CAIE A-Level Mathematics 6.4.6 Unbiased estimates

CAIE A-Level Mathematics 6.4.6 Unbiased estimates
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise calculating unbiased estimates of population mean and variance from raw lists, totals, or summarised sample data.

How this is tested

  • calculate x̄ as the unbiased estimate of the population mean from sample totals
  • rearrange the unbiased variance formula to find a missing sum

Question 3(a)

[Maximum number: 3]

The time, T minutes, for a certain daily bus journey is normally distributed. The bus company claims that the mean of T is 45. A passenger believes that the mean of T is actually greater than 45. She notes the times taken for this journey on a random sample of 60 days. The results are summarised below.

n=60∑t=2750∑t2=127000n=60 \quad \sum t=2750 \quad \sum t^{2}=127000

Calculate unbiased estimates of the population mean and variance.