Edexcel AS Paper 2 2023 June — Question 1 5 marks

Exam BoardEdexcel
ModuleAS Paper 2 (AS Paper 2)
Year2023
SessionJune
Marks5
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Mark schemeDownload PDF ↗
TopicMeasures of Location and Spread
TypeForward transformation: find new statistics
DifficultyModerate -0.8 This is a routine AS-level statistics question testing standard procedures: reading from a histogram, verifying a given mean calculation, computing standard deviation from grouped data, and applying the conceptual understanding that subtracting a constant affects the mean but not the standard deviation. All steps are algorithmic with no problem-solving or novel insight required.
Spec2.02b Histogram: area represents frequency2.02f Measures of average and spread2.02g Calculate mean and standard deviation
  1. The histogram and its frequency polygon below give information about the weights, in grams, of 50 plums. \includegraphics[max width=\textwidth, alt={}, center]{854568d2-b32d-44de-8a9c-26372e509c20-02_908_1307_328_386}
    1. Show that an estimate for the mean weight of the 50 plums is 63.72 grams.
    2. Calculate an estimate for the standard deviation of the 50 plums.
    Later it was discovered that the scales used to weigh the plums were broken.
    Each plum actually weighs 5 grams less than originally thought.
  2. State the effect this will have on the estimate of the standard deviation in part (b). Give a reason for your answer.
Question 1:
Part (a)
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(61\times(2\times3),\quad 63\times(2\times12),\quad 65\times(2\times8),\quad 67\times(2\times2)\)M1 At least 3 correct products seen (oe). Allow any 3 from 366, 1512, 1040, 268
\(\frac{61\times(2\times3)+63\times(2\times12)+65\times(2\times8)+67\times(2\times2)}{50}=63.72^*\)A1*cso Correct expression for mean (may be seen in stages) and given answer. \(\frac{3186}{50}=63.72\) on its own is M0A0, but following all 4 correct products can score M1A1
SC: B2: \(\frac{61\times3+63\times12+65\times8+67\times2}{25}=63.72^*\) scores M1A1 on epen
(2 marks)
Part (b)
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\sqrt{\frac{61^2\times6+63^2\times24+65^2\times16+67^2\times4}{50}-63.72^2}\)M1 Correct expression for standard deviation including root. Allow equivalent complete methods. NB: \(\sum fx^2 = 203138\)
\(=\sqrt{2.5216}=1.58795\ldots\quad=\text{awrt } \mathbf{1.59}\)A1 awrt 1.59 (allow \(s=\) awrt 1.60). Correct answer with no incorrect working scores 2 out of 2
SC: B2: \(\sqrt{\frac{61^2\times3+63^2\times12+65^2\times8+67^2\times2}{25}-63.72^2}=\text{awrt }1.59\) scores M1A1 on epen
(2 marks)
Part (c)
AnswerMarks Guidance
Answer/WorkingMarks Guidance
No effect (oe) since, e.g.: adding/subtracting does not affect the standard deviation (only multiplication and division do); the weights will have the same spread; the distance of each weight from the mean will not have changed; they all change by the same amountB1 Correct statement and correct explanation
(1 mark)
Total: 5 marks
## Question 1:

### Part (a)

| Answer/Working | Marks | Guidance |
|---|---|---|
| $61\times(2\times3),\quad 63\times(2\times12),\quad 65\times(2\times8),\quad 67\times(2\times2)$ | M1 | At least 3 correct products seen (oe). Allow any 3 from 366, 1512, 1040, 268 |
| $\frac{61\times(2\times3)+63\times(2\times12)+65\times(2\times8)+67\times(2\times2)}{50}=63.72^*$ | A1*cso | Correct expression for mean (may be seen in stages) and given answer. $\frac{3186}{50}=63.72$ on its own is M0A0, but following all 4 correct products can score M1A1 |

**SC:** **B2:** $\frac{61\times3+63\times12+65\times8+67\times2}{25}=63.72^*$ scores M1A1 on epen

**(2 marks)**

---

### Part (b)

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\sqrt{\frac{61^2\times6+63^2\times24+65^2\times16+67^2\times4}{50}-63.72^2}$ | M1 | Correct expression for standard deviation including root. Allow equivalent complete methods. NB: $\sum fx^2 = 203138$ |
| $=\sqrt{2.5216}=1.58795\ldots\quad=\text{awrt } \mathbf{1.59}$ | A1 | awrt 1.59 (allow $s=$ awrt 1.60). Correct answer with no incorrect working scores 2 out of 2 |

**SC:** **B2:** $\sqrt{\frac{61^2\times3+63^2\times12+65^2\times8+67^2\times2}{25}-63.72^2}=\text{awrt }1.59$ scores M1A1 on epen

**(2 marks)**

---

### Part (c)

| Answer/Working | Marks | Guidance |
|---|---|---|
| No effect (oe) since, e.g.: adding/subtracting does not affect the standard deviation (only multiplication and division do); the weights will have the same spread; the distance of each weight from the mean will not have changed; they all change by the same amount | B1 | Correct statement **and** correct explanation |

**(1 mark)**

**Total: 5 marks**
\begin{enumerate}
  \item The histogram and its frequency polygon below give information about the weights, in grams, of 50 plums.\\
\includegraphics[max width=\textwidth, alt={}, center]{854568d2-b32d-44de-8a9c-26372e509c20-02_908_1307_328_386}\\
(a) Show that an estimate for the mean weight of the 50 plums is 63.72 grams.\\
(b) Calculate an estimate for the standard deviation of the 50 plums.
\end{enumerate}

Later it was discovered that the scales used to weigh the plums were broken.\\
Each plum actually weighs 5 grams less than originally thought.\\
(c) State the effect this will have on the estimate of the standard deviation in part (b). Give a reason for your answer.

\hfill \mbox{\textit{Edexcel AS Paper 2 2023 Q1 [5]}}
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