Edexcel IAL S1 January 2021 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 · 5 marks

   A dataset of exam scores has a mean of $42$ and a standard deviation of $5$. The teacher decides to adjust the grades by multiplying every score by $2$, and then adding $10$ to each score. Find the exact value of:

   1. the new mean.

   2. the new standard deviation.

   3. the new variance.

   Worked solution

   1. When data is multiplied by $a$ and $b$ is added ($y=ax+b$), the new mean is $a\mu +b$. M1
      New mean $=2(42)+10=84+10=94$. A1

   2. Standard deviation is affected by multiplication but not by addition.
      New SD $=2\times 5=10$. A1

   3. Variance is the square of the new standard deviation. M1
      New Variance $={10}^2=100$. A1

2. Normal Distribution · 6 marks

   The lengths of a species of fish are normally distributed with mean $\mu$ cm and standard deviation $\sigma$ cm. $10\mathrm{\%}$ of the fish are longer than $80$ cm and $20\mathrm{\%}$ are shorter than $60$ cm. Find the values of $\mu$ and $\sigma$.

   Worked solution

   $z=1.2816$ for the upper $10\mathrm{\%}$ B1
   $z=-0.8416$ for the lower $20\mathrm{\%}$ B1
   $80-\mu =1.2816\sigma$ and $60-\mu =-0.8416\sigma$ M1
   subtracting: $20=2.1232\sigma$ M1
   $\sigma =9.42$ A1
   $\mu =67.9$ A1

3. Measures of Location and Spread · 4 marks

   A dataset $x$ has mean $\overline{x}=5$ 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 $\overline{y}=15$ and standard deviation ${\sigma }_y=6$. Find the values of $a$ and $b$.

   Worked solution

   1. M1 for linking the standard deviations: ${\sigma }_y=a{\sigma }_x$.
   2. A1 for solving for $a$: $6=a(2)⟹a=3$.
   3. M1 for linking the means: $\overline{y}=a\overline{x}+b$.
   4. A1 for substituting $a=3$ to find $b$: $15=3(5)+b⟹b=0$.

More on these topics: Data and Summary Statistics · Normal Distribution · Measures of Location and Spread

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 5 to 17 marks.
• Biggest question: Q5, 17 marks: performance pay: regression line.
• Marks by main topic: Probability 20, Correlation and Regression 17, Discrete Random Variables 16, Normal Distribution 13, Representation of Data 9.
• More Correlation and Regression in other sittings: October 2020 Q5 (15 marks), June 2021 Q6 (16 marks), October 2021 Q2 (12 marks).
• Against the other 14 sittings we mapped: 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. Q1Venn diagram with three events (5 marks) · S1 Probability
2. Q2Stem and leaf diagram of residents' ages (9 marks) · S1 Representation of Data, S1 Measures of Location and Spread
3. Q3Normal model for package weights (13 marks) · S1 Normal Distribution
4. Q4Spinner scores: distribution, mean and variance (16 marks) · S1 Discrete Random Variables
5. Q5Performance pay: regression line (17 marks) · S1 Correlation and Regression
6. Q6Geometric probability with a rolled disc (15 marks) · S1 Probability

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