Graph, chart & data interpretation
1. Start with the source and variables
A graph is evidence only after you understand what was measured. Read the title, place, dates, sample size, source, units, legend and axes. Distinguish totals from rates, percentages from percentage-point differences, and a stock at one time from a flow over a period. A count of journeys is not necessarily a count of people.
Identify the observational unit: a site, household, month or district. Check whether two series use the same boundaries, season and definition. A larger district may have more people but a lower population density. \(\text{Density}=\frac{\text{population}}{\text{area}}\); state people per \(\mathrm{km}^{2}\). Missing values are not zero.
All numerical examples here are synthetic teaching data. Preserve original observations, document corrections and keep unusual but valid values. Remove an observation only for a defensible recorded reason, such as a confirmed unit-entry error; an inconvenient value is not an error.
2. Choose a display that answers the question
Bar charts compare categories, with gaps between bars. Line graphs show change across ordered time or distance; do not join unrelated categories. Scatter plots show paired numerical observations, one point per site or respondent. A relationship cannot be read from two unpaired lists.
Histograms show frequencies of continuous values grouped into intervals. Adjacent bars touch. With unequal class widths, use \(\text{frequency density}=\frac{\text{frequency}}{\text{class width}}\) so bar area represents frequency. A pie chart shows parts of one whole: \(\text{angle}=\frac{\text{category value}}{\text{total}}\times360^{\circ}\). It is poor for comparing many similar slices or unrelated totals.
A choropleth map shades areas by a rate or proportion, using a clear class key; raw totals can mostly reflect different area sizes. Proportional symbols can show totals at locations. A transect or profile shows change along a route. An annotated sketch explains relationships that a photograph alone may not highlight.
Selection table in words: monthly rainfall → columns; change in monthly temperature → line; bus use versus distance to a stop → scatter; travel-mode shares → pie or percentage bars; district population density → choropleth. Several displays may be defensible: justify the choice using the variable and enquiry, not “it looks clear”.
3. Read and describe precisely
Read the interval between ticks before estimating a point. Check for a broken axis, logarithmic scale or separate left and right axes. Bar lengths should normally be compared against zero; a truncated axis can exaggerate a small difference. A line chart may use a narrower range, but the range must be clear.
Describe the general pattern, support it with two relevant values and units, then identify a turning point, fluctuation or exception. “The count rose from \(80\) to \(120\) journeys, a rise of \(40\), then fell to \(100\)” is stronger than “it fluctuates”. Avoid listing every number without a pattern.
Example monthly values are \(20\), \(35\), \(30\), \(55\) and \(60\,\mathrm{mm}\). Overall rainfall rises by \(40\,\mathrm{mm}\) from the first to last month, with a \(5\,\mathrm{mm}\) fall between months two and three. The maximum is \(60\,\mathrm{mm}\), not the \(55\,\mathrm{mm}\) point with the largest preceding increase. An overall trend need not be continuous.
A dual-axis climate graph uses different units for temperature and rainfall; equal visual heights do not mean equal values. Interpolate only within a reasonable interval and call it an estimate. Extrapolation beyond the observations is less secure because the process may change.
4. Calculate change and summarise data
\(\text{Absolute change}=\text{new}-\text{old}\). \(\text{Percentage change}=\frac{\text{new}-\text{old}}{\text{old}}\times100\%\). From \(80\) to \(100\) is a rise of \(20\) or \(25\%\); from \(100\) back to \(80\) is a fall of \(20\%\). The denominator is the starting value, so the two percentages differ. Percentage change from zero is undefined.
If walking increases from \(30\%\) to \(45\%\) of journeys, the increase is \(15\) percentage points, or \(50\%\) relative to the original share. Do not write \(15\%\) when the question asks for relative percentage increase. State which measure you use.
For values \(2\), \(4\), \(4\), \(6\) and \(9\), \(\text{total}=25\) and \(\text{mean}\) \(=25/5 \) \(= 5\). Sorted values give median \(4\) and mode \(4\). \(\text{Range}\) \(=9 - 2 \) \(= 7\). The mean uses every value and is pulled upwards by \(9\); the median is less affected. For an even number of observations, average the two central sorted values.
Do not average group percentages without considering their denominators. In one district \(10/20\) respondents walk; in another \(20/80\) walk. Combined walking share is \(30/100 = 30\%\), not the unweighted average of \(50\%\) and \(25\%\) (\(=\) \(37.5\%\)). Report both sample sizes when comparing percentages.
For pie-chart practice, \(18\) of \(60\) journeys made on foot represent \(30\%\) and an angle of \(108{}^{\circ}\). For a district with \(12{,}000\) people in \(3\,\mathrm{km}^{2}\), density is \(4{,}000\,\mathrm{people}/\mathrm{km}^{2}\). Show the working and round only the final answer to the requested precision.
5. Variability: similar means can hide different conditions
Consider two synthetic pedestrian counts per minute. Site A: \(8\), \(10\), \(12\); site B: \(2\), \(10\), \(18\). Both means are \(10\). Their ranges are \(4\) and \(16\), so B varies more; it may require a different crowd-management response even though average demand matches.
Standard deviation summarises spread around the mean in the original units. For these complete supplied sets, a statistical calculation gives standard deviations of approximately \(1.63\,\mathrm{pedestrians}/\mathrm{min}\) for A and \(6.53\,\mathrm{pedestrians}/\mathrm{min}\) for B. B therefore has greater spread around the same mean. Use a supplied result or the calculation method specified in a task, and interpret it alongside the raw data.
The EDB Supplementary Notes (\(2025\)), page \(3\), include standard deviation and correlation among appropriate statistical techniques for fieldwork analysis, but do not prescribe a population-versus-sample formula distinction. Standard deviation is never negative, and zero means all supplied values are equal. It is not the range and is not a measure of instrument accuracy.
Use median and a description of spread for skewed data; a single extreme observation can move the mean and standard deviation substantially. Explain whether an outlier could be real, a recording fault or a different event. Repeat measurement and inspect field notes before making any exclusion.
6. Correlation, explanation and defensible conclusions
A positive correlation means larger values of one variable tend to occur with larger values of the other; a negative correlation means larger values tend to pair with smaller ones. Strength concerns how closely points follow a relationship, not the steepness of the line. Look for clusters, curves and outliers as well as the overall direction.
Example: tree cover (\(\%\)) at four sites is \(10\), \(30\), \(50\), \(70\); temperature (\({}^{\circ}\,\mathrm{C}\)) is \(34\), \(33\), \(31\), \(30\). The negative association is consistent with shade and evapotranspiration reducing heat, but four observations cannot isolate that effect. Time of day, building shade, wind and surface material may confound the comparison.
Correlation does not establish causation. A plausible mechanism helps interpretation, but stronger evidence needs controls, repeated measurements or a suitable comparison design. A near-zero linear correlation does not rule out a curved relationship. Never invent a numerical correlation coefficient from appearance alone.
For paired \(x\) values \(1\), \(2\), \(3\), \(4\) and \(y\) values \(40\), \(30\), \(20\), \(10\), \(y\) falls consistently as \(x\) rises. A supplied correlation coefficient of \(-1\) indicates a perfect negative relationship for these data. Interpret a supplied coefficient with the scatter plot, sample size and possible confounding factors. The EDB Supplementary Notes (\(2025\)), page \(3\), do not prescribe a named rank-correlation calculation formula. A coefficient alone does not demonstrate statistical significance.
Finish with a bounded judgement: state what the dataset supports, quote evidence, explain a geographical process, and identify a limitation with a targeted improvement. “These four sites were cooler where tree cover was greater; repeat simultaneous readings at more matched sites” is better than “trees always reduce temperature by this amount”.
7. Build and challenge a complete data display
Synthetic rainfall table: month \(1/2/3/4\); rainfall \(20/40/60/80\,\mathrm{mm}\); number of rainy days \(4/5/6/8\). A rainfall bar chart needs a month axis, a rainfall axis in mm, equal-width bars, a zero baseline and a title stating that the data are synthetic. The tallest bar represents the greatest monthly total, not necessarily the wettest individual day.
Rainfall per rainy day is \(5\), \(8\), \(10\) and \(10\,\mathrm{mm}\) respectively. The total across four months is \(200\,\mathrm{mm}\) over \(23\) rainy days, so the combined amount per rainy day is \(200/23 \approx 8.70\,\mathrm{mm}\). Averaging the four monthly rates gives \(8.25\,\mathrm{mm}\) and is not the combined rate because the denominators differ. State whether you mean total rainfall, days with rain or rainfall per rainy day.
Histogram example: \(12\) observations fall in a \(0\text{{–}}10\) minute travel-time class, and \(18\) in a \(10\text{{–}}30\) minute class. Class widths are \(10\) and \(20\) minutes; frequency densities are \(1.2\) and \(0.9\) observations per minute. The second class contains more observations but has a lower bar. This is correct because area, not height alone, represents frequency.
For a comparison, ask whether missing data could change the conclusion. If rainy days at one station were not recorded, a blank denominator does not mean there were no rainy days. Do not calculate a rate using invented zeros. Display the gap and explain which comparison remains possible.
Answer framework: finding → numerical support → geographical interpretation → limit. A correlation question needs paired observations; a trend question needs ordered time; an evaluation needs a reason why the source or method affects confidence. A clear graph supports a carefully bounded answer, not a stronger claim than the data allow.