Knowledge organisers

Statistics: Cambridge IGCSE Maths (0580) knowledge organiser

Everything to know about statistics on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Mean: The total of the values divided by how many there are.
Median: The middle value when the data are in order.
Interquartile range: Q₃ − Q₁: the spread of the middle half of the data.
Frequency density: Frequency ÷ class width; the heights of a histogram's bars.

Key formulas

Mean from a frequency table	\(\bar x=\frac{\sum fx}{\sum f}\)
Estimated mean, grouped data (class midpoints \(m\))	\(\bar x\approx\frac{\sum fm}{\sum f}\)
Median position (\(n\) values in order)	\(\tfrac{n+1}2\text{th value}\)
Range	\(\text{largest}-\text{smallest}\)
Interquartile range	\(Q_3-Q_1\)
Histogram	\(\text{frequency density}=\frac{\text{frequency}}{\text{class width}}\)

Worked example

Find the mean of this frequency table: score 1, 2, 3, 4 with frequencies 3, 5, 8, 4.

Σf = 3 + 5 + 8 + 4 = 20
Σfx = 3 + 10 + 24 + 16 = 53
Mean = 53 ÷ 20

Answer: Mean = 2.65

Common mistakes

Using class widths instead of midpoints for an estimated mean
Drawing histogram bars with heights equal to the frequency instead of the frequency density

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Classify data as discrete or continuous and qualitative or quantitative, and organise it in frequency tables and grouped tables.
Draw and interpret ordered stem-and-leaf diagrams with a key and frequency distributions, and use them to find averages.
Draw lines of best fit through the mean point of a scatter diagram and use them to estimate values, discussing reliability.
Draw and interpret histograms with equal class widths for grouped continuous data, and compare them with bar charts.
Draw and interpret histograms with unequal class widths using frequency density.
Compare two distributions in words, using a measure of average and a measure of spread and referring to the context of the data.

The printable sheet

Statistics knowledge organiser for Cambridge IGCSE Maths (0580): one A4 page of key definitions, formulas, a worked example and common mistakes — Statistics knowledge organiser (Cambridge IGCSE Maths (0580)), A4. Download the PDF.

Revise it next

Other Cambridge IGCSE Maths (0580) topics: Number · Algebra and graphs · Coordinate geometry · Geometry · Mensuration · Trigonometry · Transformations and vectors · Probability · All Cambridge IGCSE Maths (0580) organisers