| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Calculate frequency density from frequency |
| Difficulty | Moderate -0.8 This is a routine statistics question testing standard histogram/frequency density calculations and understanding of summary statistics. Part (i) is a straightforward proportion calculation using frequency density, parts (ii)-(iii) are textbook procedures for grouped data, and part (iv) tests conceptual understanding of how outliers affect measures. All techniques are standard S1 content with no novel problem-solving required. |
| Spec | 2.02b Histogram: area represents frequency2.02g Calculate mean and standard deviation |
| Time (minutes) | \(t \leqslant 27\) | \(28 \leqslant t \leqslant 30\) | \(31 \leqslant t \leqslant 35\) | \(36 \leqslant t \leqslant 45\) | \(46 \leqslant t \leqslant 60\) | \(t \geqslant 61\) |
| Number of people | 0 | 4 | 28 | 14 | 4 | 0 |
4 The table shows information about the time, $t$ minutes correct to the nearest minute, taken by 50 people to complete a race.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Time (minutes) & $t \leqslant 27$ & $28 \leqslant t \leqslant 30$ & $31 \leqslant t \leqslant 35$ & $36 \leqslant t \leqslant 45$ & $46 \leqslant t \leqslant 60$ & $t \geqslant 61$ \\
\hline
Number of people & 0 & 4 & 28 & 14 & 4 & 0 \\
\hline
\end{tabular}
\end{center}
(i) In a histogram illustrating the data, the height of the block for the $31 \leqslant t \leqslant 35$ class is 5.6 cm . Find the height of the block for the $28 \leqslant t \leqslant 30$ class. (There is no need to draw the histogram.)\\
(ii) The data in the table are used to estimate the median time. State, with a reason, whether the estimated median time is more than 33 minutes, less than 33 minutes or equal to 33 minutes.\\
(iii) Calculate estimates of the mean and standard deviation of the data.\\
(iv) It was found that the winner's time had been incorrectly recorded and that it was actually less than 27 minutes 30 seconds. State whether each of the following will increase, decrease or remain the same:
\begin{enumerate}[label=(\alph*)]
\item the mean,
\item the standard deviation,
\item the median,
\item the interquartile range.
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2011 Q4 [16]}}