Home › Business Analytics › Formula Sheet Business Analytics Formula Sheet (BBA) 119 formulas for BBA, MBA and business analytics courses in one place: statistics, probability, sampling, hypothesis tests and ANOVA,
regression, forecasting, finance, supply chain and business metrics. Formulas marked “Calculate” open a step-by-step calculator.
Contents Descriptive statistics Probability and distributions Sampling and statistical inference Hypothesis testing and ANOVA Correlation and regression Forecasting and time series Finance analytics Logistics and supply chain Research methods and multivariate analysis Business metrics Programming in R: common functions 1. Descriptive statistics Concept Formula Calculator Arithmetic mean x̄ = Σxᵢ ÷ n Calculate Weighted mean x̄w = Σ(wᵢxᵢ) ÷ Σwᵢ — Median Sorted value at position (n + 1) ÷ 2; for even n, the mean of the two middle values Calculate Population variance σ² = Σ(xᵢ − μ)² ÷ N Calculate Sample variance s² = Σ(xᵢ − x̄)² ÷ (n − 1) Calculate Population standard deviation σ = √[Σ(xᵢ − μ)² ÷ N] Calculate Sample standard deviation s = √[Σ(xᵢ − x̄)² ÷ (n − 1)] Calculate Mean absolute deviation (about the mean) MAD = Σ|xᵢ − x̄| ÷ n Calculate Range Maximum − Minimum Calculate Coefficient of variation CV = (s ÷ x̄) × 100 % Calculate z-score z = (x − μ) ÷ σ Calculate Quartile deviation QD = (Q₃ − Q₁) ÷ 2 —
Sample variance and standard deviation divide by n − 1; population versions divide by N. MAD uses absolute deviations, while the standard deviation squares them.
2. Probability and distributions Concept Formula Calculator Complement rule P(A′) = 1 − P(A) — Addition rule P(A ∪ B) = P(A) + P(B) − P(A ∩ B) — Conditional probability P(A | B) = P(A ∩ B) ÷ P(B) — Multiplication rule P(A ∩ B) = P(A | B) × P(B) — Bayes’ theorem P(A | B) = P(B | A) × P(A) ÷ P(B) — Expected value E(X) = Σ x p(x) — Variance of a random variable Var(X) = E(X²) − [E(X)]² — Binomial probability P(X = x) = C(n, x) pˣ (1 − p)ⁿ⁻ˣ — Binomial mean and variance Mean = np; Variance = np(1 − p) — Poisson probability P(X = x) = e^(−λ) λˣ ÷ x! — Normal standardisation z = (x − μ) ÷ σ Calculate
3. Sampling and statistical inference Concept Formula Calculator Standard error of the mean SE(x̄) = s ÷ √n Calculate Standard error of a proportion SE(p̂) = √[p̂(1 − p̂) ÷ n] Calculate CI for a mean, σ known x̄ ± z(α/2) × σ ÷ √n Calculate CI for a mean, σ unknown x̄ ± t(α/2, n−1) × s ÷ √n Calculate CI for a proportion p̂ ± z(α/2) × √[p̂(1 − p̂) ÷ n] Calculate Sample size for a mean n = z²σ² ÷ E² Calculate Sample size for a proportion n = z² p(1 − p) ÷ E² Calculate Finite population adjustment n = n₀ ÷ [1 + (n₀ − 1) ÷ N] Calculate
E is the margin of error. Simple random sampling with replacement (SRSWR) allows repeat selections; without replacement (SRSWOR) does not, and a finite population correction may then apply to standard errors.
4. Hypothesis testing and ANOVA Concept Formula Calculator One-sample z statistic z = (x̄ − μ₀) ÷ (σ ÷ √n) — One-sample t statistic t = (x̄ − μ₀) ÷ (s ÷ √n), df = n − 1 — Pooled variance sₚ² = [(n₁ − 1)s₁² + (n₂ − 1)s₂²] ÷ (n₁ + n₂ − 2) — Pooled two-sample t t = (x̄₁ − x̄₂) ÷ [sₚ √(1/n₁ + 1/n₂)] — Chi-square statistic χ² = Σ(O − E)² ÷ E Calculate Expected count (contingency table) Eᵢⱼ = (row total × column total) ÷ grand total Calculate ANOVA F statistic F = MS_between ÷ MS_within — Mean square MS = SS ÷ df — Total sum of squares SST = Σ(yᵢ − ȳ)² —
CRD: completely randomised design Concept Formula Calculator Total sum of squares SS_T = ΣᵢΣⱼ(xᵢⱼ − x̄..)² — Treatment sum of squares SS_treat = Σᵢ rᵢ(x̄ᵢ. − x̄..)² — Error sum of squares SS_E = SS_T − SS_treat — Degrees of freedom Treatments t − 1; error N − t; total N − 1 —
RBD: randomised block design (balanced) Concept Formula Calculator Correction factor CF = G² ÷ N — Total sum of squares SS_T = Σxᵢⱼ² − CF — Treatment sum of squares SS_treat = ΣTᵢ² ÷ b − CF — Block sum of squares SS_blocks = ΣBⱼ² ÷ t − CF — Error sum of squares SS_E = SS_T − SS_treat − SS_blocks — Degrees of freedom Treatments t − 1; blocks b − 1; error (t − 1)(b − 1); total tb − 1 —
For a balanced RBD: t treatments, b blocks, N = tb, Tᵢ treatment totals, Bⱼ block totals, G grand total. Treatment F = MS_treat ÷ MS_E.
5. Correlation and regression Concept Formula Calculator Pearson correlation r = Σ(xᵢ − x̄)(yᵢ − ȳ) ÷ √[Σ(xᵢ − x̄)² Σ(yᵢ − ȳ)²] Calculate Simple linear regression ŷ = a + bx Calculate Regression slope b = Σ(xᵢ − x̄)(yᵢ − ȳ) ÷ Σ(xᵢ − x̄)² Calculate Regression intercept a = ȳ − b x̄ Calculate Multiple regression ŷ = b₀ + b₁x₁ + … + bₖxₖ — R-squared R² = 1 − SSE ÷ SST Calculate Adjusted R-squared 1 − (1 − R²)(n − 1) ÷ (n − k − 1) —
6. Forecasting and time series Concept Formula Calculator Naive forecast Fₜ₊₁ = Aₜ — Simple moving average Fₜ₊₁ = (sum of the last m actual values) ÷ m Calculate Weighted moving average Fₜ₊₁ = ΣwᵢAᵢ, with weights summing to 1 — Exponential smoothing Fₜ₊₁ = αAₜ + (1 − α)Fₜ Calculate Forecast error eₜ = Aₜ − Fₜ Calculate Mean absolute error MAE = Σ|Aₜ − Fₜ| ÷ n Calculate Mean squared error MSE = Σ(Aₜ − Fₜ)² ÷ n Calculate Root mean squared error RMSE = √MSE Calculate Mean absolute percentage error MAPE = (100 ÷ n) Σ|(Aₜ − Fₜ) ÷ Aₜ| Calculate Linear trend Ŷ = a + bt, with b = Σ(t − t̄)(Y − Ȳ) ÷ Σ(t − t̄)² — Multiplicative model Y = T × S × C × I — Additive model Y = T + S + C + I —
Aₜ is the actual value and Fₜ the forecast; α lies between 0 and 1 and m is the moving-average window. MAPE is undefined when an actual value is zero.
7. Finance analytics Time value of money Concept Formula Calculator Simple interest SI = P × R × T ÷ 100 Calculate Compound future value FV = PV(1 + r)ⁿ Calculate Present value PV = FV ÷ (1 + r)ⁿ Calculate Future value of an ordinary annuity FV = PMT[(1 + r)ⁿ − 1] ÷ r Calculate Present value of an ordinary annuity PV = PMT[1 − (1 + r)⁻ⁿ] ÷ r Calculate Effective annual rate EAR = (1 + r/m)ᵐ − 1 Calculate
Investment appraisal Concept Formula Calculator Net present value NPV = Σ CFₜ ÷ (1 + r)ᵗ − C₀ Calculate Profitability index PI = PV of future inflows ÷ Initial investment Calculate Accounting rate of return ARR = Average annual accounting profit ÷ Average investment × 100 % — Return on investment ROI = (Gain − Cost) ÷ Cost × 100 % Calculate Internal rate of return The discount rate at which NPV = 0 Calculate Payback period Time for cumulative cash inflows to recover the initial cost Calculate
Financial ratios and risk Concept Formula Calculator Current ratio Current assets ÷ Current liabilities Calculate Quick ratio (Current assets − Inventory − Prepaid expenses) ÷ Current liabilities Calculate Debt-to-equity Total debt ÷ Shareholders’ equity Calculate Gross profit margin Gross profit ÷ Revenue × 100 % Calculate Net profit margin Net profit ÷ Revenue × 100 % Calculate Return on assets Net income ÷ Average total assets × 100 % Calculate Return on equity Net income ÷ Average shareholders’ equity × 100 % Calculate Earnings per share (Net income − Preferred dividends) ÷ Weighted-average ordinary shares Calculate Break-even quantity Fixed costs ÷ (Price per unit − Variable cost per unit) Calculate Contribution per unit Price per unit − Variable cost per unit Calculate Expected return E(R) = ΣpᵢRᵢ — Portfolio expected return E(Rₚ) = ΣwᵢE(Rᵢ) — CAPM E(Rᵢ) = Rf + βᵢ[E(Rm) − Rf] Calculate Sharpe ratio (Portfolio return − Risk-free rate) ÷ Portfolio standard deviation Calculate
8. Logistics and supply chain Concept Formula Calculator Economic order quantity EOQ = √(2DS ÷ H) Calculate Orders per year Annual demand ÷ Order quantity Calculate Average cycle stock Order quantity ÷ 2 Calculate Reorder point Demand during lead time + Safety stock Calculate Simple safety stock Maximum lead-time demand − Average lead-time demand — Inventory turnover Cost of goods sold ÷ Average inventory — Average inventory (Opening inventory + Closing inventory) ÷ 2 — Days inventory outstanding (Average inventory ÷ COGS) × 365 — Capacity utilisation Actual output ÷ Design capacity × 100 % — Labour productivity Output ÷ Labour hours — Fill rate Units fulfilled immediately ÷ Units demanded × 100 % —
In EOQ, D is annual demand, S the cost per order and H the holding cost per unit per year. The basic model assumes steady demand and lead time.
9. Research methods and multivariate analysis Concept Formula Calculator Sample covariance Cov(X, Y) = Σ(xᵢ − x̄)(yᵢ − ȳ) ÷ (n − 1) Calculate Standardised regression coefficient βⱼ = bⱼ × (s_xⱼ ÷ s_y) — Cronbach’s alpha α = [k ÷ (k − 1)] × [1 − Σsᵢ² ÷ sₜ²] —
Cronbach’s alpha measures the internal consistency of a multi-item scale (k items, item variances sᵢ², total-score variance sₜ²). Factor analysis and principal component analysis work with eigenvalues and explained variance.
10. Business metrics Concept Formula Calculator Percentage change (New − Old) ÷ Old × 100 % Calculate Sales growth (Current sales − Previous sales) ÷ Previous sales × 100 % Calculate Conversion rate Conversions ÷ Total leads × 100 % — Customer acquisition cost Acquisition spending ÷ New customers acquired — Customer retention rate (E − N) ÷ S × 100 % — Average order value Revenue ÷ Number of orders — Revenue per customer Revenue ÷ Number of customers — Market share Company sales ÷ Total market sales × 100 % — CAGR (Ending value ÷ Beginning value)^(1/n) − 1 Calculate Weighted score Σwᵢxᵢ, with weights summing to 1 —
Retention rate: E customers at the end of the period, N new customers gained during it, S customers at the start.
11. Programming in R: common functions Task R function Mean mean(x)Median median(x)Sample variance var(x)Sample standard deviation sd(x)Correlation cor(x, y)Covariance cov(x, y)Linear regression lm(y ~ x, data = df)One-way ANOVA aov(y ~ group, data = df)Chi-square test chisq.test(table)Frequency table table(x)Summary statistics summary(x)Normal probability P(X ≤ x) pnorm(x, mean, sd)Random normal values rnorm(n, mean, sd)
R’s var() and sd() use the sample formulas, dividing by n − 1.
Frequently asked questions When do I divide by n − 1 instead of N? Divide by n − 1 for the variance or standard deviation of a sample used to estimate a population; divide by N only when the data cover the whole population.
Which formula gives the confidence interval for a mean? x̄ ± t(α/2, n−1) × s ÷ √n when the population standard deviation is unknown (the usual case), or x̄ ± z(α/2) × σ ÷ √n when it is known.
How is NPV different from IRR? NPV is the value added at a chosen discount rate; IRR is the discount rate at which NPV is zero. Accept projects with NPV > 0, which for conventional cash flows is the same as IRR above the required return.