CAIE S1 2024 November — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2024
SessionNovember
TopicMeasures of Location and Spread
TypeConstruct back-to-back stem-and-leaf from raw data

6 Teams of 15 runners took part in a charity run last Saturday. The times taken, in minutes, to complete the course by the runners from the Falcons and the runners from the Kites are shown in the table.
Falcons383942444648505152565859646976
Kites324040454748525458595960616365
  1. Draw a back-to-back stem-and-leaf diagram to represent this information, with the Falcons on the left-hand side.
  2. Find the median and the interquartile range of the times for the Falcons.
    Let \(x\) and \(y\) denote the times, in minutes, of a runner from the Falcons and a runner from the Kites respectively. It is given that $$\sum x = 792 , \quad \sum x ^ { 2 } = 43504 , \quad \sum y = 783 , \quad \sum y ^ { 2 } = 42223 .$$
  3. Find the mean and the standard deviation of the times taken by all 30 runners from the two teams.