| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Data representation |
| Type | Estimate mean and standard deviation from histogram |
| Difficulty | Easy -1.2 This is a standard statistics question testing histogram interpretation, mean/standard deviation from grouped data using midpoints, and outlier identification. All techniques are routine A-level procedures with no problem-solving insight required—purely mechanical application of formulas taught in S1/statistics modules. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
The masses of a random sample of 120 boulders in a certain area were recorded. The results are summarized in the histogram.
\includegraphics{figure_5}
\begin{enumerate}[label=(\alph*)]
\item Calculate the number of boulders with masses between 60 and 65 kg. [2]
\item \begin{enumerate}[label=(\roman*)]
\item Use midpoints to find estimates of the mean and standard deviation of the masses of the boulders in the sample. [3]
\item Explain why your answers are only estimates. [1]
\end{enumerate}
\item Use your answers to part (b)(i) to determine an estimate of the number of outliers, if any, in the distribution. [2]
\item Give one advantage of using a histogram rather than a pie chart in this context. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q10 [9]}}