Knowledge organisers

Statistics and probability: Edexcel IGCSE Maths (4MA1) knowledge organiser

Everything to know about statistics and probability 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

Statistical Measures: Mean = total ÷ count. Median = middle when ordered. Mode = most common. Range = max − min.
Histograms and Frequency Density: In a histogram the bar AREA shows the frequency: frequency density = frequency ÷ class width.
Probability: Multiply along the branches of a tree diagram, add the paths you want. Without replacement, the numbers on the second branches change.

Key formulas

Mean from a table	\(\bar x=\frac{\sum fx}{\sum f}\)
Median position (\(n\) values)	\(\tfrac{n+1}2\text{th value}\)
Interquartile range	\(Q_3-Q_1\)
Histogram	\(\text{frequency density}=\frac{\text{frequency}}{\text{class width}}\)
Probability	\(P(\text{not }A)=1-P(A);\) \(\text{expected frequency}=n\times P(A)\)
Mutually exclusive	\(P(A\text{ or }B)=P(A)+P(B)\)
Any two events	\(P(A\cup B)=P(A)+P(B)\) \(-P(A\cap B)\)
Independent	\(P(A\text{ and }B)=P(A)\times P(B)\)
Conditional	\(P(B\mid A)=\frac{P(A\cap B)}{P(A)}\)
Tree diagrams: multiply along branches, add the outcomes you want; without replacement, change the second branch

Worked example

A bag has 3 red and 5 blue counters. Two are taken without replacement. P(both red)?

3/8 × 2/7 = 6/56 = 3/28.

Common mistakes

Histograms: reading heights as frequencies
Cumulative frequency plotted at midpoints
Forgetting to order data before finding the median
Pie-chart angles not totalling 360°

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

You should be able to…

Classify data as qualitative or quantitative and discrete or continuous, and complete and interpret two-way tables.
Find the mean, median and mode from a frequency table of discrete data, and interpret what they show about the data.
Calculate frequency density as frequency ÷ class width and draw histograms for grouped continuous data with unequal class widths.
Complete cumulative frequency tables from grouped data and draw cumulative frequency curves, plotting at the upper class boundaries.
Estimate probabilities from experiments using relative frequency, and use probabilities to calculate expected frequencies for a number of trials.
Find conditional probabilities from two-way tables and Venn diagrams, restricting attention to the given event before calculating the probability.

The printable sheet

Statistics and probability knowledge organiser for Edexcel IGCSE Maths (4MA1): one A4 page of key definitions, formulas, a worked example and common mistakes — Statistics and probability knowledge organiser (Edexcel IGCSE Maths (4MA1)), A4. Download the PDF.

Revise it next

Other Edexcel IGCSE Maths (4MA1) topics: Number · Algebra · Graphs, sequences and calculus · Geometry and trigonometry · All Edexcel IGCSE Maths (4MA1) organisers