S1 June 2015 Q1

EdexcelOld spec14 marksData Processing

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.

Box plot on a grid, size of angle from 0 to 50: lower whisker 9, lower quartile 12, median 16, upper quartile 25, upper whisker 39, outlier cross at 48
(a) Find the range for these data. (1)
(b) Find the interquartile range for these data. (1)

The students were then asked to draw a \(70^\circ\) angle.
The results are summarised in the table below.

Angle, \(a\), (degrees)Number of students
\(55 \leqslant a \lt 60\)6
\(60 \leqslant a \lt 65\)15
\(65 \leqslant a \lt 70\)13
\(70 \leqslant a \lt 75\)11
\(75 \leqslant a \lt 80\)8
\(80 \leqslant a \lt 85\)7
(c) Use linear interpolation to estimate the size of the median angle drawn. Give your answer to 1 decimal place. (2)
(d) Show that the lower quartile is \(63^\circ\) (2)

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.

(e)
(i) Show that there are no outliers for these data.
(ii) Draw a box plot for these data on the grid below. (5)
Blank grid with horizontal axis, size of angle, from 40 to 90
(f) State which angle the students were more accurate at drawing. Give reasons for your answer. (3)
‹ Previous23 of 134 in Data ProcessingNext ›