3 (a) The table shows the times, in seconds, taken for each of 12 members of an athletics club to run 400 metres and 800 metres. (i) On the grid, complete the scatter diagram. The first six points have been plotted for you. (ii) Runners who took less than 55 seconds to run 400 metres and less than 125 seconds to run 800 metres are selected to enter an athletics competition. How many of these runners are selected for the competition? (iii) What type of correlation does the scatter diagram show? (iv) Draw a line of best fit on the scatter diagram. (v) Another runner took 65 seconds to run 400 metres. Use your line of best fit to estimate how long they would take to run 800 metres. (b) 50 members of the athletics club attempted the high jump. The table summarises the heights, in centimetres, of their jumps. The athletics coach uses the mid-interval values to calculate an estimate of the mean height jumped by the 50 athletes. His estimate of the mean is 153.6 cm. (i) Explain why p+q = 12. (ii) Show that 142.5p+162.5q = 1870. (iii) Find the value of p and the value of q. Show your working.