CAIE S2 2022 June — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2022
SessionJune
TopicMeasures of Location and Spread
TypeReverse-engineering from given variance

6 A random sample of 5 values of a variable \(X\) is given below. $$\begin{array} { l l l l l } 2 & 3 & 3 & 5 & a \end{array}$$
  1. Find an expression, in terms of \(a\), for the mean of these values.
    It is given that an unbiased estimate of the population variance of \(X\), using these values, is 4 . It is also given that \(a\) is positive.
  2. Find and simplify a quadratic equation in terms of \(a\) and hence find the value of \(a\).