Knowledge organisers

Statistics 1 (S1): Edexcel IAL Maths knowledge organiser

Everything to know about statistics 1 (s1) 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

Discrete random variable: Takes separate values, each with a probability; the probabilities add to 1.
Expected value: E(X) = Σx P(X = x), the long-run mean.
Product moment correlation coefficient: r = Sxy/√(Sxx Syy) measures linear correlation, from −1 to 1.
Interpolation: Estimating the median or a quartile from grouped data, assuming values are spread evenly in each class.

Key formulas

Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.

Mean; variance	\(\bar x=\frac{\sum fx}{\sum f},\) \(\sigma^2=\frac{\sum fx^2}{\sum f}-\bar x^2\)
Coding \(y=\frac{x-a}b\)	\(\bar x=a+b\bar y,\) \(\sigma_x=\|b\|\sigma_y\)
Median by interpolation	\(Q_2=L+\frac{\frac n2-F}{f}\times w\)
Outliers (if asked)	\( \(\text{or}\) \(>Q_3+k(Q_3-Q_1)\)
UnionIn the formula booklet	\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
IntersectionIn the formula booklet	\(P(A\cap B)=P(A)P(B\mid A)\)
Conditional; independent	\(P(A\mid B)=\frac{P(A\cap B)}{P(B)};\) \(P(A\cap B)=P(A)P(B)\)
Discrete r.v.In the formula booklet	\(E(X)=\sum xP(X=x),\) \(\mathrm{Var}(X)=\sum x^2P(X=x)-\mu^2\)
Function of \(X\)In the formula booklet	\(E\big(g(X)\big)=\sum g(x)P(X=x)\)
Linear	\(E(aX+b)=aE(X)+b,\) \(\mathrm{Var}(aX+b)=a^2\mathrm{Var}(X)\)
Discrete uniform on \(1,\dots,n\)	\(E(X)=\tfrac{n+1}2,\) \(\mathrm{Var}(X)=\tfrac{n^2-1}{12}\)
\(S_{xx}\), \(S_{xy}\)In the formula booklet	\(S_{xx}=\sum x^2-\frac{(\sum x)^2}n,\) \(S_{xy}=\sum xy-\frac{\sum x\sum y}n\)
PMCCIn the formula booklet	\(r=\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}\)
Regression line \(y=a+bx\)In the formula booklet	\(b=\frac{S_{xy}}{S_{xx}},\) \(a=\bar y-b\bar x\)
Normal	\(Z=\frac{X-\mu}\sigma\sim N(0,1)\)

Worked example

X takes the values 1, 2 and 3 with probabilities 0.2, 0.5 and 0.3. Find E(X) and Var(X).

E(X) = 1(0.2) + 2(0.5) + 3(0.3) = 2.1
E(X²) = 1(0.2) + 4(0.5) + 9(0.3) = 4.9
Var(X) = 4.9 − 2.1²

Answer: E(X) = 2.1 and Var(X) = 0.49

Common mistakes

Standardisation not shown when the question requires it
Outliers: rule applied but no conclusion
Interpolation using class midpoints
Variance formula missing the −x̄²

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

You should be able to…

Explain how statistical models are used and refined, and classify data as qualitative or quantitative and discrete or continuous.
Draw and interpret stem-and-leaf diagrams, including back-to-back diagrams, and identify outliers using a rule based on the quartiles.
Use the rules for mutually exclusive and independent events, and test whether two events are independent using P(A ∩ B) = P(A)P(B).
Calculate Sxx, Syy and Sxy from summary statistics and use them to find the product moment correlation coefficient, interpreting its value.
Calculate the expectation E(X) and the variance Var(X) of a discrete random variable from its probability distribution.
Solve normal distribution problems in context, such as the proportion of items rejected, combining normal probabilities with independent events.

The printable sheet

Statistics 1 (S1) knowledge organiser for Edexcel IAL Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Statistics 1 (S1) knowledge organiser (Edexcel IAL Maths), A4. Download the PDF.

Revise it next

Other Edexcel IAL Maths topics: Pure Mathematics 1 (P1) · Pure Mathematics 2 (P2) · Pure Mathematics 3 (P3) · Pure Mathematics 4 (P4) · Mechanics 1 (M1) · All Edexcel IAL Maths organisers