Statistical Skills for Geography

GCSE Geography · Geographical Applications

Why Statistical Skills Matter

Statistical techniques help geographers identify patterns, trends, relationships, and anomalies in data. AQA GCSE Geography expects you to understand and apply several statistical methods.

Measures of Central Tendency

Mean (Average)

Add all values together and divide by the number of values
Formula: Mean = Σx ÷ n (sum of values ÷ number of values)
Example: River depths of 12, 15, 18, 22, 28 cm → Mean = (12+15+18+22+28) ÷ 5 = 95 ÷ 5 = 19 cm
Advantage: uses all the data
Disadvantage: affected by extreme values (outliers) — e.g. one very deep reading would pull the mean up

Median

The middle value when all data is arranged in order (ascending or descending)
If there is an even number of values, the median is the mean of the two middle values
Example: 12, 15, 18, 22, 28 → Median = 18 (the 3rd value out of 5)
Advantage: not affected by extreme values
Disadvantage: does not use all the data

Mode

The most frequently occurring value in the data set
There can be no mode, one mode, or multiple modes (bimodal, multimodal)
Example: 3, 4, 4, 5, 6, 6, 6, 7 → Mode = 6
Advantage: easy to identify; useful for categorical data
Disadvantage: may not exist; not representative if it occurs at the extreme

Measures of Spread (Dispersion)

Range

The difference between the highest and lowest values
Range = Maximum − Minimum
Example: 12, 15, 18, 22, 28 → Range = 28 − 12 = 16 cm
Simple but affected by extreme values

Interquartile Range (IQR)

The range of the middle 50% of the data, which excludes the extreme values
Steps:

1. Arrange data in ascending order

2. Find the lower quartile (Q1) — the median of the lower half of the data (25th percentile)

3. Find the upper quartile (Q3) — the median of the upper half (75th percentile)

4. IQR = Q3 − Q1

Example: Data (in order): 3, 5, 7, 8, 12, 14, 16, 19, 22, 25, 30

Q1 = 7 (median of lower half: 3, 5, 7, 8, 12)
Q3 = 22 (median of upper half: 16, 19, 22, 25, 30)
IQR = 22 − 7 = 15

Advantage: not affected by extreme values; shows how spread out the middle data is
Disadvantage: ignores the top and bottom 25% of data

Spearman's Rank Correlation Coefficient

This test measures the strength and direction of a relationship between two variables. The result (rs) ranges from −1 to +1:

+1 = perfect positive correlation (as one increases, so does the other)
0 = no correlation
−1 = perfect negative correlation (as one increases, the other decreases)

Steps to Calculate Spearman's Rank

1. Rank each variable separately (1 = highest value)

2. If values are tied, give them the average rank (e.g. if two values share ranks 3 and 4, both get 3.5)

3. Calculate d (difference between the two ranks for each pair)

4. Calculate d² (square each difference)

5. Sum all d² values (Σd²)

6. Apply the formula:

rs = 1 − (6 × Σd²) ÷ (n³ − n)

Where n = number of pairs of data

Example (Simplified)

Testing: "Does environmental quality decrease with distance from the city centre?"

Site	Distance rank	EQS rank	d	d²
A	1	6	−5	25
B	2	5	−3	9
C	3	4	−1	1
D	4	3	1	1
E	5	2	3	9
F	6	1	5	25

Σd² = 70, n = 6

rs = 1 − (6 × 70) ÷ (216 − 6) = 1 − 420 ÷ 210 = 1 − 2 = −1.0

This shows a perfect negative correlation — environmental quality decreases as distance from the city centre increases (which actually disproves the usual pattern — in practice, EQS often improves away from the CBD). Always check the direction makes geographical sense.

Testing Significance

After calculating rs, compare it to the critical value in a significance table for your sample size:

If rs exceeds the critical value, the result is statistically significant (unlikely to be due to chance)
At GCSE, you typically test at the 95% confidence level (0.05 significance level)
The critical value depends on n (sample size) — larger samples need a smaller rs to be significant

Percentage and Percentage Change

Percentage: (part ÷ whole) × 100
Percentage change: ((new value − original value) ÷ original value) × 100
A positive result = increase; negative = decrease

Example: Population rises from 50,000 to 62,000

Change = 12,000; Percentage change = (12,000 ÷ 50,000) × 100 = 24% increase

Using Statistics in Fieldwork

When writing up fieldwork or answering exam questions about data:

1. Calculate the appropriate statistic

2. State what the result shows

3. Interpret what it means geographically

4. Evaluate — is the sample large enough? Are there anomalies? Is the result significant?

Exam tip: You will not always have to calculate Spearman's Rank in the exam — you may be asked to interpret a given result or explain the steps. Make sure you understand what the numbers mean, not just how to calculate them.