Draw box plot from cumulative frequency

A question is this sub-type if and only if it provides a cumulative frequency graph or curve and asks the student to read off or estimate the summary statistics from the graph before drawing the box-and-whisker plot.

2 questions

CAIE S1 2015 June Q3
3
\includegraphics[max width=\textwidth, alt={}, center]{b4bd1629-e2ae-4395-9773-4b14ce428ca6-2_1147_1182_884_477} In an open-plan office there are 88 computers. The times taken by these 88 computers to access a particular web page are represented in the cumulative frequency diagram.
  1. On graph paper draw a box-and-whisker plot to summarise this information. An 'outlier' is defined as any data value which is more than 1.5 times the interquartile range above the upper quartile, or more than 1.5 times the interquartile range below the lower quartile.
  2. Show that there are no outliers.
    \includegraphics[max width=\textwidth, alt={}, center]{b4bd1629-e2ae-4395-9773-4b14ce428ca6-3_451_1561_258_292} Nikita goes shopping to buy a birthday present for her mother. She buys either a scarf, with probability 0.3 , or a handbag. The probability that her mother will like the choice of scarf is 0.72 . The probability that her mother will like the choice of handbag is \(x\). This information is shown on the tree diagram. The probability that Nikita's mother likes the present that Nikita buys is 0.783 .
  3. Find \(x\).
CAIE S1 2011 November Q5
5
\includegraphics[max width=\textwidth, alt={}, center]{b72ace6b-d3d4-401d-bffe-403c9127f2a8-3_1157_1001_258_573} The cumulative frequency graph shows the annual salaries, in thousands of euros, of a random sample of 500 adults with jobs, in France. It has been plotted using grouped data. You may assume that the lowest salary is 5000 euros and the highest salary is 80000 euros.
  1. On graph paper, draw a box-and-whisker plot to illustrate these salaries.
  2. Comment on the salaries of the people in this sample.
  3. An 'outlier' is defined as any data value which is more than 1.5 times the interquartile range above the upper quartile, or more than 1.5 times the interquartile range below the lower quartile.
    (a) How high must a salary be in order to be classified as an outlier?
    (b) Show that none of the salaries is low enough to be classified as an outlier.