OCR S1 2013 June — Question 4

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

4 At a stall in a fair, contestants have to estimate the mass of a cake. A group of 10 people made estimates, \(m \mathrm {~kg}\), and for each person the value of \(( m - 5 )\) was recorded. The mean and standard deviation of \(( m - 5 )\) were found to be 0.74 and 0.13 respectively.
  1. Write down the mean and standard deviation of \(m\). The mean and standard deviation of the estimates made by another group of 15 people were found to be 5.6 kg and 0.19 kg respectively.
  2. Calculate the mean of all 25 estimates.
  3. Fiona claims that if a group's estimates are more consistent, they are likely to be more accurate. Given that the true mass of the cake is 5.65 kg , comment on this claim.