| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | January |
| Marks | 19 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Estimate mean and standard deviation from frequency table |
| Difficulty | Moderate -0.3 This is a standard grouped data statistics question covering histogram drawing, mean/SD calculation, outlier discussion, and linear transformations. All parts are routine S1 techniques with no novel problem-solving required. The unequal class widths add minor complexity to the histogram, but this is a textbook exercise slightly easier than average A-level difficulty. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread2.02g Calculate mean and standard deviation5.02c Linear coding: effects on mean and variance |
| Income (x thousand pounds) | \(0 \leqslant x \leqslant 20\) | \(20 < x \leqslant 40\) | \(40 < x \leqslant 60\) | \(60 < x \leqslant 100\) | \(100 < x \leqslant 200\) |
| Frequency | 238 | 365 | 142 | 128 | 45 |
The incomes of a sample of 918 households on an island are given in the table below.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
Income (x thousand pounds) & $0 \leqslant x \leqslant 20$ & $20 < x \leqslant 40$ & $40 < x \leqslant 60$ & $60 < x \leqslant 100$ & $100 < x \leqslant 200$ \\
\hline
Frequency & 238 & 365 & 142 & 128 & 45 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\roman*)]
\item Draw a histogram to illustrate the data. [5]
\item Calculate an estimate of the mean income. [3]
\item Calculate an estimate of the standard deviation of the incomes. [4]
\item Use your answers to parts (ii) and (iii) to show there are almost certainly some outliers in the sample. Explain whether or not it would be appropriate to exclude the outliers from the calculation of the mean and the standard deviation. [4]
\item The incomes were converted into another currency using the formula $y = 1.15x$. Calculate estimates of the mean and variance of the incomes in the new currency. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2011 Q7 [19]}}