Business Mathematics and Statistics: Ratios, Interest, Averages and Dispersion
Core concepts
This section covers percentages and profit-loss, ratio and proportion, simple and compound interest, averages, and basic statistics: mean, median, mode, range, variance, standard deviation, and interpretation of tables. Candidates should be fluent with formula rearrangement and unit consistency (annual versus monthly rates, percentage versus decimal).
Traps to watch
Frequent errors include using simple interest when compounding is implied, confusing markup with margin, and forgetting that the median depends on ordered data. In dispersion questions, remember standard deviation is the square root of variance; mixing the two is a classic trap. Percentage change is calculated on the original value, not the new one. Also check whether a rate is annual while time is given in months.
Worked example
Find the compound interest on 10,000 at 10% per annum for two years, compounded annually. Amount = 10,000 × (1.10)^2 = 10,000 × 1.21 = 12,100. Compound interest = 12,100 − 10,000 = 2,100. Rule of thumb: for two years, total growth is 2r + r² in decimal terms, here 0.20 + 0.01 = 0.21, confirming 21% growth.
Strategy
Write the given values with units first, then pick the formula. Estimate the answer before calculating to catch absurd results. For statistics, sort data before finding the median, and distinguish population from sample notation where relevant.