| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| 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 data handling question requiring only basic skills: reading values from a stem-and-leaf diagram, finding the median by counting to the middle position(s), identifying the mode by inspection, and performing simple arithmetic. All parts are routine recall and mechanical procedures with no problem-solving or conceptual challenge. |
| Spec | 2.02f Measures of average and spread |
| 0 | 0 | 0 | 1 | 1 | 3 | 5 | 7 | 7 | 7 | 8 | 8 |
| 1 | 0 | 1 | 2 | 3 | 3 | 4 | 4 | 6 | 9 | ||
| 2 | 0 | 1 | 3 | 3 | 7 | ||||||
| 3 | 5 | 7 | |||||||||
| 4 | |||||||||||
| 5 | 8 |
1 Alice carries out a survey of the 28 students in her class to find how many text messages each sent on the previous day. Her results are shown in the stem and leaf diagram.
\begin{center}
\begin{tabular}{ l | l l l l l l l l l l l }
0 & 0 & 0 & 1 & 1 & 3 & 5 & 7 & 7 & 7 & 8 & 8 \\
1 & 0 & 1 & 2 & 3 & 3 & 4 & 4 & 6 & 9 & & \\
2 & 0 & 1 & 3 & 3 & 7 & & & & & & \\
3 & 5 & 7 & & & & & & & & & \\
4 & & & & & & & & & & & \\
5 & 8 & & & & & & & & & & \\
\end{tabular}
\end{center}
Key: 2 | 3 represents 23
\begin{enumerate}[label=(\roman*)]
\item Find the mode and median of the number of text messages.
\item Identify the type of skewness of the distribution.
\item Alice is considering whether to use the mean or the median as a measure of central tendency for these data.\\
(A) In view of the skewness of the distribution, state whether Alice should choose the mean or the median.\\
(B) What other feature of the distribution confirms Alice's choice?
\item The mean number of text messages is 14.75 . If each message costs 10 pence, find the total cost of all of these messages.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2008 Q1 [7]}}