Numerical and statistical skills

Geography uses statistics to summarise data, test hypotheses and reveal patterns. AQA expects you to be able to calculate, interpret and select the right measure for a given dataset.

Percentages and percentage change

• Percentage = (part / whole) × 100.
• Percentage change = (new − old) / old × 100.
• e.g. UK self-sufficiency fell from 78 % to 60 %: change = (60 − 78) / 78 × 100 = −23 %.

Ratio

• Comparison of two quantities.
• e.g. People per doctor: UK 360:1 vs Niger 19 600:1.
• Simplify by dividing both sides by their HCF.

Mean, median, mode

• Mean = sum / count. Sensitive to outliers.
• Median = middle value when ordered. Resilient to outliers — preferred for skewed data (incomes, river depths).
• Mode = most common value. Useful for categorical data.
• Range = max − min.

Worked: river depths (cm) at 8 sites: 12, 15, 18, 22, 22, 25, 30, 47.

• Mean = 191 / 8 = 23.9 cm
• Median = (22 + 22) / 2 = 22 cm
• Mode = 22 cm
• Range = 47 − 12 = 35 cm.
• Note the 47 cm outlier pulls the mean up but not the median — that's why median is often preferred.

Quartiles and interquartile range (IQR)

Order the data, then split into quarters:

• Lower quartile (Q1) — 25 % of data below.
• Median (Q2) — 50 %.
• Upper quartile (Q3) — 75 %.
• IQR = Q3 − Q1. Range of the middle 50 %.

Worked (8 values above): Q1 = 16.5, Q3 = 27.5, IQR = 11.

Percentiles

Divide ordered data into 100 equal parts. The 90th percentile = value below which 90 % of data lies. Used in income distributions, exam scores.

Standard form

Used for very large or small numbers in geography (CO₂ concentrations, populations).

• 4 200 000 = 4.2 × 10⁶
• 0.000 037 = 3.7 × 10⁻⁵

Drawing and reading graphs

• Trend line / line of best fit — pass through middle of points, balancing above and below.
• Predict from extrapolation — extending the trend; warn that this assumes the trend continues.
• Frequency distribution — group continuous data into bins (e.g. ages 0–4, 5–9).

Choosing the right statistic

• Skewed data (income, river discharge) → use median and IQR.
• Symmetric data (test scores) → use mean and range or standard deviation.
• Two variables — test correlation with a scatter plot plus r (Pearson) or rank correlation (Spearman) for non-linear.

Examiner tips

• For 2-mark calculation questions, show working — partial credit for the method even if the final answer is wrong.
• Always quote the units (cm, %, km²).
• Round sensibly — to 2 d.p. or 3 s.f. unless the question states otherwise.
• For "comment on the data" questions, link the statistic back to the geography (e.g. "the high IQR suggests inconsistent river depths, perhaps due to local channel features").