Numerical and Statistical Skills in Geography
Welcome to your complete revision guide for Numerical and Statistical Skills in OCR GCSE (9–1) Geography A (J383). Numbers and data appear across all three of your exam papers: Living in the UK Today (Paper 1), The World Around Us (Paper 2), and especially Geographical Skills (Paper 3). Don't worry if maths isn't your favourite subject—geographical calculations are straightforward once you learn the step-by-step methods below!
1. Measures of Central Tendency (Averages)
Geographers use averages to summarize large sets of data, such as rainfall totals, temperatures, or population figures. There are three main types of average you need to master:
A. The Mean
The mean is the most common average. You calculate it by adding together all the numbers in a data set and dividing by the total number of items.
Formula:
\(\text{Mean} = \frac{\text{Total sum of all values}}{\text{Number of values}}\)
Worked Example:
A student records the daily rainfall (in mm) over 5 days: \(4\), \(6\), \(0\), \(12\), \(8\).
1. Add them together: \(4 + 6 + 0 + 12 + 8 = 30\)
2. Divide by the number of days (\(5\)): \(\frac{30}{5} = 6\text{ mm}\)
B. The Median
The median is the middle value when all the numbers are arranged in order from smallest to largest.
Step-by-Step Method:
1. Put all your numbers in order from smallest to largest.
2. Find the middle number.
3. If there is an even number of values, find the mean of the two middle numbers by adding them together and dividing by \(2\).
Worked Example:
Find the median of: \(14\), \(3\), \(22\), \(7\), \(9\).
1. Put them in order: \(3\), \(7\), \(9\), \(14\), \(22\)
2. Identify the middle value: \(9\)
C. The Mode
The mode is the most frequently occurring value in a data set.
Worked Example:
Temperatures recorded in a town over 7 days (°C): \(15, 17, 15, 18, 20, 15, 19\).
The value \(15\) appears three times, so the mode = \(15\text{ °C}\).
Memory Trick:
• MOde = MOst often
• MEdian = MEdium (middle)
• Mean = The one that makes you do the most work (add and divide)!
Key Takeaway: Always check which average the question asks for. Calculating the mean when the question asked for the median is a common mistake where students lose marks!
2. Measures of Dispersion (Spread of Data)
Measures of dispersion tell us how spread out or consistent our data is.
A. The Range
The range is the simplest measure of spread. It is the difference between the highest and lowest values in a data set.
Formula:
\(\text{Range} = \text{Highest Value} - \text{Lowest Value}\)
Example: If the highest temperature is \(28\text{ °C}\) and the lowest is \(12\text{ °C}\), the range is \(28 - 12 = 16\text{ °C}\).
B. Quartiles and the Interquartile Range (IQR)
While the range uses all values, it can be distorted by extreme numbers (outliers). To solve this, geographers use the Interquartile Range (IQR), which measures the spread of the middle 50% of the data.
Key Definitions:
• Lower Quartile (\(Q_1\)): The median of the lower half of the data (the 25% mark).
• Upper Quartile (\(Q_3\)): The median of the upper half of the data (the 75% mark).
• Interquartile Range (IQR): The difference between the upper and lower quartiles.
Formula:
\(\text{IQR} = Q_3 - Q_1\)
Worked Example:
Ordered data set of 7 wind speed measurements (knots): \(8, 10, 12, 15, 18, 20, 24\)
1. Median (\(Q_2\)) = \(15\)
2. Lower half = \(8, 10, 12\) \(\implies\) Lower Quartile (\(Q_1\)) = \(10\)
3. Upper half = \(18, 20, 24\) \(\implies\) Upper Quartile (\(Q_3\)) = \(20\)
4. \(\text{IQR} = Q_3 - Q_1 = 20 - 10 = 10\text{ knots}\)
Key Takeaway: The IQR is useful because it is not affected by extreme high or low values (anomalies).
3. Percentages, Proportions, and Ratios
A. Percentage Change
Questions often ask you to calculate the percentage increase or decrease between two time periods or locations.
Formula:
\(\text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\)
Worked Example (Increase):
A town's population grew from \(50,000\) to \(65,000\).
1. Find the change: \(65,000 - 50,000 = 15,000\)
2. Divide by the original value: \(\frac{15,000}{50,000} = 0.3\)
3. Multiply by \(100\): \(0.3 \times 100 = 30\%\) increase.
Worked Example (Decrease):
River discharge drops from \(80\text{ m}^3/\text{s}\) to \(60\text{ m}^3/\text{s}\).
1. \(\text{Change} = 60 - 80 = -20\)
2. \(\frac{-20}{80} \times 100 = -25\%\) (or a \(25\%\) decrease).
Exam Warning: If the result is negative, make sure you write the minus sign (\(-\)) or state clearly that it is a decrease.
B. Ratios and Proportions
A ratio compares the size of one part to another part. For example, comparing dependent people (young and elderly) to the working population (dependency ratios).
Example: In a survey of \(30\) shoppers, \(20\) are local residents and \(10\) are tourists. The ratio of residents to tourists is \(20 : 10\), which simplifies by dividing both sides by \(10\) to \(2 : 1\).
C. Map Scale and Distance Ratios
Map scales are written as representative ratios:
• \(1 : 25,000\) means \(1\text{ cm}\) on the map represents \(25,000\text{ cm}\) in real life (\(250\text{ m}\) or \(0.25\text{ km}\)). So, \(4\text{ cm} = 1\text{ km}\).
• \(1 : 50,000\) means \(1\text{ cm}\) on the map represents \(50,000\text{ cm}\) in real life (\(500\text{ m}\) or \(0.5\text{ km}\)). So, \(2\text{ cm} = 1\text{ km}\).
Key Takeaway: Always divide by the original value when calculating percentage change, not the new value!
4. Data Representation, Scatter Graphs, and Correlation
A. Scatter Graphs and Correlation
A scatter graph shows the relationship between two variables:
• Positive Correlation: As one variable increases, the other variable increases (e.g., higher GDP per capita often links to higher life expectancy). The points slope upwards from left to right.
• Negative Correlation: As one variable increases, the other decreases (e.g., higher female literacy rates link to lower birth rates). The points slope downwards from left to right.
• No Correlation: There is no clear pattern or link between the two variables.
B. Line of Best Fit
A line of best fit is a straight line drawn through the middle of the plotted points on a scatter graph to show the general trend. When drawing one in an exam:
1. Use a clear ruler and pencil.
2. Make sure roughly half the points lie above your line and half lie below it.
3. Follow the direction of the points rather than connecting point to point.
C. Anomalies
An anomaly (or outlier) is a data point that does not fit the general pattern or trend shown by the rest of the data. When asked to identify one, look for the point that sits far away from the line of best fit.
Key Takeaway: Scatter graphs show relationships (correlation), but they do not automatically prove that one variable causes the other.
5. Essential OCR Exam Rules & Common Pitfalls
Make sure you don't drop easy marks by following these examiner conventions:
1. Always Bring a Calculator
You are allowed and expected to use a scientific calculator in all OCR Geography examinations.
2. Rounding and Decimals
OCR mark schemes standardly require answers to one decimal place (e.g., \(14.6\)) unless the question specifically states otherwise (such as "give your answer to the nearest whole number").
3. Always Include the Units
A numerical answer without units often loses the final mark. Always check the graph or question for units such as \(\text{mm}\), \(\text{°C}\), \(\%\), \(\text{km}\), or \(\text{millions}\).
4. Complete the Graph Questions
Look out for easy 1-mark questions asking you to "Complete Figure X by plotting the data for...". Students often miss these by skipping straight to the writing lines below the graph. Always check figures carefully for unplotted points!
5. Percentage vs. Percentage Point
If an unemployment rate rises from \(10\%\) to \(15\%\):
• It is a \(5\) percentage point increase.
• As a percentage change, it is an increase of \(\frac{15 - 10}{10} \times 100 = 50\%\).
Be precise in your written answers!
Quick Review Summary
• Mean: Add all values and divide by the count.
• Median: Put values in order and find the middle number.
• Mode: The value that appears most often.
• Range: \(\text{Highest} - \text{Lowest}\).
• Interquartile Range: \(Q_3 - Q_1\) (middle 50% spread).
• Percentage Change: \(\frac{\text{New} - \text{Original}}{\text{Original}} \times 100\).
• Rounding rule: Default to 1 decimal place and always write the units!