OCR MEI S1 — Question 3 8 marks

Exam BoardOCR MEI
ModuleS1 (Statistics 1)
Marks8
PaperDownload PDF ↗
TopicData representation
TypeDraw cumulative frequency graph from frequency table (unequal class widths)
DifficultyEasy -1.3 This is a routine S1 statistics question requiring standard procedures: calculating cumulative frequencies from a frequency table, plotting points on a graph, and reading off median/quartiles. It involves only mechanical application of well-practiced techniques with no problem-solving or conceptual challenge beyond basic recall of definitions.
Spec2.02a Interpret single variable data: tables and diagrams

3 Answer part (i) of this question on the insert provided. A taxi driver operates from a taxi rank at a main railway station in London. During one particular week he makes 120 journeys, the lengths of which are summarised in the table.
Length
\(( x\) miles \()\)
\(0 < x \leqslant 1\)\(1 < x \leqslant 2\)\(2 < x \leqslant 3\)\(3 < x \leqslant 4\)\(4 < x \leqslant 6\)\(6 < x \leqslant 10\)
Number of
journeys
3830211498
  1. On the insert, draw a cumulative frequency diagram to illustrate the data.
  2. Use your graph to estimate the median length of journey and the quartiles. Hence find the interquartile range.
  3. State the type of skewness of the distribution of the data.

3 Answer part (i) of this question on the insert provided.
A taxi driver operates from a taxi rank at a main railway station in London. During one particular week he makes 120 journeys, the lengths of which are summarised in the table.

\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
\begin{tabular}{ l }
Length \\
$( x$ miles $)$ \\
\end{tabular} & $0 < x \leqslant 1$ & $1 < x \leqslant 2$ & $2 < x \leqslant 3$ & $3 < x \leqslant 4$ & $4 < x \leqslant 6$ & $6 < x \leqslant 10$ \\
\hline
\begin{tabular}{ l }
Number of \\
journeys \\
\end{tabular} & 38 & 30 & 21 & 14 & 9 & 8 \\
\hline
\end{tabular}
\end{center}

(i) On the insert, draw a cumulative frequency diagram to illustrate the data.\\
(ii) Use your graph to estimate the median length of journey and the quartiles.

Hence find the interquartile range.\\
(iii) State the type of skewness of the distribution of the data.

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