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Edexcel IAL S1 Maths Revision: Statistics 1

Everything for Edexcel International A Level S1 (Statistics 1) in one place: what each topic covers, an exam-style question with its mark scheme for each topic, and 245 practice questions with instant marking.

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S1 topics

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 · Practise data and summary statistics →

Example question · 4 marks · medium

A dataset summarizing the time spent by students on a project has a lower quartile of $15$ minutes and an upper quartile of $45$ minutes. The maximum value recorded in the dataset is $95$ minutes.

  1. Calculate the interquartile range (IQR).
  2. Determine mathematically whether the maximum value of $95$ minutes should be classified as an outlier.
Show the mark scheme
  1. M1 for subtracting quartiles: $\text{IQR} = 45 - 15$.
    A1 for $\text{IQR} = 30$ minutes.
  2. M1 for calculating the upper boundary for outliers: $Q_3 + 1.5 \times \text{IQR} = 45 + 1.5(30) = 45 + 45 = 90$.
    B1 for stating that since $95 > 90$, the maximum value is indeed an outlier.

S1 Representation of Data

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

35 practice questions with mark schemes · Practise representation of data →

Example question · 4 marks · medium

The following values are recorded: $4, 18, 22, 23, 24, 26, 28, 50$. Using the rule $Q_1 - 1.5\times\text{IQR}$ and $Q_3 + 1.5\times\text{IQR}$, identify any outliers in the data set.

Show the mark scheme
  1. M1 for finding the quartiles: $n=8$. $Q_1 = \frac{18+22}{2} = 20$, $Q_3 = \frac{26+28}{2} = 27$.
  2. M1 for calculating $\text{IQR} = 27 - 20 = 7$.
  3. M1 for calculating the boundaries: Lower = $20 - 1.5(7) = 9.5$, Upper = $27 + 1.5(7) = 37.5$.
  4. A1 for identifying the outliers: $4$ (since $4 < 9.5$) and $50$ (since $50 > 37.5$).

S1 Probability

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

35 practice questions with mark schemes · Practise probability →

S1 Correlation and Regression

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

35 practice questions with mark schemes · Practise correlation and regression →

Example question · 4 marks · medium

For a set of 10 data points, $\bar{x} = 8$, $\bar{y} = 20$, $S_{xx} = 40$, and $S_{xy} = -30$. Find the equation of the regression line of $y$ on $x$ in the form $y = a + bx$.

Show the mark scheme
  1. M1 for finding $b = \frac{S_{xy}}{S_{xx}} = \frac{-30}{40}$.
  2. A1 for $b = -0.75$.
  3. M1 for finding $a = \bar{y} - b\bar{x} = 20 - (-0.75)(8)$.
  4. A1 for finding $a = 26$, giving the final equation $y = 26 - 0.75x$.

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 · Practise discrete random variables →

Example question · 4 marks · hard

The discrete random variable $X$ takes the values $1, 2,$ and $3$ with probabilities $a, b,$ and $0.3$ respectively. Given that $E(X) = 1.9$, find the values of $a$ and $b$.

Show the mark scheme
  1. M1 for forming the sum of probabilities equation: $a + b + 0.3 = 1 \implies a + b = 0.7$.
  2. M1 for forming the expected value equation: $1(a) + 2(b) + 3(0.3) = 1.9 \implies a + 2b = 1.0$.
  3. M1 for solving the simultaneous equations (e.g., subtracting the first from the second: $b = 1.0 - 0.7$).
  4. A1 for concluding $b = 0.3$ and $a = 0.4$.

S1 Normal Distribution

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

5 practice questions with mark schemes · Practise normal distribution →

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 · Practise measures of location and spread →

Example question · 4 marks · hard

A dataset $x$ has mean $\bar{x} = 5$ and standard deviation $\sigma_x = 2$. A new dataset $y$ is formed using the linear transformation $y = ax + b$, where $a > 0$. The new dataset has mean $\bar{y} = 15$ and standard deviation $\sigma_y = 6$. Find the values of $a$ and $b$.

Show the mark scheme
  1. M1 for linking the standard deviations: $\sigma_y = a \sigma_x$.
  2. A1 for solving for $a$: $6 = a(2) \implies a = 3$.
  3. M1 for linking the means: $\bar{y} = a\bar{x} + b$.
  4. A1 for substituting $a=3$ to find $b$: $15 = 3(5) + b \implies b = 0$.

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. You still need to show full method to earn the M marks.

How many S1 practice questions are there?

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

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