OCR PURE — Question 7

Exam BoardOCR
ModulePURE
TopicProof

7
  1. Two real numbers are denoted by \(a\) and \(b\).
    1. Write down expressions for the following.
      • The mean of the squares of \(a\) and \(b\)
  2. The square of the mean of \(a\) and \(b\)
    (ii) Prove that the mean of the squares of \(a\) and \(b\) is greater than or equal to the square of their mean.
  3. You are given that the result in part (a)(ii) is true for any two or more real numbers.
  4. Explain what this result shows about the variance of a set of data.