| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from stem-and-leaf diagram |
| Difficulty | Easy -1.8 This is a straightforward stem-and-leaf diagram question requiring only basic data reading skills: counting to find median/quartiles, identifying mode and mean from context, and applying the standard outlier formula Q1 - 1.5×IQR. All techniques are routine recall with no problem-solving or novel insight required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02h Recognize outliers |
| 3 | 5 | ||||||||
| 4 | 0 | 9 | |||||||
| 5 | 2 | 3 | 6 | ||||||
| 6 | 0 | 1 | 3 | 5 | 6 | ||||
| 7 | 0 | 1 | 2 | 5 | 6 | 8 | 9 | 9 | |
| 8 | 3 | 4 | 6 | 6 | 8 | 8 | 9 | ||
| 9 | 5 | 5 | 5 | 6 | 7 | ||||
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Negative skew | B1 (AO1.2) | |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| (used) the mode | B1 (AO1.1) | |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| (used) the median | B1 (AO1.1) | |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(61-1.5\times(88-61)\) | M1 (AO2.1) | Alternatively: \(73.61-2\times17.03\) |
| \(20.5<35\) [so 35 is not an outlier] so he does not move to set 2 | A1 (AO2.2b) | \(39.6>35\) [so 35 is an outlier] so he moves to set 2; allow e.g. only marks below 20.5 (or 39.6) would lead to a move down plus correct conclusion |
| [2] |
## Question 9(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Negative skew | B1 (AO1.2) | |
| **[1]** | | |
## Question 9(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| (used) the mode | B1 (AO1.1) | |
| **[1]** | | |
## Question 9(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| (used) the median | B1 (AO1.1) | |
| **[1]** | | |
## Question 9(iv):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $61-1.5\times(88-61)$ | M1 (AO2.1) | Alternatively: $73.61-2\times17.03$ |
| $20.5<35$ [so 35 is not an outlier] so he does not move to set 2 | A1 (AO2.2b) | $39.6>35$ [so 35 is an outlier] so he moves to set 2; allow e.g. only marks below 20.5 (or 39.6) would lead to a move down plus correct conclusion |
| **[2]** | | |
---9 At the end of each school term at North End College all the science classes in year 10 are given a test. The marks out of 100 achieved by members of set 1 are shown in Fig. 9.
\begin{table}[h]
\begin{center}
\begin{tabular}{ l | l l l l l l l l l }
3 & 5 & & & & & & & & \\
4 & 0 & 9 & & & & & & & \\
5 & 2 & 3 & 6 & & & & & & \\
6 & 0 & 1 & 3 & 5 & 6 & & & & \\
7 & 0 & 1 & 2 & 5 & 6 & 8 & 9 & 9 & \\
8 & 3 & 4 & 6 & 6 & 8 & 8 & 9 & & \\
9 & 5 & 5 & 5 & 6 & 7 & & & & \\
& & & & & & & & & \\
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 9}
\end{center}
\end{table}
Key $5 \quad$ 2 represents a mark of 52\\
(i) Describe the shape of the distribution.\\
(ii) The teacher for set 1 claimed that a typical student in his class achieved a mark of 95. How did he justify this statement?\\
(iii) Another teacher said that the average mark in set 1 is 76 . How did she justify this statement?
Benson's mark in the test is 35 . If the mark achieved by any student is an outlier in the lower tail of the distribution, the student is moved down to set 2 .\\
(iv) Determine whether Benson is moved down to set 2 .
\hfill \mbox{\textit{OCR MEI Paper 2 2018 Q9 [5]}}