| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2015 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Interpret or analyse given back-to-back stem-and-leaf |
| Difficulty | Moderate -0.8 This is a straightforward S1 question requiring basic statistical measures from a stem-and-leaf diagram. Parts (a) and (b) involve counting positions and reading values directly, (c) requires simple comparison of quartile positions (standard textbook skill), and (d) asks for recall of conditions for normal distribution. All parts are routine applications with no problem-solving or novel insight required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Totals | Year 7 class | Year 11 class | Totals | |
| (6) | 876554 | 1 | ||
| (10) | 9776544422 | 2 | 0569 | (4) |
| (7) | 8754330 | 3 | 34588 | (5) |
| (5) | 99722 | 4 | 05679 | (5) |
| (3) | 840 | 5 | 03556677799 | (11) |
| 6 | 0333348 | (7) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Year 7 median \(= 29\); Year 11 median \(= 54\) | B1, B1 | In (a) at least one of the values should be assigned to a Year group. If you see just "29" and "54" award SC B1B0. 1st B1 for 29 seen; 2nd B1 for 54 seen |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Lower quartile \(= 22\); Upper quartile \(= 42\) | B1, B1 | 1st B1 for 22 and 2nd B1 for 42 (these values may be circled on the diagram) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Year 7: \(Q_3 - Q_2\ (=13) > Q_2 - Q_1\ (=7)\), Positive skew; Year 11: \(Q_3 - Q_2\ (=5) < Q_2 - Q_1\ (=16)\), Negative skew | M1, A1, A1 | M1 for a comparison for either year using quartiles only. For either "\(Q_3 - Q_2 > Q_2 - Q_1\) and positive skew" or "\(Q_3 - Q_2 < Q_2 - Q_1\) and negative skew" — statements should be compatible with their values. 1st A1 for Year 7 clearly labelled "positive skew" (both words). 2nd A1 for Year 11 clearly labelled "negative skew" (both words). ("correlation" is A0). If no comparison is stated then award M1A1A1 only if both statements are correct and compatible with their medians and quartiles, so score is 0 or 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Data is skewed | B1 | 1st B1 for a statement mentioning (or implying) that the data is skew (or not symmetric). Ignore ref to \(+\)ve or \(-\)ve. Allow "mean \(\neq\) median" if mean \(= 48.8\) and median \(= 54\) or \(53\) seen |
| Data is not continuous | B1 | 2nd B1 for a statement mentioning data is not continuous (allow identifiable spelling). Allow "this data is discrete" for 2nd B1 |
# Question 2:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Year 7 median $= 29$; Year 11 median $= 54$ | B1, B1 | In (a) at least one of the values should be assigned to a Year group. If you see just "29" and "54" award SC B1B0. 1st B1 for 29 seen; 2nd B1 for 54 seen |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Lower quartile $= 22$; Upper quartile $= 42$ | B1, B1 | 1st B1 for 22 and 2nd B1 for 42 (these values may be circled on the diagram) |
## Part (c)
| Answer | Mark | Guidance |
|--------|------|----------|
| Year 7: $Q_3 - Q_2\ (=13) > Q_2 - Q_1\ (=7)$, Positive skew; Year 11: $Q_3 - Q_2\ (=5) < Q_2 - Q_1\ (=16)$, Negative skew | M1, A1, A1 | M1 for a comparison for either year using quartiles only. For either "$Q_3 - Q_2 > Q_2 - Q_1$ and positive skew" or "$Q_3 - Q_2 < Q_2 - Q_1$ and negative skew" — statements should be compatible with their values. 1st A1 for Year 7 clearly labelled "positive skew" (both words). 2nd A1 for Year 11 clearly labelled "negative skew" (both words). ("correlation" is A0). If no comparison is stated then award M1A1A1 only if **both** statements are correct and compatible with their medians and quartiles, so score is 0 or 3 |
## Part (d)
| Answer | Mark | Guidance |
|--------|------|----------|
| Data is skewed | B1 | 1st B1 for a statement mentioning (or implying) that the data is skew (or not symmetric). Ignore ref to $+$ve or $-$ve. Allow "mean $\neq$ median" if mean $= 48.8$ and median $= 54$ or $53$ seen |
| Data is not continuous | B1 | 2nd B1 for a statement mentioning data is not continuous (allow identifiable spelling). Allow "this data is discrete" for 2nd B1 |\begin{enumerate}
\item A sports teacher recorded the number of press-ups done by his students in two minutes. He recorded this information for a Year 7 class and for a Year 11 class.
\end{enumerate}
The back-to-back stem and leaf diagram shows this information.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
Totals & Year 7 class & & Year 11 class & Totals \\
\hline
(6) & 876554 & 1 & & \\
\hline
(10) & 9776544422 & 2 & 0569 & (4) \\
\hline
(7) & 8754330 & 3 & 34588 & (5) \\
\hline
(5) & 99722 & 4 & 05679 & (5) \\
\hline
(3) & 840 & 5 & 03556677799 & (11) \\
\hline
& & 6 & 0333348 & (7) \\
\hline
\end{tabular}
\end{center}
Key: $2 | 4 | 0$ means 42 press-ups for a Year 7 student and 40 press-ups for a Year 11 student\\
(a) Find the median number of press-ups for each class.
For the Year 11 class, the lower quartile is 38 and the upper quartile is 59\\
(b) Find the lower quartile and the upper quartile for the Year 7 class.\\
(c) Use the medians and quartiles to describe the skewness of each of the two distributions.\\
(d) Give two reasons why the normal distribution should not be used to model the number of press-ups done by the Year 11 class.
\hfill \mbox{\textit{Edexcel S1 2015 Q2 [9]}}