Quantitative Methods, Statistics and Data Interpretation
Descriptive and inferential tools
Quantitative methods support measurement, comparison and forecasting. Statistics describes data and draws inferences under uncertainty.
- Data types: nominal, ordinal, interval and ratio. Only ratio has a true zero.
- Central tendency: mean, median and mode. Dispersion: range, variance and standard deviation.
- Sampling: probability samples support inference; convenience samples do not.
- Rates, ratios and percentages must use a stated base. Index numbers compare a value with a base period.
- Probability ranges from 0 to 1; mutually exclusive events cannot occur together.
Worked example: Five salary offers are 20,000; 22,000; 24,000; 26,000; and 200,000. The mean is 58,400, but the median is 24,000. The mean is distorted by the outlier, so the median better represents a typical offer. If the question asks for total payroll, use the mean or the raw sum; if it asks for 'typical,' use the median. Stating the reason earns the interpretation mark.
Traps
Reporting a percentage change as percentage points; using the mean for skewed data without comment; failing to check the base year; treating correlation as causation; ignoring non-response bias.