| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Replacing data values |
| Difficulty | Moderate -0.8 This is a straightforward statistics question requiring basic mean calculations and a simple z-score interpretation. Part (i) is direct arithmetic, part (ii) involves understanding rolling means with one algebraic step, and part (iii) is standard z-score comparison. All techniques are routine for AS-level with no conceptual challenges or novel problem-solving required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Rose | 10014 | 11262 | 10149 | 9361 | 9708 | 9921 | 10369 |
| Emma | 9204 | 9913 | 8741 | 10015 | 10261 | 7391 | 10856 |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (i) | 9483 |
| [1] | 1.1 | BC |
| 7 | (ii) | 7 × 10 112 +10259 ‒ 10014 soi |
| Answer | Marks |
|---|---|
| Emma needs to make 13852 steps | M1 |
| Answer | Marks |
|---|---|
| [4] | 3.1a |
| Answer | Marks |
|---|---|
| 3.2a | NB Rose’s new mean is 10147 |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (iii) | 10341 + 2×948 soi |
| Answer | Marks |
|---|---|
| an unusually high number of steps on day 8 | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.1b |
| Answer | Marks |
|---|---|
| 3.2b | Soi |
Question 7:
7 | (i) | 9483 | B1
[1] | 1.1 | BC
7 | (ii) | 7 × 10 112 +10259 ‒ 10014 soi
= 71029
66381 ‒ 9204 + x = “71029”
Emma needs to make 13852 steps | M1
A1
M1
A1
[4] | 3.1a
1.1
1.1
3.2a | NB Rose’s new mean is 10147
Using 8 days can gain M1 only
7 | (iii) | 10341 + 2×948 soi
= 12237
Comparison of their 13852 with their 12237
13852 is an outlier, so Emma would need to make
an unusually high number of steps on day 8 | M1
M1
A1
[3] | 3.1b
1.1
3.2b | Soi
Conclusion; ‘outlier’ not essential.
Dep M2 wwwRose and Emma each wear a device that records the number of steps they take in a day. All the results for a 7-day period are given in Fig. 7.
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline
Day & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
Rose & 10014 & 11262 & 10149 & 9361 & 9708 & 9921 & 10369 \\
\hline
Emma & 9204 & 9913 & 8741 & 10015 & 10261 & 7391 & 10856 \\
\hline
\end{tabular}
Fig. 7
The 7-day mean is the mean number of steps taken in the last 7 days. The 7-day mean for Rose is 10112.
\begin{enumerate}[label=(\roman*)]
\item Calculate the 7-day mean for Emma. [1]
\end{enumerate}
At the end of day 8 a new 7-day mean is calculated by including the number of steps taken on day 8 and omitting the number of steps taken on day 1. On day 8 Rose takes 10259 steps.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Determine the number of steps Emma must take on day 8 so that her 7-day mean at the end of day 8 is the same as for Rose. [4]
\end{enumerate}
In fact, over a long period of time, the mean of the number of steps per day that Emma takes is 10341 and the standard deviation is 948.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Determine whether the number of steps Emma needs to take on day 8 so that her 7-day mean is the same as that for Rose in part (ii) is unusually high. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2018 Q7 [8]}}