| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Estimate percentages or proportions from graphs |
| Difficulty | Moderate -0.8 This is a straightforward box plot interpretation question requiring only basic reading of the diagram (identifying quartiles, median) and standard knowledge that box plots show quartiles dividing data into quarters. Part (e) involves a simple normal distribution calculation using quartiles, which is a standard S1 technique with minimal problem-solving required. |
| Spec | 2.02f Measures of average and spread2.02h Recognize outliers2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2}\) | B1 (1 mark) | Accept 50% or half or 0.5. Units not required. |
| Answer | Marks | Guidance |
|---|---|---|
| \(54\) | B1 (1 mark) | Correct answer only. Units not required. |
| Answer | Marks | Guidance |
|---|---|---|
| \(+\) is an 'outlier' or 'extreme value'; any heavy musical instrument or statement that the instrument is heavy | B1, B1 (2 marks) | 'Anomaly' only award B0. Accept '85kg was heaviest instrument on the trip' or equivalent. Examples of acceptable instruments: double bass, cello, harp, piano, drums, tuba. Examples of unacceptable instruments: violin, viola, trombone, trumpet, french horn, guitar. |
| Answer | Marks | Guidance |
|---|---|---|
| \(Q_3 - Q_2 = Q_2 - Q_1\) so symmetrical or no skew | B1, B1 (2 marks) | 'Quartiles equidistant from median' or equivalent for first B1, then symmetrical/no skew for second B1 (dependent). Alternative: 'Positive tail longer than negative tail' so slight positive skew. B0 for 'evenly' etc. instead of 'symmetrical'. B0 for 'normal' only. |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(W < 54) = 0.75\) (or \(P(W > 54) = 0.25\)) or correctly labelled and shaded diagram | M1 | |
| \(\frac{54 - 45}{\sigma} = 0.67\) | M1B1 | Note B mark appears first on ePEN. First line might be missing so first M1 can be implied by second. Second M1 for standardising with \(\sigma\) and equating to z-value. NB Using 0.7734 should not be awarded second M1. Anything rounding to 0.67 for B1. Accept 0.675 (3sf by interpolation). |
| \(\sigma = 13.43...\) | A1 (4 marks) | Anything rounding to \(13.3 - 13.4\) for A1. |
## Question 2:
**Part (a):**
$\frac{1}{2}$ | B1 (1 mark) | Accept 50% or half or 0.5. Units not required.
**Part (b):**
$54$ | B1 (1 mark) | Correct answer only. Units not required.
**Part (c):**
$+$ is an 'outlier' or 'extreme value'; any heavy musical instrument or statement that the instrument is heavy | B1, B1 (2 marks) | 'Anomaly' only award B0. Accept '85kg was heaviest instrument on the trip' or equivalent. Examples of acceptable instruments: double bass, cello, harp, piano, drums, tuba. Examples of unacceptable instruments: violin, viola, trombone, trumpet, french horn, guitar.
**Part (d):**
$Q_3 - Q_2 = Q_2 - Q_1$ so symmetrical or no skew | B1, B1 (2 marks) | 'Quartiles equidistant from median' or equivalent for first B1, then symmetrical/no skew for second B1 (dependent). Alternative: 'Positive tail longer than negative tail' so slight positive skew. B0 for 'evenly' etc. instead of 'symmetrical'. B0 for 'normal' only.
**Part (e):**
$P(W < 54) = 0.75$ (or $P(W > 54) = 0.25$) or correctly labelled and shaded diagram | M1 |
$\frac{54 - 45}{\sigma} = 0.67$ | M1B1 | Note B mark appears first on ePEN. First line might be missing so first M1 can be implied by second. Second M1 for standardising with $\sigma$ and equating to z-value. NB Using 0.7734 should not be awarded second M1. Anything rounding to 0.67 for B1. Accept 0.675 (3sf by interpolation).
$\sigma = 13.43...$ | A1 (4 marks) | Anything rounding to $13.3 - 13.4$ for A1.
---2. The box plot in Figure 1 shows a summary of the weights of the luggage, in kg, for each musician in an orchestra on an overseas tour.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{045e10d2-1766-4399-aa0a-5619dd0cce0f-03_346_1452_324_228}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
The airline's recommended weight limit for each musician's luggage was 45 kg . Given that none of the musicians' luggage weighed exactly 45 kg ,
\begin{enumerate}[label=(\alph*)]
\item state the proportion of the musicians whose luggage was below the recommended weight limit.
A quarter of the musicians had to pay a charge for taking heavy luggage.
\item State the smallest weight for which the charge was made.
\item Explain what you understand by the + on the box plot in Figure 1, and suggest an instrument that the owner of this luggage might play.
\item Describe the skewness of this distribution. Give a reason for your answer.
One musician of the orchestra suggests that the weights of luggage, in kg, can be modelled by a normal distribution with quartiles as given in Figure 1.
\item Find the standard deviation of this normal distribution.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2007 Q2 [10]}}