Economic data, indices and statistical reasoning
Quantitative economic reasoning
Begin by identifying the variable, unit, time period, population and comparison being made. A total, a per-person amount, a percentage share and a rate of growth answer different questions. An arithmetic mean adds values and divides by their number; a weighted mean also specifies the weights and their sum. A median is based on ordered position. An extreme value can influence the mean substantially, so a claim about the typical observation should be checked against the distribution rather than inferred from one average alone.
A price index compares a stated basket or aggregation across periods. In a fixed-base-quantity model, value the same quantities at new and base prices before forming the ratio and multiplying by 100. An index rising from 125 to 130 increases by five index points but by 4 percent relative to its original level. Nominal expenditure divided by an appropriate price index, with its base normalization accounted for, produces a corresponding real measure. The chosen index must match the question; a GDP deflator and a household consumer basket are not interchangeable merely because both measure prices.
State the elasticity convention. An initial-base finite percentage calculation, a midpoint arc elasticity and a point elasticity can give different numerical values. For a midpoint calculation, divide each change by the average of its two endpoint values. This symmetric convention can help relate finite price and quantity changes to revenue comparisons, but it does not prove a constant elasticity across a whole demand curve. A fitted straight line has constant slope while its point elasticity generally varies with price and quantity.
Variation also needs a definition. A population variance and the usual sample variance have different denominators; use the formula supplied. A standard error describes the sampling variability of an estimator under its model, not the spread of every individual observation. If a confidence-interval exercise supplies an estimate, standard error and critical value, calculate estimate plus or minus critical value times standard error and state the assumptions. An observed frequentist interval does not assign that confidence percentage to the fixed parameter itself.
Correlation and regression summarize patterns. A fitted positive association is not proof that intervening on one variable causes a change in another. Confounding, reverse causation, selection and measurement can matter. Predicting within the observed range differs from extrapolating far beyond it. A voluntary online survey may exclude important groups even if it receives many responses; sample size does not automatically cure selection bias.
Finally, use exact ratios when precision matters. Per-person output growth is the growth factor of output divided by the growth factor of population, minus one. Subtracting growth rates is an approximation. Carry units through every step, avoid unnecessary intermediate rounding and distinguish the arithmetic result from the causal or policy conclusion the evidence can actually support.