CAIE S1 2011 June — Question 3

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2011
SessionJune
TopicMeasures of Location and Spread
TypeCompare using diagrams only

3 The following cumulative frequency table shows the examination marks for 300 candidates in country \(A\) and 300 candidates in country \(B\).
Mark\(< 10\)\(< 20\)\(< 35\)\(< 50\)\(< 70\)\(< 100\)
Cumulative frequency, \(A\)2568159234260300
Cumulative frequency, \(B\)104672144198300
  1. Without drawing a graph, show that the median for country \(B\) is higher than the median for country \(A\).
  2. Find the number of candidates in country \(A\) who scored between 20 and 34 marks inclusive.
  3. Calculate an estimate of the mean mark for candidates in country \(A\).