| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Session | Specimen |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw box plot from summary statistics |
| Difficulty | Easy -1.2 This is a straightforward S1 statistics question testing basic understanding of quartiles, box plots, and outliers. Parts (a) and (b) require recall of standard definitions. Part (c) involves routine calculation of outlier boundaries and drawing a box plot with given summary statistics. Part (d) requires standard comparative statements about center and spread. No problem-solving or novel insight needed—purely procedural application of learned concepts. |
| Spec | 2.02f Measures of average and spread2.02i Select/critique data presentation |
| Answer | Marks | Guidance |
|---|---|---|
| Any 4 sensible comments – at least one advantage and one disadvantage | B1 B1 B1 B1 | (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Any 4 sensible comments | B1 B1 B1 | (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(Q_1 - 1.5(Q_3 - Q_1) = -4 \Rightarrow\) no outlier below lower quartile | B1 | |
| \(Q_2 + 1.5(Q_3 - Q_1) = 52 \Rightarrow\) an outlier (55) above upper quartile | B1 | |
| [Boxplot for School B shown with appropriate scale and label] | B1 | |
| \(Q_1, Q_2, Q_3, 3, 52\) | B1 | |
| \(55\) | B1 | (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(A: Q_3 - Q_2 = 10; Q_2 - Q_1 = 10 \Rightarrow\) symmetrical | \(\begin{rcases} \text{both distributions} \\ \text{are symmetrical} \end{rcases}\) | |
| \(B: Q_3 - Q_2 = 7; Q_2 - Q_1 = 7 \Rightarrow\) symmetrical | ||
| Median B (24) > Median A (22) \(\Rightarrow\) on average teachers in B travel slightly further to school than those in A | B1 B1 B1 B1 | (4 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Any 4 sensible comments | B1 B1 B1 B1 | (4 marks) |
## (a)
**Advantages:**
- Uses central 50% of the data
- Not affected by extreme values (outliers)
- Provide an alternative measure of spread to the variance/standard deviation, i.e. IQR/STQR
**Disadvantages:**
- Not always a simple calculation, e.g. interpolation for a grouped frequency distribution
- Different measures of calculation – no single argued method
- Does not use all the data directly
Any 4 sensible comments – at least one advantage and one disadvantage | B1 B1 B1 B1 | (4 marks)
## (b)
- Indicates maximum/minimum observations and possible outliers
- Indicates relative positions of the quartiles
- Indicates skewness
- When plotted on the same scale enables comparisons of distributions
Any 4 sensible comments | B1 B1 B1 | (3 marks)
## (c)
$Q_1 - 1.5(Q_3 - Q_1) = -4 \Rightarrow$ no outlier below lower quartile | B1 |
$Q_2 + 1.5(Q_3 - Q_1) = 52 \Rightarrow$ an outlier (55) above upper quartile | B1 |
[Boxplot for School B shown with appropriate scale and label] | B1 |
$Q_1, Q_2, Q_3, 3, 52$ | B1 |
$55$ | B1 | (3 marks)
## (d)
$A: Q_3 - Q_2 = 10; Q_2 - Q_1 = 10 \Rightarrow$ symmetrical | $\begin{rcases} \text{both distributions} \\ \text{are symmetrical} \end{rcases}$ |
$B: Q_3 - Q_2 = 7; Q_2 - Q_1 = 7 \Rightarrow$ symmetrical |
Median B (24) > Median A (22) $\Rightarrow$ on average teachers in B travel slightly further to school than those in A | B1 B1 B1 B1 | (4 marks)
Range of B is greater than that of A
25% of teachers in A travel 12 km or less compared with 25% of teachers in B who travel 17 km or less
50% of teachers in A travel between 12 km and 32 km as compared with 17 km and 31 km for B
Any 4 sensible comments | B1 B1 B1 B1 | (4 marks)
**(16 marks)**
---\begin{enumerate}[label=(\alph*)]
\item Explain briefly the advantages and disadvantages of using the quartiles to summarise a set of data. [4]
\item Describe the main features and uses of a box plot. [3]
\end{enumerate}
The distances, in kilometres, travelled to school by the teachers in two schools, $A$ and $B$, in the same town were recorded. The data for School $A$ are summarised in Diagram 1.
\includegraphics{figure_1}
For School $B$, the least distance travelled was 3 km and the longest distance travelled was 55 km. The three quartiles were 17, 24 and 31 respectively.
An outlier is an observation that falls either $1.5 \times$ (interquartile range) above the upper quartile or $1.5 \times$ (interquartile range) below the lower quartile.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Draw a box plot for School $B$. [5]
\item Compare and contrast the two box plots. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5 [16]}}