| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from grouped frequency table |
| Difficulty | Moderate -0.8 This is a routine S1 question requiring standard calculations from a grouped frequency table: finding mean and standard deviation using midpoints, then applying the outlier rule (Q3 + 1.5×IQR). All steps are algorithmic with no problem-solving or insight required, making it easier than average but not trivial due to the computational work involved. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| Area \(( x )\) | \(0 < x \leqslant 3\) | \(3 < x \leqslant 5\) | \(5 < x \leqslant 7\) | \(7 < x \leqslant 10\) | \(10 < x \leqslant 20\) |
| Frequency | 3 | 8 | 13 | 14 | 6 |
6 In a survey, a sample of 44 fields is selected. Their areas ( $x$ hectares) are summarised in the grouped frequency table.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Area $( x )$ & $0 < x \leqslant 3$ & $3 < x \leqslant 5$ & $5 < x \leqslant 7$ & $7 < x \leqslant 10$ & $10 < x \leqslant 20$ \\
\hline
Frequency & 3 & 8 & 13 & 14 & 6 \\
\hline
\end{tabular}
\end{center}
(i) Calculate an estimate of the sample mean and the sample standard deviation.\\
(ii) Determine whether there could be any outliers at the upper end of the distribution.
\hfill \mbox{\textit{OCR MEI S1 Q6 [6]}}