future sum, and exchange spreads.~26 min
- 9.4Taxes and feesThe after-tax rate r(1 − t), the tax-equivalent rate r ÷ (1 − t), a flat tax plus a fixed contribution and its effective rate, and how a yearly fee compounds against you.~38 min
Module examComplete 4 more lessons to unlock