| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from discrete frequency table |
| Difficulty | Easy -1.2 This is a straightforward application of standard formulas for mean and standard deviation from a frequency table, plus a basic probability calculation using combinations. Both parts require only routine recall and calculation with no problem-solving insight needed. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.03a Mutually exclusive and independent events |
| Prize money | \(\pounds 0\) | \(\pounds 10\) | \(\pounds 100\) | \(\pounds 5000\) |
| Frequency | 9929 | 50 | 20 | 1 |
6 A supermarket chain buys a batch of 10000 scratchcard draw tickets for sale in its stores. 50 of these tickets have a $\pounds 10$ prize, 20 of them have a $\pounds 100$ prize, one of them has a $\pounds 5000$ prize and all of the rest have no prize. This information is summarised in the frequency table below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | }
\hline
Prize money & $\pounds 0$ & $\pounds 10$ & $\pounds 100$ & $\pounds 5000$ \\
\hline
Frequency & 9929 & 50 & 20 & 1 \\
\hline
\end{tabular}
\end{center}
(i) Find the mean and standard deviation of the prize money per ticket.\\
(ii) I buy two of these tickets at random. Find the probability that I win either two $\pounds 10$ prizes or two $\pounds 100$ prizes.
\hfill \mbox{\textit{OCR MEI S1 Q6 [7]}}