What does the Statistics and Probability strand of N(A)-Level Mathematics cover?

This strand of SEAB 4045 (Mathematics Syllabus A) covers the three averages (mean, median and mode) and the range as a measure of spread; organising data into a frequency table and displaying it with bar charts, pictograms and pie charts; and basic probability for equally likely outcomes, including the rule that the probability of an event and its complement add to one.

When should I use the mean, the median or the mode?

Use the mean for data that is fairly evenly spread, because it uses every value. Use the median (the middle value of the ordered data) when there are extreme values, since they would pull the mean away from the centre. Use the mode (the most frequent value) for the most popular category, especially with non-numerical data such as favourite colours.

How do I find the median of an even number of values?

First order the data from smallest to largest. With an odd number of values the median is the single middle value. With an even number of values there are two middle values, and the median is their average: add them and divide by two. For example, the median of $3, 5, 8, 10$ is $\dfrac{5 + 8}{2} = 6.5$.

How do I work out the angle of a pie-chart sector?

A pie chart divides a full circle of $360^\circ$ in proportion to the frequencies. The angle for each category is its frequency divided by the total frequency, multiplied by $360^\circ$. Always check that all the sector angles add up to $360^\circ$, which confirms there is no arithmetic error.

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N(A)-Level Mathematics Statistics and Probability: averages and range, statistical diagrams, and basic probability

Q: What does a probability of zero or one mean?

Probability measures likelihood on a scale from $0$ to $1$. A probability of $0$ means the event is impossible, and a probability of $1$ means it is certain. For equally likely outcomes, the probability of an event is the number of favourable outcomes divided by the total number of outcomes, and the probabilities of an event and its opposite always add to $1$.

An overview of the N(A)-Level Mathematics Statistics and Probability strand (SEAB 4045). The mean, median, mode and range as measures of average and spread, data handling with bar charts, pictograms and pie charts, and basic probability on the zero-to-one scale, with links to every dot point.

Generated by Claude Opus 4.86 min readSEAB-4045Updated 2026-06-13

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

Jump to a section

Why statistics and probability matter
Averages and range
Data handling and statistical diagrams
Basic probability
Check your knowledge

Why statistics and probability matter

This strand of N(A)-Level Mathematics (SEAB 4045, Mathematics Syllabus A) is about making sense of data and measuring chance. Statistics turns a list of numbers into a single average, a measure of spread and a clear diagram; probability puts a number on how likely an event is. Both skills appear in everyday contexts, from survey results to games of chance, so the questions reward careful reading as much as calculation. This overview links to every dot point in the module, each with its own worked answers and practice.

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

Averages and range

Averages: mean, median and mode covers the three averages and the range. The mean adds all the values and divides by the count; the median is the middle value of the ordered data (the average of the two middle values when there is an even number); and the mode is the most frequent value. The range, found by subtracting the smallest value from the largest, measures the spread. Choose the mean for evenly spread data, the median when extreme values would distort it, and the mode for the most popular category.

Data handling and statistical diagrams

Data handling and statistical diagrams starts with organising raw data into a frequency table, then displaying it. Bar charts use equal-width bars whose heights show frequency; pictograms use a symbol worth a fixed amount given in a key; and pie charts split a $360^\circ$ circle into sectors, each angle being the frequency over the total frequency times $360^\circ$ . Choose the diagram to suit the data, label everything, and check that the pie-chart angles sum to $360^\circ$ .

Basic probability

Basic probability measures likelihood on a scale from $0$ (impossible) to $1$ (certain). For equally likely outcomes, the probability of an event is

\text{P(event)} = \frac{\text{number of favourable outcomes}}{\text{total number of outcomes}},

written as a simplified fraction, decimal or percentage. The probabilities of an event and its opposite add to

1

, so

\text{P(not A)} = 1 - \text{P(A)}

, which is the quick way to handle "not" questions.

Check your knowledge

A mix of averages, diagram and probability questions covering the strand. Attempt them, then check the solutions.

Find the mean of $4, 7, 7, 10, 12$ . (1 mark)
Find the median of $9, 3, 7, 5, 8, 6$ . (2 marks)
State the mode and range of $2, 5, 5, 8, 11$ . (2 marks)
In a survey of $60$ people, $15$ chose tea. Find the angle of the tea sector in a pie chart. (2 marks)
A fair six-sided die is rolled. Find the probability of getting a number greater than $4$ . (2 marks)

Solutions

These five questions practise mean, median, mode, range, pie chart angles, and probability. Work through each, then verify your reasoning below.

Step 1: Calculate the mean in Q1

The mean is the sum of all values divided by how many values there are. Add the five numbers first, then divide by $5$ :

\text{mean} = \frac{4 + 7 + 7 + 10 + 12}{5} = \frac{40}{5} = 8.

Final answer (Q1): mean $= 8$ .

Step 2: Find the median in Q2

The median is the middle value when all data are placed in ascending order. With six values, there is no single middle value, so the median is the average of the third and fourth values:

\text{ordered data: } 3, 5, 6, 7, 8, 9.

\text{median} = \frac{6 + 7}{2} = 6.5.

Final answer (Q2): median $= 6.5$ .

Step 3: State the mode and range in Q3

The mode is the value that appears most often. Scan the list and count repeats to identify it. The range measures how spread out the data are and is always the largest value minus the smallest:

\text{mode} = 5 \quad \text{(appears most often)}, \qquad \text{range} = 11 - 2 = 9.

Final answer (Q3): mode $= 5$ ; range $= 9$ .

Step 4: Find the sector angle for tea in Q4

In a pie chart, each category's angle is proportional to its share of the total. Divide the category frequency by the total frequency and multiply by $360^\circ$ :

\text{angle for tea} = \frac{15}{60} \times 360^\circ = \frac{1}{4} \times 360^\circ = 90^\circ.

Final answer (Q4): $90^\circ$ .

Step 5: Find the probability in Q5

Probability equals the number of favourable outcomes divided by the total number of equally likely outcomes. Rolling a fair die can produce $1, 2, 3, 4, 5, 6$ , and the outcomes greater than $4$ are $5$ and $6$ , giving $2$ favourable outcomes out of $6$ :

\text{P(greater than 4)} = \frac{2}{6} = \frac{1}{3}.

Final answer (Q5): $\dfrac{1}{3}$ .

Sources & how we know this

Singapore-Cambridge GCE N(A)-Level Mathematics (Syllabus A, 4045) — Singapore Examinations and Assessment Board (2026)