Business Mathematics and Statistics
Percentages, ratios and interest
Percentage change = (new − old) / old × 100. Simple interest = P × r × t; compound interest uses (1+r)^n. Ratios express relative size; proportion scales quantities. Break-even quantity = fixed costs / (price − variable cost per unit).
Averages and dispersion
Mean, median and mode measure central tendency; the median resists outliers. Range, variance and standard deviation measure spread. The coefficient of variation (standard deviation / mean) compares risk across different scales.
Probability and distributions
Probability lies between 0 and 1. Mutually exclusive events add; independent events multiply. The normal distribution is symmetric and defined by mean and standard deviation; roughly 68% of values fall within one standard deviation, 95% within two. Sampling error falls as sample size rises.
Traps to watch
- Averaging percentages without weighting by base size.
- Confusing standard deviation with variance (variance is the square).
- Adding probabilities of events that are not mutually exclusive - subtract the overlap.
- Mixing up correlation with causation.
Worked example
Fixed costs 50,000; price 25; variable cost 15. Contribution per unit = 10. Break-even = 50,000 / 10 = 5,000 units. To earn a target profit of 20,000, required units = (50,000 + 20,000) / 10 = 7,000. Rule of thumb: divide total fixed costs plus target profit by unit contribution.