Edexcel IAL S1 January 2023 mark scheme and question paper (WST01/01)

3 S1 questions like these, with worked solutions

Written and checked by us, not taken from the Pearson paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Data and Summary Statistics · 9 marks

   The mean of three numbers, $a$, $b$, and $c$, is exactly $8$. The variance of these three numbers is $10$.

   1. Using the formula for variance, prove that $a^2+b^2+c^2=222$.

   2. Given that $c=10$, find the mean and the variance of the remaining two numbers, $a$ and $b$.

   Worked solution

   1. Let the sum of squares be $\sum x^2=a^2+b^2+c^2$.
      Using the variance formula: $\text{Var}(X)=\frac{\sum x^2}{n}-{\mu }^2$. M1
      $10=\frac{a^2+b^2+c^2}{3}-8^2$. M1
      $10=\frac{a^2+b^2+c^2}{3}-64⟹74=\frac{a^2+b^2+c^2}{3}$. A1
      $a^2+b^2+c^2=3\times 74=222$. A1 *

   2. If $c=10$, then $a+b+10=3\times 8=24⟹a+b=14$. M1
      New mean for just $a$ and $b$: $\frac{14}{2}=7$. A1
      Substitute $c=10$ into sum of squares: $a^2+b^2+100=222⟹a^2+b^2=122$. M1
      New Variance for $a$ and $b$ $=\frac{a^2+b^2}{2}-(\text{New Mean}{)}^2$. M1
      $=\frac{122}{2}-7^2=61-49=12$. A1

2. Correlation and Regression · 4 marks

   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 $\sum xy=1100$. Calculate the product moment correlation coefficient.

   Worked solution

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

3. Discrete Random Variables · 4 marks

   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 $b$.

   Worked solution

   1. M1 for forming the sum of probabilities equation: $a+b+0.3=1⟹a+b=0.7$.
   2. M1 for forming the expected value equation: $1(a)+2(b)+3(0.3)=1.9⟹a+2b=1.0$.
   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 $a=0.4$.

More on these topics: Data and Summary Statistics · Correlation and Regression · Discrete Random Variables

What's on this paper

What this paper is like

• Shape: 6 questions, 75 marks in 1 h 30 min (about 1.2 minutes a mark); questions from 10 to 17 marks.
• Biggest question: Q5, 17 marks: normal model for housefly wing lengths.
• Marks by main topic: Probability 23, Normal Distribution 17, Correlation and Regression 14, Discrete Random Variables 11, Representation of Data 10.
• More Normal Distribution in other sittings: October 2022 Q5 (12 marks), June 2023 Q7 (14 marks), June 2022 Q6 (11 marks).
• Against the other 14 sittings we mapped: more marks on Probability (23 marks here, 16 on average) and Normal Distribution (17 marks here, 12 on average); fewer on Measures of Location and Spread (0 marks here, 5 on average).
• Not on this paper: Data and Summary Statistics, Measures of Location and Spread.
• Calculator: allowed.

WST01/01: question by question

Labels and topics are ours, read from the WST01/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Histogram of swimming times (10 marks) · S1 Representation of Data, S1 Measures of Location and Spread
2. Q2Marbles from two bags: tree diagram (10 marks) · S1 Probability
3. Q3Discrete distribution: mean and variance (11 marks) · S1 Discrete Random Variables
4. Q4Venn diagram with unknown probabilities (13 marks) · S1 Probability
5. Q5Normal model for housefly wing lengths (17 marks) · S1 Normal Distribution
6. Q6Sugar that dissolves: regression (14 marks) · S1 Correlation and Regression

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