Business Mathematics and Statistics
The Business Mathematics and Statistics domain tests numerical fluency and interpretation, not proof-writing. Expect compound interest and annuities, permutation and combination, matrices, basic calculus, measures of central tendency and dispersion, correlation and regression, probability, and index numbers. Questions often use Nepali data such as NRB inflation figures or the NEPSE index, so read the base year carefully.
Core rules
- Simple interest I = PRT; compound amount A = P(1 + i)^n. The effective annual rate is (1 + i)^m − 1 when compounding is m times a year.
- An ordinary annuity's future value is A × [((1+i)^n − 1)/i]; use the present-value factor for loan instalments.
- Mean is affected by extreme values; median is positional; mode is the most frequent value. For a sample, variance uses n − 1; for a population, n.
- Standard deviation is the square root of variance; coefficient of variation = (SD ÷ mean) × 100 and compares risk across series.
- Karl Pearson's correlation r lies between −1 and +1. Regression predicts one variable from another; correlation does not prove causation.
- Laspeyres uses base-year quantities, Paasche uses current-year quantities, and Fisher's ideal index is the geometric mean of the two.
Worked example
Rs 100,000 is invested at 10% compounded annually for two years. A = 100,000 × (1.10)^2 = Rs 121,000, so compound interest is Rs 21,000; simple interest would be Rs 20,000. For the data 2, 4, 6, 8, 10, the mean is 6; squared deviations are 16, 4, 0, 4, 16, total 40. Population variance is 40 ÷ 5 = 8 and SD ≈ 2.83.
Traps
Mixing monthly and annual rates; applying simple interest to sinking funds; using n instead of n − 1 in a sample; forgetting to order data before finding the median; reversing the Paasche and Laspeyres formulas; and treating a high correlation as proof of cause.