Consider the data set \(\{ k - 2,{\text{ }}k,{\text{ }}k + 1,{\text{ }}k + 4\} {\text{ , where }}k \in \mathbb{R}\) .

(a)     Find the mean of this data set in terms of k.

Each number in the above data set is now decreased by 3.

(b)     Find the mean of this new data set in terms of k.

(a)     Use of \(\bar x = \frac{{\sum\limits_{i = 1}^4 {{x_i}} }}{n}\)     (M1)

\(\bar x = \frac{{(k - 2) + k + (k + 1) + (k + 4)}}{4}\)     (A1)

\(\bar x = \frac{{4k + 3}}{4}\,\,\,\,\,\left( { = k + \frac{3}{4}} \right)\)     A1     N3

(b)     Either attempting to find the new mean or subtracting 3 from their \({\bar x}\)     (M1)

\(\bar x = \frac{{4k + 3}}{4} - 3\,\,\,\,\,\left( { = \frac{{4k - 9}}{4},{\text{ }}k - \frac{9}{4}} \right)\)     A1     N2

[5 marks]

This was an easy question that was well done by most candidates. Careless arithmetic errors caused some candidates not to earn full marks. Only a few candidates realised that part (b) could be answered correctly by directly subtracting 3 from their answer to part (a). Most successful responses were obtained by redoing the calculation from part (a).