4 The data set 4, 6, 9, a, 3, b has a mean and mode of 6. Find the values of a and b given that a>b. 5 Consider the data set: k - 2, k, k +3, k +3. a Show that the mean of the data set is equal to k + 1. b Suppose each number in the data set is increased by 2. Find the new mean of the data set in terms of k. 6 The winning margins in 100 basketball games were recorded. Margin (points) Frequency The results are summarised alongside. 1 - 10 13 a Explain why you cannot calculate the mean winning 11 - 20 35 margin from the table exactly. 21 - 30 27 b Estimate the mean winning margin. 31 - 40 18 41 - 50 7