Edexcel S1 2017 October — Question 1

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2017
SessionOctober
TopicData representation
TypeCalculate range and interquartile range
  1. At the start of a course, an instructor asked a group of 80 apprentices to estimate the length of a piece of pipe. The error (true length - estimated length) was recorded in centimetres. The results are summarised in the box plot below.
    \includegraphics[max width=\textwidth, alt={}, center]{77ae01cd-2b58-48ab-889f-272e27ecf99d-02_291_1445_397_246}
    1. Find the range for these data.
    2. Find the interquartile range for these data.
    One month later, the instructor asked the 80 apprentices to estimate the length of a different piece of pipe and recorded their errors. The results are summarised in the table below.
    Error ( \(\boldsymbol { e }\) cm)Number of apprentices
    \(- 40 < e \leqslant - 16\)2
    \(- 16 < e \leqslant - 8\)18
    \(- 8 < e \leqslant 0\)33
    \(0 < e \leqslant 8\)14
    \(8 < e \leqslant 16\)10
    \(16 < e \leqslant 40\)3
  2. Use linear interpolation to estimate the median error for these data.
  3. Show that the upper quartile for these data, to the nearest centimetre, is 4 . For these data, the lower quartile is - 8 and the five worst errors were \(- 25 , - 21,18,23,28\) An outlier is a value that falls either more than \(1.5 \times\) (interquartile range) above the upper quartile or more than \(1.5 \times\) (interquartile range) below the lower quartile.
    1. Show that there are only 2 outliers for these data.
    2. Draw a box plot for these data on the grid on page 3.
  5. State, giving reasons, whether or not the apprentices' ability to estimate the length of a piece of pipe has improved over the first month of the course. \includegraphics[max width=\textwidth, alt={}, center]{77ae01cd-2b58-48ab-889f-272e27ecf99d-03_412_1520_2222_173}
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