OCR MEI S1 (Statistics 1)

Question 2
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2 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]{b4bf1bd0-f85d-42b7-ad15-6672387bb208-2_998_1466_566_367}
\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.
Question 3
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3 The stem and leaf diagram illustrates the heights in metres of 25 young oak trees.
3467899
402234689
501358
6245
746
81
Key: 4 |2 represents 4.2
  1. State the type of skewness of the distribution.
  2. Use your calculator to find the mean and standard deviation of these data.
  3. Determine whether there are any outliers.
Question 4
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4 At a call centre, \(85 \%\) of callers are put on hold before being connected to an operator. A random sample of 30 callers is selected.
  1. Find the probability that exactly 29 of these callers are put on hold.
  2. Find the probability that at least 29 of these callers are put on hold.
  3. If 10 random samples, each of 30 callers, are selected, find the expected number of samples in which at least 29 callers are put on hold.