Data Presentation and Analysis

• Bar Charts: Ideal for discrete data. Each bar must be equidistant (separated by an equal gap) and of the same width. If asked to justify this method, state: 'This is suitable because the data is discrete and categorical.'
• Histograms: Used for continuous data frequency, such as pebble size classes. Unlike bar charts, histograms have no gaps between the bars.
• Line Graphs: Best for continuous data to show changes over time or distance. Points are connected by a line. A common AQA application is a river cross-section, where a line connects depth measurements to show the channel shape.
• Pie Charts: Used to display Quantitative Data as proportions of a whole. The total must add up to 100%.
• Scatter Graphs: Used for Bivariate Data to identify a relationship (correlation) between two variables. The points are plotted but never connected; instead, a Line of Best Fit is drawn to show the trend.
• Isoline Maps: Lines connect points of equal value (like contour lines for height) to show continuous spatial distribution.
• Qualitative Data: For non-numerical, descriptive data (like field sketches or interview opinions), graphical methods are generally unsuitable, and you must rely on annotations or coding frameworks.

Worked Example: Calculating Pie Chart Angles

The formula to find the correct angle is:

$$\text{Degrees} = \left( \frac{\text{Category Value}}{\text{Total Value}} \right) \times 360$$

Step 1: Identify your values. For example, if 20 out of 80 people chose 'bus'.

Step 2: Substitute into the formula.

• $(20 / 80) \times 360$

Step 3: Calculate the result.

• $0.25 \times 360 = 90^\circ$

Selecting Cartographic Methods (Maps)

Why do some election maps make large rural areas look overwhelmingly dominant, even if very few people live there? This is a common issue with map design, and choosing the right cartographic method prevents this misrepresentation of Locational Data.

• Choropleth Maps: These use different shades or patterns to represent pre-defined enumeration units. You must use standardised data (like percentages or density) rather than raw totals to avoid 'area bias'.
  • Justification: It effectively shows spatial patterns across a large area, allowing for immediate visual comparison.
  • Negative Feature: It gives a false impression of abrupt change at boundaries and hides internal variations.
  • Exam detail: In AQA black and white exams, these maps use cross-hatching or grey-shading. Darker shades must represent higher values.
• Proportional Symbol Maps: Symbols (like circles) are placed at specific locations, and their area is proportional to the data value.
  • Justification: Used because the data represents absolute magnitudes at specific points, preventing large empty areas from dominating the visual impact.
  • Negative Feature: If sites are close together or values are very large, overlapping symbols create clutter, making the map hard to read.

Using Statistical Techniques

If a billionaire walks into a small café, the mean wealth of everyone inside skyrockets, but the median wealth barely changes. Understanding different statistical techniques allows you to interpret data accurately, even when extreme values are present.

Measures of Central Tendency identify the middle or average of your data.

• The Mean summarises overall trends.
• The Median is the middle value. It is preferred when data has extreme outliers or anomalies, as it is not skewed by them.
• The Mode is the most frequently occurring value or category.

Measures of Dispersion describe the spread or variation in your data.

• The Range is the difference between the highest and lowest values.
• The Interquartile Range (IQR) represents the spread of the middle 50% of the data, ignoring extreme ends.

Worked Example: Descriptive Statistics

Calculate the mean, median, mode, and range for the following pebble sizes: $3\,\text{cm}$, $5\,\text{cm}$, $5\,\text{cm}$, $8\,\text{cm}$, $14\,\text{cm}$.

Step 1: Calculate the Mean

• Formula: $\text{Mean} = \frac{\sum x}{n}$
• Substitute: $(3 + 5 + 5 + 8 + 14) / 5 = 35 / 5$
• Answer: $7\,\text{cm}$

Step 2: Find the Median

• The numbers are already in rank order. The middle value is $5\,\text{cm}$.
• Answer: $5\,\text{cm}$

Step 3: Identify the Mode

• The value $5\,\text{cm}$ appears most frequently (twice).
• Answer: $5\,\text{cm}$

Step 4: Calculate the Range

• Formula: $\text{Highest Value} - \text{Lowest Value}$
• Substitute: $14 - 3$
• Answer: $11\,\text{cm}$

Describing, Analysing, and Explaining Results

Every time you look at a graph in an exam, the examiner is waiting to see if you can spot the general rule—and the one data point that breaks it. To secure Level 3 marks (6–9 marks) when asked to describe or analyse data, you must establish links and use the TEA structure.

When describing a pattern, structure your answer using Trend (T), Evidence (E), and Anomaly (A). For map patterns, you can also use the CLOCCK Acronym (Continent, Latitude, Ocean, Country, Compass direction, Kilometres) to describe specific spatial distributions.

• Trend: State the general direction or pattern (e.g., 'a steady increase' or a 'positive correlation').
• Evidence: Provide specific numerical data points, units, and dates taken directly from the resource. You must manipulate the data to show true analysis, for example by calculating a percentage change:

$$\text{Percentage Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100$$

• Anomaly: Identify a specific data point that does not fit the trend or deviates significantly from the line of best fit.

Establishing Links and Inter-relationships When an exam question asks you to 'explain' your results, you must provide a causal mechanism—the reason why the data behaves that way. This involves establishing causal links within bivariate data.

• Physical Geography Example: You might find a negative correlation between river bedload size and distance downstream. The explanation is that attrition causes rocks to collide and break apart during high-energy transport, making them smaller and rounder over time.
• Human Geography Example: Environmental Quality Survey (EQS) scores often show a positive correlation with distance from the CBD. This could be because older industrial areas near the centre are replaced by newer suburban residential developments with more green space.