Edexcel IAL S1 Maths Revision: Statistics 1

Edexcel International A Level S1 (Statistics 1): every topic with an exam-style question and its mark scheme, and 253 practice questions with mark schemes.

1h 30min written paper (75 marks), calculator permitted
7 topics
253 questions

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Discrete Random Variables · S1 paper · 5 marks · hard

A discrete random variable $X$ has $E (X) = 2$ and $V a r (X) = 4$ . Another variable is defined as $Y = a X + b$ , where $a > 0$ . Given that $E (Y) = 10$ and $V a r (Y) = 36$ , find the values of the constants $a$ and $b$ .

Worked answer

M1 for using the variance property $V a r (Y) = a^{2} V a r (X)$ to write $36 = a^{2} (4)$ .
A1 for solving to find $a^{2} = 9 ⟹ a = 3$ (since $a > 0$ ).
M1 for using the expectation property $E (Y) = a E (X) + b$ to write $10 = a (2) + b$ .
M1 for substituting $a = 3$ into the equation: $10 = 3 (2) + b$ .
A1 for concluding $b = 4$ .

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S1 topics

"Tested in" counts come from our question-by-question mapping of the 4 Pearson S1 papers from June 2024 to June 2025.

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Question 1 of 5
Question 2 of 5
Question 3 of 5
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Question 5 of 5

5 quick questions from across IAL S1. No sign-in needed.

Find the mean of the data in the table.

$x$	2	4	6	8
Frequency	1	4	4	1

Choose your answer · keys 1–4

12.5

50

2.5

5

$x$	0	1	2
$P (X = x)$	$\frac{1}{4}$	$\frac{1}{2}$	$\frac{1}{4}$

S1 past papers

Official Pearson S1 papers and mark schemes, with a timer: all IAL S1 past papers. Most recent: June 2025 · January 2025 · October 2024 · June 2024.

Examiner Insights for IAL S1: every examiner report since June 2024, the top mistakes and what to focus on next →

Knowledge organiser: Statistics 1 (S1) on one page (key facts, formulas and mistakes to avoid; printable PDF)

S1 Data and Summary Statistics

Types of data (qualitative/quantitative, discrete/continuous); mean, median, mode, quartiles and percentiles; variance and standard deviation; coding; outliers. (Sampling methods are not in IAL S1.)

70 practice questions with mark schemes · Worked examples → · Notes → · Practise data and summary statistics →

Example question · 9 marks · hard

Two different groups of students took a memory test. Group A consists of $20$ students. Their mean score is $15$ and the standard deviation is $3$ . Group B consists of $30$ students. Their mean score is $20$ and the standard deviation is $4$ . The two groups are combined into a single group of $50$ students.

Find the combined mean score.
By calculating the total sum of squares ( $\sum x^{2}$ ) for each group separately, find the overall standard deviation of the combined group.

Show the mark scheme

Sum A $= 20 \times 15 = 300$ . Sum B $= 30 \times 20 = 600$ . M1
Total Sum $= 300 + 600 = 900$ . Total students $= 50$ .
Combined mean $= \frac{900}{50} = 18$ . A1
For Group A: $σ_{A}^{2} = 3^{2} = 9$ .
$9 = \frac{\sum x_{A}^{2}}{20} - 15^{2} ⟹ \frac{\sum x_{A}^{2}}{20} = 9 + 225 = 234 ⟹ \sum x_{A}^{2} = 4680$ . M1A1
For Group B: $σ_{B}^{2} = 4^{2} = 16$ .
$16 = \frac{\sum x_{B}^{2}}{30} - 20^{2} ⟹ \frac{\sum x_{B}^{2}}{30} = 16 + 400 = 416 ⟹ \sum x_{B}^{2} = 12480$ . M1A1
Total sum of squares $\sum x^{2} = 4680 + 12480 = 17160$ . A1
Combined Variance $= \frac{17160}{50} - 18^{2} = 343.2 - 324 = 19.2$ . M1
Combined SD $= \sqrt{19.2} = 4.3817 . . . ⟹ 4.38$ (3sf). A1

S1 Representation of Data

Histograms (frequency density), stem-and-leaf, box plots, cumulative frequency, outliers, skewness; comparing distributions.

35 practice questions with mark schemes · Worked examples → · Notes → · Calculator steps → · Practise representation of data →

Example question · 5 marks · hard

The data in a histogram is grouped into classes. A bar representing the class $100 \leq x < 150$ has a width of $2.5 cm$ and a height of $4 cm$ . The total area of all bars in the histogram is $90 {cm}^{2}$ . If the bar for $100 \leq x < 150$ represents a frequency of $20$ , calculate the total frequency of the entire data set.

Show the mark scheme

M1 for calculating the area of the specified bar: $2.5 \times 4 = 10 {cm}^{2}$ .
M1 for establishing the relationship between area and frequency: $10 {cm}^{2}$ represents a frequency of $20$ .
A1 for calculating the scale factor: $1 {cm}^{2}$ represents $2$ items (since $20 / 10 = 2$ ).
M1 for using the total area to find total frequency: $90 {cm}^{2} \times 2$ .
A1 for the final answer: $180$ items.

S1 Probability

Venn diagrams, tree diagrams, mutually exclusive vs independent events, conditional probability P(A|B).

35 practice questions with mark schemes · Worked examples → · Notes → · Practise probability →

Example question · 3 marks · hard

A bag contains 5 green counters and 3 yellow counters. A counter is drawn at random, its colour is noted, and it is replaced. This is done 3 times in total. Find the probability that exactly 2 green counters are drawn.

Show the mark scheme

M1 for identifying the 3 ways to draw exactly 2 green counters: GGY, GYG, YGG.
M1 for calculating the probability of one such arrangement, e.g., $(\frac{5}{8}) \times (\frac{5}{8}) \times (\frac{3}{8}) = \frac{75}{512}$ .
A1 for multiplying by 3 to find the total probability: $\frac{225}{512}$ .

S1 Correlation and Regression

Product-moment correlation coefficient (PMCC), scatterplots, least-squares regression line y on x.

35 practice questions with mark schemes · Worked examples → · Notes → · Calculator steps → · Practise correlation and regression →

Example question · 4 marks · hard

A dataset of 20 observations produced the following summary statistics: $\sum x = 140$ , $\sum y = 200$ , $\sum x^{2} = 1250$ , $\sum y^{2} = 2600$ , and $\sum x y = 1100$ . Calculate the product moment correlation coefficient.

Show the mark scheme

M1 for calculating $S_{x x} = 1250 - \frac{140^{2}}{20} = 270$ and $S_{y y} = 2600 - \frac{200^{2}}{20} = 600$ .
M1 for calculating $S_{x y} = 1100 - \frac{140 \times 200}{20} = - 300$ .
M1 for setting up the PMCC calculation $r = \frac{- 300}{\sqrt{270 \times 600}}$ .
A1 for evaluating the final correlation coefficient as $r \approx - 0.745$ (to 3 s.f.).

S1 Discrete Random Variables

Probability distributions of discrete random variables, expectation E(X), variance Var(X), cumulative distribution functions.

35 practice questions with mark schemes · Worked examples → · Notes → · Practise discrete random variables →

Example question · 5 marks · hard

Show the mark scheme

M1 for using the variance property $V a r (Y) = a^{2} V a r (X)$ to write $36 = a^{2} (4)$ .
A1 for solving to find $a^{2} = 9 ⟹ a = 3$ (since $a > 0$ ).
M1 for using the expectation property $E (Y) = a E (X) + b$ to write $10 = a (2) + b$ .
M1 for substituting $a = 3$ into the equation: $10 = 3 (2) + b$ .
A1 for concluding $b = 4$ .

S1 Normal Distribution

The normal distribution N(μ, σ²); standardising with Z; using tables for probabilities and inverse problems; finding μ and/or σ.

13 practice questions with mark schemes · Worked examples → · Notes → · Calculator steps → · Practise normal distribution →

Example question · 4 marks · medium

The diameters of bolts made by a machine are normally distributed with mean $12 mm$ and standard deviation $0.2 mm$ . A bolt is rejected if its diameter is less than $11.7 mm$ or more than $12.3 mm$ . Find the expected number of rejected bolts in a batch of $1000$ .

Show the mark scheme

$z = \pm \frac{0.3}{0.2} = \pm 1.5$ M1
$P (Z > 1.5) = 1 - 0.9332 = 0.0668$ A1
$1000 \times 2 \times 0.0668$ M1
$= 133.6$ , so about $134$ bolts A1

S1 Measures of Location and Spread

Mean, median, mode, quartiles and percentiles (incl. interpolation), variance and standard deviation; coding.

30 practice questions with mark schemes · Worked examples → · Notes → · Calculator steps → · Practise measures of location and spread →

Example question · 5 marks · hard

For a sample of $n = 10$ observations, $Σ x = 120$ and $Σ x^{2} = 1800$ . A new variable $y$ is defined as $y = 3 x - 2$ . Calculate the mean and variance of $y$ .

Show the mark scheme

M1 for calculating $\bar{x} = \frac{120}{10} = 12$ .
M1 for finding $\bar{y} = 3 (12) - 2 = 34$ .
M1 for calculating $V a r (x) = \frac{1800}{10} - 12^{2} = 180 - 144 = 36$ .
M1 for applying the variance transformation rule $V a r (y) = 3^{2} \times V a r (x)$ .
A1 for finding $V a r (y) = 9 \times 36 = 324$ .

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FAQ

What is on the Edexcel IAL S1 exam?

S1 Statistics 1 is assessed by a 1h 30min written paper (75 marks), calculator permitted. It covers Data and Summary Statistics, Representation of Data, Probability, Correlation and Regression, Discrete Random Variables, Normal Distribution, Measures of Location and Spread.

Can I use a calculator in S1?

Yes, a calculator is permitted in S1, as in every IAL maths unit. You still need to show full method to earn the M marks.

How many S1 practice questions are there?

253 exam-style S1 questions across 7 topics, each with an Edexcel-style mark scheme (M, A and B marks).

Which S1 topics come up most?

In our mapping of the 4 Pearson S1 papers from June 2024 to June 2025, Measures of Location and Spread (8 questions), Probability (7 questions), Representation of Data (6 questions) were tested most. Every topic can be examined in any series.

Where can I find S1 past papers?

Pearson publishes them. Our IAL S1 past papers page links to each official paper and mark scheme by series, with an exam timer.

How should I revise for S1?

Read the note for a topic, study the worked example and its mark scheme, practise that topic's questions, then sit a timed S1 past paper and check the common mistakes examiners report.

What is free on this page?

Everything here, with no sign-in: one example question with its mark scheme for every S1 topic, the worked examples on the topic pages and a quick quiz.

What does a free account add?

A free account (no card) adds 5 more practice questions on every topic with instant feedback, answers and mark schemes on free questions, 3 AI-marked answers a week, free, and your streak and progress on any device. The rest of the S1 bank with its mark schemes is part of the paid plans.

Other IAL units: IAL P1 Pure Mathematics 1 · IAL P2 Pure Mathematics 2 · IAL P3 Pure Mathematics 3 · IAL P4 Pure Mathematics 4 · IAL M1 Mechanics 1

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