CAIE S1 2010 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionJune
TopicMeasures of Location and Spread
TypeInterpret or analyse given back-to-back stem-and-leaf

6 The lengths of some insects of the same type from two countries, \(X\) and \(Y\), were measured. The stem-and-leaf diagram shows the results.
Country \(X\)Country \(Y\)
(10)976664443280
(18)888776655544333220811122333556789(13)
(16)999887765532210082001233394566788(15)
(16)87655533222111008301224444556677789(17)
(11)8765544331184001244556677789(15)
85\(12 r 335566788\)(12)
8601223555899(11)
Key: 5 | 81 | 3 means an insect from country \(X\) has length 0.815 cm and an insect from country \(Y\) has length 0.813 cm .
  1. Find the median and interquartile range of the lengths of the insects from country \(X\).
  2. The interquartile range of the lengths of the insects from country \(Y\) is 0.028 cm . Find the values of \(q\) and \(r\).
  3. Represent the data by means of a pair of box-and-whisker plots in a single diagram on graph paper.
  4. Compare the lengths of the insects from the two countries.