CAIE S1 2013 November — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2013
SessionNovember
TopicMeasures of Location and Spread
TypeStandard combined mean and SD

4 Barry weighs 20 oranges and 25 lemons. For the oranges, the mean weight is 220 g and the standard deviation is 32 g . For the lemons, the mean weight is 118 g and the standard deviation is 12 g .
  1. Find the mean weight of the 45 fruits.
  2. The individual weights of the oranges in grams are denoted by \(x _ { o }\), and the individual weights of the lemons in grams are denoted by \(x _ { l }\). By first finding \(\Sigma x _ { o } ^ { 2 }\) and \(\Sigma x _ { l } ^ { 2 }\), find the variance of the weights of the 45 fruits.