Welcome to Geography Maths!

In Geography B (1GB0), you aren't just learning about mountains and cities—you're also becoming a data detective. Being able to use numerical and statistical techniques allows you to prove your points with evidence. Whether you are calculating the power of a tropical cyclone or measuring how quickly a coastline is disappearing, these skills are your "geographer's toolkit."

Don't worry if you find maths a bit scary! We will break everything down step-by-step. Remember: you can use a calculator in all three geography exams, so you just need to know which buttons to press and why.

1. Calculating Change and Growth

Geographers love to see how things change over time. This might be how a city's population grows or how a glacier shrinks.

Percentage Increase and Decrease

To find the percentage change between two numbers, use this simple "formula":
\( \text{Percentage Change} = \frac{\text{Difference between the two numbers}}{\text{Original number}} \times 100 \)

Example: If a town had \( 200 \) people in \( 2010 \) and \( 250 \) people in \( 2020 \):
1. The difference is \( 250 - 200 = 50 \).
2. Divide by the original: \( 50 \div 200 = 0.25 \).
3. Multiply by \( 100 \) to get \( 25\% \).

Rates of Change

A rate tells us how much something changes over a specific time (like a year or a decade).
Mean rate of coastal erosion: If a cliff retreats by \( 10 \) metres over \( 5 \) years, the mean rate is \( 10 \div 5 = 2 \) metres per year.

Quick Review: Always check if the question asks for the total change or the rate per year!

2. Central Tendency (Averages)

Averages help us find a "typical" value in a big pile of data.

  • Mean: Add all the numbers together and divide by how many numbers there are.
  • Median: The middle number in a list ordered from smallest to largest. If there are two middle numbers, find the halfway point between them.
  • Mode: The number that appears most often.
  • Modal Class: In a table of grouped data (e.g., \( 0-10 \) kg, \( 11-20 \) kg), the "class" or group with the most results is the modal class.

3. Measuring Spread (Dispersion)

Sometimes the average doesn't tell the whole story. We also need to know how "spread out" the data is.

Range and Quartiles

  • Range: The difference between the highest and lowest value (\( \text{Max} - \text{Min} \)).
  • Quartiles: These divide your data into four equal quarters. Lower Quartile (Q1) is at \( 25\% \), and Upper Quartile (Q3) is at \( 75\% \).
  • Inter-quartile Range (IQR): This is the difference between the upper and lower quartiles (\( Q3 - Q1 \)). It tells you the spread of the middle \( 50\% \) of your data, which ignores extreme "outliers."

Difference from the Mean

This shows how much a specific area varies from the average. This is often used to compare core and periphery regions (e.g., how much richer London is compared to the UK average income).

4. Advanced Data Techniques

The exam might ask you to interpret more complex ways of grouping people or data.

Income Quintiles

A quintile is simply a \( 20\% \) chunk of the population. Geographers use these to measure inequality. If the top quintile (richest \( 20\% \)) earns significantly more than the bottom quintile, the area has high inequality.

Cumulative Frequency and Percentiles

Cumulative frequency is a "running total" of data. A percentile tells you where a value stands relative to \( 100 \). For example, if a city is in the \( 90\text{th} \) percentile for pollution, it is more polluted than \( 90\% \) of other cities.

Carbon and Ecological Footprints

These measure the impact of human activity. A carbon footprint counts the total greenhouse gases produced, while an ecological footprint measures how much land is needed to support a person’s lifestyle.

Key Takeaway: These techniques help geographers compare the "development gap" between different countries or cities.

5. Magnitude and Frequency

This is used mainly in Topic 1 (Hazardous Earth).

  • Richter Scale: Used to compare the magnitude (power) of earthquakes.
  • Saffir-Simpson Scale: Used to categorise tropical cyclones based on wind speed and potential storm-surge damage.

Magnitude refers to how strong the event is, while frequency refers to how often it happens. Usually, high-magnitude events (big disasters) have a low frequency (they don't happen very often).

When looking at scatter plots, we look for relationships between two things (like GDP and life expectancy).

  • Trend Lines / Lines of Best Fit: A straight line drawn through the middle of the points on a scatter graph to show the general direction of the data.
  • Interpolation: Estimating a value inside the range of your data points using your line of best fit.
  • Extrapolation: Extending your line of best fit to predict a value outside your data range (e.g., predicting the population in \( 2050 \) based on current trends). Note: This is less reliable because trends can change!

7. Ratios and Proportions

Ratios compare two different amounts. For example, a dependency ratio compares the number of people who are too young or old to work with the number of people in the working-age population. Written as \( A:B \).

Proportion is a part of a whole, often shown as a fraction or a percentage (e.g., "The proportion of the population living in urban areas is \( \frac{3}{4} \)").

8. Critical Thinking: Selective Statistical Presentation

Be a skeptic! Sometimes, people present data in a way that is "selective" to make a point seem stronger than it is.
Common tricks:

  • Using the mean when there are massive outliers (this can hide the truth about the "typical" person).
  • Changing the scale on a graph to make a small rise look like a huge jump.
  • Ignoring data that doesn't fit the argument.

Exam Tip: If a question asks you to "evaluate" or "assess" a set of data, look for these weaknesses!

Summary Table: The Geographer's "Cheat Sheet"

Ratio: Comparison of two values (e.g., \( 2:1 \)).
Mean: The mathematical average.
Median: The middle value.
IQR: Spread of the middle \( 50\% \).
Extrapolation: Predicting the future based on a trend line.

Don't forget: You can find more information on how to draw these in the "Graphs, charts and data presentation" chapter. This chapter focuses on the maths behind them!