Data Representation

A bar chart shows how often each category appears. The categories sit along the horizontal axis, the frequency goes up the vertical axis, and each bar should be:

• the same width as the others,
• separated by small gaps,
• read off the scale carefully — count the gridlines, not the bars.

A dual bar chart puts two related sets side by side so you can compare two groups across the same categories — boys vs girls, before vs after, brand A vs brand B. Use the same scale and a clear key.

When you describe a bar chart, lead with the modal category, then mention the smallest. A sentence like "Chips were the most popular snack in both classes, with the largest difference between the classes appearing for apples," is more useful than just reading the numbers.

A pie chart is a circle split into sectors. Each sector's angle is the category's share of the total:

$\text{angle} = \frac{\text{frequency}}{\text{total}} \times 360°.$

A line graph plots a measurement against time and joins the points with straight lines. Use line graphs when both axes are continuous — temperature through the day, population by year, speed by second.

The shape of the line tells the story:

• A rising line means the value is increasing.
• A falling line means it is decreasing.
• A flat segment means it is unchanged.
• A steep line means the change is faster.

A frequency diagram is the chart of choice for grouped numerical data — heights, masses, times. It looks like a bar chart but with the bars touching, because the data is continuous. The bars sit between the class boundaries, and the height of each bar is the frequency.

When you describe a line graph, name the maximum, the minimum and the overall shape. "Temperature rose from $$C at 8 am to a peak of C at noon, then dropped slowly to C by 4 pm" is the kind of sentence the question is looking for.

A scatter graph plots each piece of data as a point $(x, y)$. Each axis represents a different measurement — say height on $x$ and shoe size on $y$ — and the pattern of the points reveals the relationship.

We describe the relationship with correlation:

• Positive correlation: as one variable goes up, the other tends to go up too. Points rise from bottom-left to top-right.
• Negative correlation: as one goes up, the other tends to go down. Points fall from top-left to bottom-right.
• No correlation: the points are scattered with no pattern.

Correlation can also be strong (points cluster tightly along a line) or (points scatter loosely). And remember — . Two variables can rise together without one causing the other.

A line of best fit is a single straight line drawn through a scatter that shows correlation. It should:

• pass through the middle of the points,
• have about as many points above as below,
• ignore obvious outliers,
• not be forced through the origin or the first point.

Drawn well, the line lets you make estimates: pick an $x$-value on the horizontal axis, go up to the line, then read across to the $y$-axis. So if your line says a student of height $160$ cm has shoe size $7$, that's a reasonable estimate.

Two important limits. Interpolation — estimating the range of the data — is generally reliable. — estimating the range of the data — is risky, because you can't see what the pattern does there. A line of best fit predicting shoe size for an adult of height m, when the data only ran from to cm, is much less trustworthy.

Charts and graphs are how you communicate data quickly, so you'll meet them everywhere:

• Science uses line graphs, scatter graphs and lines of best fit to spot relationships in experiments.
• Geography and economics rely on bar and line charts for change over time.
• IGCSE statistics extends scatter graphs into regression, and frequency diagrams into histograms.
• In everyday life, news headlines and infographics use these chart types every day — being able to read them critically is a life skill.

Practise both reading and drawing — labels, units, scale, key. Those four words win more marks than any clever interpretation.