This module covers how to read, build and judge the displays used in IGCSE statistics: histograms with unequal class widths, cumulative frequency curves, scatter diagrams with a line of best fit, comparisons between two data sets, and the choice of display itself. The common thread is asking what a picture actually shows before you read a number off it.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact content points in your exam year, including which ones belong to the Core and Extended routes. The reasoning habits here stay the same across versions. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You need to find the mean, median and range of a small list, work with fractions, decimals and percentages, and read values from a labelled axis. You should also be comfortable substituting into y = mx + c and finding a gradient from two points. Nothing here needs algebra beyond that.
An orienting example
The times, in minutes, for 40 students to finish a task have these cumulative frequencies: 4 by 10 minutes, 14 by 20, 32 by 30 and 40 by 40. Estimate the median time.
Step 1, position: 40 ÷ 2 = 20, so we want the 20th value.
Step 2, locate: the 20th value lies between (20, 14) and (30, 32).
Step 3, interpolate: the curve rises 18 over this stretch, and we need to rise 20 − 14 = 6. That is 6/18 = 1/3 of the way across, so the time is 20 + 10 × 1/3 ≈ 23.3.
Median ≈ 23.3 minutes, an estimate because the individual values are hidden.
Check: 23.3 lies inside the 20 to 30 class, the class where the running total passes 20. The answer is also plausible against the data: 14 students finished within 20 minutes and 32 within 30.
That one question used the idea of a running total, a position rule, a horizontal reading and a comment on estimation. It shows how the lessons in this module connect.
In which order should you study it?
- Read a histogram using frequency density: the skill of reading area, not height, which gives class frequencies.
- Estimate a median from cumulative frequency: turns those frequencies into a running total and reads medians and quartiles.
- Use a scatter diagram without inferring causation: moves from one variable to two, with prediction and careful wording.
- Compare two distributions with compatible scales: puts averages, spreads and proportions side by side.
- Choose a display that preserves the data meaning: pulls everything together by asking which chart fits which question.
Then work through the mixed practice set. One lesson a day and the practice set at the weekend is a steady pace.
Which traps catch most students here?
- Reading a histogram bar’s height as the frequency when the classes have different widths.
- Plotting cumulative frequency at the midpoint of a class instead of its upper boundary.
- Reading a median off the frequency axis instead of the horizontal axis.
- Extrapolating a line of best fit far outside the data.
- Writing “causes” when the diagram only shows association.
- Comparing counts between groups of different sizes instead of proportions.
Each lesson shows one of these slips in full and then corrects it.
How should you use the practice set?
Attempt each question on paper before opening the answer, and write the working as you would in an exam. The non-calculator working trainer lets you check the fraction and division steps, and the percentage-base explorer helps with proportions.
When a question goes wrong, read the routing notes at the end of the practice set and return to the lesson it names. Record the error in the mistake log and retest queue, and retry a fresh question a few days later. If you want a teacher to watch you work through chart questions, that is what we do in online one-to-one Mathematics tuition.