Statistical Methods

Statistics turns geographical observations into evidence. Primary data is collected first-hand through fieldwork, while secondary data comes from censuses, maps, reports and other existing records. After data is checked and organised, learners should calculate and interpret arithmetic mean, median, mode, percentage and range. Mean uses every value but can be distorted by extremes; median is the middle value after ordering; mode is the most frequent value; range is highest minus lowest. Presentation must match purpose: line graphs show change over time; bars compare categories; pie charts show proportions using sector angle = value/total × 360 degrees; proportional circles compare totals by area; population and age-sex pyramids show structure; dot maps show distribution; choropleth maps use classed shading to show rates or densities. Interpretation should first describe pattern, concentration, low values, gradients and anomalies before offering geographical explanations. Always check title, key, units, scale and class intervals. Worked example: for 24, 26, 26, 27 and 32, mean = 27, median = 26, mode = 26 and range = 8. The 32 raises the mean, so the median may better represent the typical value. A choropleth is normally more suitable for population density than raw totals because density standardises population by area.

A strong statistical answer separates calculation, presentation and interpretation. When raw field data contains repeated observations, first inspect for recording errors and decide whether the variable is discrete, continuous or categorical. Percentages are useful for comparing samples of unequal size. A pie chart is appropriate when categories form one whole, but becomes difficult to read when there are many small classes. A proportional circle compares totals through area, so radii are not directly proportional to values; if one value is four times another, the radius is twice as large. Dot maps preserve a sense of spatial distribution but depend heavily on dot value and placement. Choropleths require class intervals; equal-interval, quantile and other classifications can produce different visual impressions, so learners must read the key before describing a pattern. Population pyramids combine age and sex data and can suggest high dependency, ageing, migration effects or demographic transition, but shape alone does not prove a cause. In KCSE interpretation, start with observable evidence: highest/lowest, concentration, direction of change, contrast and anomaly. Then explain using relevant geography. For example, if an urban county records higher population density, plausible causes include employment, transport, services and historical concentration, but the data must support the claim. In fieldwork, sampling matters. Random sampling reduces selection bias where a complete list exists; systematic sampling follows a fixed interval; stratified sampling ensures important groups are represented. A small convenient sample can still teach method, but its limitations must be stated. Data should be presented with titles, units, labelled axes, correct scale and accurate plotting. Calculations should show working because method marks can be awarded even when a final value is wrong.

📋 ACTIVITY

Fieldwork: survey transport modes used by 30 learners. Tally responses, calculate percentages, draw one suitable graph, write four evidence-based observations and identify one limitation of the sample.

💡 NOTE

Remediation: distribution describes where something occurs; density relates quantity to area. A choropleth showing density should use comparable rates, not simply shade the largest totals darkest.