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Statistical techniques allow geographers to summarise data, identify patterns and test whether results are significant. At GCSE you need to be able to calculate and interpret a range of statistical measures. This lesson covers all the statistical skills required for AQA GCSE Geography.
Central tendency measures tell you the typical or average value in a dataset.
The mean is the sum of all values divided by the number of values.
Formula: Mean = Σx / n
where Σx = sum of all values and n = number of values
Example: River pebble sizes (mm): 12, 15, 18, 22, 25, 30, 35
Mean = (12 + 15 + 18 + 22 + 25 + 30 + 35) / 7 = 157 / 7 = 22.4 mm
Advantages: Uses all the data; widely understood.
Disadvantages: Can be distorted by extreme values (outliers).
The median is the middle value when the data is arranged in order from smallest to largest.
How to find it:
Example: The same data in order: 12, 15, 18, 22, 25, 30, 35
Median = 22 mm (the 4th value out of 7)
Advantages: Not affected by extreme values; easy to find.
Disadvantages: Does not use all the data.
The mode is the most frequently occurring value.
Example: Pedestrian counts: 5, 8, 12, 12, 15, 18, 12, 20
Mode = 12 (appears 3 times)
A dataset can be:
Advantages: Easy to find; useful for categorical data.
Disadvantages: May not be representative; there may be no mode or several modes.
Exam Tip: The exam may ask you to choose the most appropriate measure of central tendency. The median is usually best when there are outliers. The mean is best when data is evenly spread. The mode is best for categorical data.
Dispersion measures tell you how spread out the data is.
The range is the difference between the highest and lowest values.
Formula: Range = maximum value − minimum value
Example: Maximum pebble size = 35 mm, minimum = 12 mm
Range = 35 − 12 = 23 mm
Advantages: Simple to calculate.
Disadvantages: Only uses two values; heavily affected by outliers.
The IQR measures the spread of the middle 50% of the data, making it less affected by extreme values.
How to find it:
Example: Data (n=7): 12, 15, 18, 22, 25, 30, 35
Exam Tip: The IQR is a better measure of spread than the range because it ignores extreme values at either end. If asked to justify your choice of measure, this is the key point to make.
| Term | Definition |
|---|---|
| Lower quartile (Q1) | The value below which 25% of the data falls |
| Median (Q2) | The value below which 50% of the data falls |
| Upper quartile (Q3) | The value below which 75% of the data falls |
| Interquartile range | Q3 − Q1 (the middle 50% of the data) |
The standard deviation measures how far values are spread from the mean. A small standard deviation means data is closely clustered around the mean; a large standard deviation means data is widely spread.
Formula:
SD = √(Σ(x − x̄)² / n)
where x = each value, x̄ = mean, n = number of values
Step-by-step method:
Example:
| Value (x) | x − x̄ | (x − x̄)² |
|---|---|---|
| 12 | −10.4 | 108.16 |
| 15 | −7.4 | 54.76 |
| 18 | −4.4 | 19.36 |
| 22 | −0.4 | 0.16 |
| 25 | 2.6 | 6.76 |
| 30 | 7.6 | 57.76 |
| 35 | 12.6 | 158.76 |
Mean (x̄) = 22.4. Sum of (x − x̄)² = 405.72. Divide by 7 = 57.96. Square root = 7.61
Exam Tip: You may be asked to calculate standard deviation in the exam. Always set up a table like the one above — it keeps your working clear and helps you avoid errors. The examiner can award method marks even if your final answer is wrong.
This test determines whether there is a statistically significant relationship between two sets of ranked data.
Formula:
rs = 1 − (6Σd² / n(n² − 1))
where d = difference between the two ranks for each item, n = number of items
Steps:
Interpreting the result:
| rs value | Interpretation |
|---|---|
| +1.0 | Perfect positive correlation |
| +0.5 to +1.0 | Strong positive correlation |
| 0 to +0.5 | Weak positive correlation |
| 0 | No correlation |
| 0 to −0.5 | Weak negative correlation |
| −0.5 to −1.0 | Strong negative correlation |
| −1.0 | Perfect negative correlation |
You then compare your rs value against the critical value for your sample size at the 0.05 significance level. If your rs exceeds the critical value, the result is statistically significant (i.e. unlikely to have occurred by chance).
Exam Tip: You will be given the formula and a table of critical values in the exam. Focus on understanding the steps and interpreting the result — do not try to memorise the formula.
The chi-squared test checks whether there is a significant difference between observed and expected frequencies.
Formula:
χ² = Σ((O − E)² / E)
where O = observed frequency, E = expected frequency
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