Edexcel S1 2015 June — Question 1

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2015
SessionJune
TopicData representation
TypeCalculate range and interquartile range
  1. Each of 60 students was asked to draw a \(20 ^ { \circ }\) angle without using a protractor. The size of each angle drawn was measured. The results are summarised in the box plot below.
    \includegraphics[max width=\textwidth, alt={}, center]{9626e3ce-35d6-41b5-a0bd-1185f38b9e36-02_371_1040_340_461}
    1. Find the range for these data.
    2. Find the interquartile range for these data.
    The students were then asked to draw a \(70 ^ { \circ }\) angle.
    The results are summarised in the table below.
    Angle, \(\boldsymbol { a }\), (degrees)Number of students
    \(55 \leqslant a < 60\)6
    \(60 \leqslant a < 65\)15
    \(65 \leqslant a < 70\)13
    \(70 \leqslant a < 75\)11
    \(75 \leqslant a < 80\)8
    \(80 \leqslant a < 85\)7
  2. Use linear interpolation to estimate the size of the median angle drawn. Give your answer to 1 decimal place.
  3. Show that the lower quartile is \(63 ^ { \circ }\) For these data, the upper quartile is \(75 ^ { \circ }\), the minimum is \(55 ^ { \circ }\) and the maximum is \(84 ^ { \circ }\) An outlier is an observation 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 no outliers for these data.
    2. Draw a box plot for these data on the grid on page 3.
  5. State which angle the students were more accurate at drawing. Give reasons for your answer.
    (3) \includegraphics[max width=\textwidth, alt={}, center]{9626e3ce-35d6-41b5-a0bd-1185f38b9e36-03_378_1059_2067_447}
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