OCR MEI S1 — Question 7 18 marks

Exam BoardOCR MEI
ModuleS1 (Statistics 1)
Marks18
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicData representation
TypeEstimate single values from cumulative frequency graph
DifficultyEasy -1.3 This is a routine statistics question testing standard cumulative frequency graph skills: reading median/quartiles, drawing a box plot, converting between cumulative and grouped frequency, and calculating means. All parts follow textbook procedures with no problem-solving or novel insight required. The only slight complexity is part (v) requiring adjustment of the mean, but this is still straightforward arithmetic.
Spec2.02f Measures of average and spread2.02g Calculate mean and standard deviation
7 The cumulative frequency graph below illustrates the distances that 176 children live from their primary school. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Distance from school} \includegraphics[alt={},max width=\textwidth]{1ad9c390-b42f-47d8-86c5-f73a42d97721-04_1073_1571_580_340}
\end{figure}
  1. Use the graph to estimate, to the nearest 10 metres,
    (A) the median distance from school,
    (B) the lower quartile, upper quartile and interquartile range.
  2. Draw a box and whisker plot to illustrate the data. The graph on page 4 used the following grouped data.
    Distance (metres)20040060080010001200
    Cumulative frequency2064118150169176
  3. Copy and complete the grouped frequency table below describing the same data.
    Distance ( \(d\) metres)Frequency
    \(0 < d \leqslant 200\)20
    \(200 < d \leqslant 400\)
  4. Hence estimate the mean distance these children live from school. It is subsequently found that none of the 176 children lives within 100 metres of the school.
  5. Calculate the revised estimate of the mean distance.
  6. Describe what change needs to be made to the cumulative frequency graph.
7 The cumulative frequency graph below illustrates the distances that 176 children live from their primary school.

\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Distance from school}
  \includegraphics[alt={},max width=\textwidth]{1ad9c390-b42f-47d8-86c5-f73a42d97721-04_1073_1571_580_340}
\end{center}
\end{figure}
\begin{enumerate}[label=(\roman*)]
\item Use the graph to estimate, to the nearest 10 metres,\\
(A) the median distance from school,\\
(B) the lower quartile, upper quartile and interquartile range.
\item Draw a box and whisker plot to illustrate the data.

The graph on page 4 used the following grouped data.

\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Distance (metres) & 200 & 400 & 600 & 800 & 1000 & 1200 \\
\hline
Cumulative frequency & 20 & 64 & 118 & 150 & 169 & 176 \\
\hline
\end{tabular}
\end{center}
\item Copy and complete the grouped frequency table below describing the same data.

\begin{center}
\begin{tabular}{ | c | c | }
\hline
Distance ( $d$ metres) & Frequency \\
\hline
$0 < d \leqslant 200$ & 20 \\
\hline
$200 < d \leqslant 400$ &  \\
\hline
 &  \\
\hline
 &  \\
\hline
 &  \\
\hline
 &  \\
\hline
\end{tabular}
\end{center}
\item Hence estimate the mean distance these children live from school.

It is subsequently found that none of the 176 children lives within 100 metres of the school.
\item Calculate the revised estimate of the mean distance.
\item Describe what change needs to be made to the cumulative frequency graph.
\end{enumerate}

\hfill \mbox{\textit{OCR MEI S1  Q7 [18]}}
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Q3 8 Q7 18