| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2019 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from stem-and-leaf diagram |
| Difficulty | Easy -1.3 This is a straightforward data handling question requiring only standard procedures: reading values from a stem-and-leaf diagram, finding median/quartiles by position, and calculating mean/standard deviation using a calculator. The only mild challenge is the outlier at 99cm for part (c), but this is a routine observation. No problem-solving or conceptual depth required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| 5 | 5 | 7 | 9 | 9 | |||
| 6 | 3 | 4 | 5 | 5 | 5 | 9 | 9 |
| 7 | 4 | 5 | 7 | 9 | 9 | ||
| 8 | |||||||
| 9 | 9 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(65\) | B1 | |
| Quartiles are 76 and 61; \(= 15\) | M1, A1 | Allow (75 to 77) and (59 to 63); Must come from \(76 - 61\); SC Misread \(5 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Mean \(= 69\) | B1 | Allow 6.9 |
| sd \(= 10.5\) (3 sf) | B1 | Allow 1.05 (3 sf) |
| Answer | Marks | Guidance |
|---|---|---|
| Less (or not) affected by the outlier or anomaly 99; Mean (more) affected by the outlier of 99 | B1 [1] | Must mention 99; Allow "Median is less skewed by the 99" |
# Question 8:
## Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $65$ | B1 | |
| Quartiles are 76 and 61; $= 15$ | M1, A1 | Allow (75 to 77) and (59 to 63); Must come from $76 - 61$; SC Misread $5|6 = 5.6$: lose B1 only |
## Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Mean $= 69$ | B1 | Allow 6.9 |
| sd $= 10.5$ (3 sf) | B1 | Allow 1.05 (3 sf) |
# Question 8(c):
| Less (or not) affected by the outlier or anomaly 99; Mean (more) affected by the outlier of 99 | B1 [1] | Must mention 99; Allow "Median is less skewed by the 99" |
---8 The stem-and-leaf diagram shows the heights, in centimetres, of 17 plants, measured correct to the nearest centimetre.
\begin{center}
\begin{tabular}{ l | l l l l l l l }
5 & 5 & 7 & 9 & 9 & & & \\
6 & 3 & 4 & 5 & 5 & 5 & 9 & 9 \\
7 & 4 & 5 & 7 & 9 & 9 & & \\
8 & & & & & & & \\
9 & 9 & & & & & & \\
\end{tabular}
\end{center}
Key: 5 | 6 means 56
\begin{enumerate}[label=(\alph*)]
\item Find the median and inter-quartile range of these heights.
\item Calculate the mean and standard deviation of these heights.
\item State one advantage of using the median rather than the mean as a measure of average for these heights.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2019 Q8 [6]}}