What does the Statistics and Probability strand of O-Level E-Maths cover?

This part of SEAB 4052 covers the three averages (mean, median and mode), including from a frequency table, and the range as a measure of spread; constructing and interpreting bar charts, pie charts, line graphs, histograms and stem-and-leaf diagrams, and choosing a suitable display; building a cumulative frequency curve and using it to estimate the median, quartiles, interquartile range and percentiles; and calculating the probability of single events and of combined events using the addition and multiplication rules with tree diagrams. It is the data-handling strand of the syllabus.

What is the difference between the mean, the median and the mode?

The mean is the sum of the values divided by how many there are. The median is the middle value when the data are arranged in order (or the average of the two middle values for an even count). The mode is the value that occurs most often. The median is preferred when the data contain extreme values, because the mean is pulled toward outliers while the median is not.

How do you find the median and quartiles from a cumulative frequency curve?

On a cumulative frequency curve, the median is the value at the cumulative frequency equal to half the total, the lower quartile is the value at one quarter of the total, and the upper quartile is the value at three quarters of the total. The interquartile range is the upper quartile minus the lower quartile and measures the spread of the middle half of the data, ignoring extremes.

When do I add probabilities and when do I multiply them?

Add probabilities for mutually exclusive outcomes of a single trial, using the addition rule, the probability of A or B. Multiply probabilities for independent events happening in sequence, using the multiplication rule, the probability of A and then B. On a tree diagram you multiply along the branches for a path and then add the probabilities of the different paths that give the required outcome.

What is the interquartile range and why is it useful?

The interquartile range is the upper quartile minus the lower quartile, so it is the spread of the central half of the data. It is useful because, unlike the range, it ignores the most extreme values at each end, so it is not distorted by a single very large or very small observation. A larger interquartile range indicates more variability in the bulk of the data.

SingaporeMaths

O-Level E-Maths Statistics and Probability: averages and spread, statistical diagrams, cumulative frequency and quartiles, and the probability of single and combined events

An overview of the O-Level E-Maths Statistics and Probability strand (SEAB 4052). The mean, median and mode and the range, statistical diagrams from bar charts to histograms and stem-and-leaf plots, the cumulative frequency curve with median, quartiles and interquartile range, and the probability of single and combined events with tree diagrams, with links to every dot point.

Generated by Claude Opus 4.86 min readSEAB-4052Updated 2026-06-13

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

What this strand is about
Averages and spread
Displaying data
Cumulative frequency and quartiles
Probability
How the strand is examined
Check your knowledge

What this strand is about

Statistics and probability is the data-handling strand: summarising data with averages and spread, displaying it clearly, and reasoning about chance. The marks reward correct calculation, accurate reading from diagrams, and clear interpretation of what a figure means. This overview ties the strand together and links to every dot point, each with worked answers and practice.

See the full set of dot points at /sg-o-level/mathematics/syllabus.

Averages and spread

The strand opens with averages and measures of spread: the mean (sum divided by count), the median (the middle value in order) and the mode (the most frequent value), each computable from a frequency table, plus the range (largest minus smallest) as a simple measure of spread. Choosing a suitable average, the median when there are outliers, is part of the skill.

Displaying data

Data handling and statistical diagrams covers the standard displays: bar charts, pie charts, line graphs, histograms and stem-and-leaf diagrams. You read values off each and choose an appropriate display for a given data set, for example a pie chart for proportions of a whole and a line graph for a trend over time.

Cumulative frequency and quartiles

Cumulative frequency and quartiles builds the cumulative frequency curve, then reads the median (at half the total), the lower and upper quartiles (at one quarter and three quarters), the interquartile range and percentiles. The interquartile range measures the spread of the middle half, ignoring extremes.

Probability

Probability of single and combined events covers the probability of a single event (favourable outcomes over total outcomes), mutually exclusive and independent events, the addition rule (for or) and the multiplication rule (for and), and tree diagrams for sequences of events, where you multiply along branches and add across paths.

How the strand is examined

Calculate averages carefully from tables. For a frequency table, the mean uses the sum of (value times frequency) divided by the total frequency.
Read diagrams and curves accurately. Use a ruler on a cumulative frequency curve to locate the median and quartiles, and quote estimates sensibly.
Apply the right probability rule. Add for mutually exclusive outcomes; multiply for independent events in sequence; on a tree, multiply along a path then add the paths.

Check your knowledge

Attempt these, then check the solutions.

Find the mean, median and mode of the data $4, 7, 7, 2, 5$ . (3 marks)
A bag holds $3$ red and $5$ blue balls. One ball is drawn at random. Find the probability that it is red. (2 marks)
On a cumulative frequency curve for $80$ students, at what cumulative frequency do you read the upper quartile? (1 mark)
Two fair coins are tossed. Find the probability of getting two heads. (2 marks)
The interquartile range of a data set is the upper quartile minus the lower quartile. If the lower quartile is $12$ and the upper quartile is $20$ , find the interquartile range. (1 mark)

Sources & how we know this

Singapore-Cambridge GCE O-Level Mathematics (Syllabus 4052) — Singapore Examinations and Assessment Board (2026)