12.64 Cricket by Chance One measure of form for a bowler is the average run rate, defined as the number of runs given per wicket taken. A bowler is considered to be efficient if the run rate is close to optimum. The data shown in the following table provide information for 10 cricket bowlers from various countries (based on all matches up to and including Test 1825).

a. Plot the average run rate versus number of overs completed. Does it appear that there is any relationship between run rate and number of completed overs?

b. Is there a significant correlation between number of completed overs and run rate? Test at the 5% level of significance.

c. Do you think that the relationship between these two variables would be different if we had looked at all the bowlers, rather than a few selected ones? Any suggestions?

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Name K.D. Mills No. of No. of Overs Runs Wickets Average Team/ Completed Given Taken Run Rate Country 87.3 261 14 18.64 New Zealand C.R.D. Fernando 104.0 312 13 24.00 Sri Lanka S.C.G. MacGill 125.5 436 20 21.80 Australia S.E. Bond 131.4 471 18 26.16 New Zealand L.E. Plunkett 139.0 476 14 34.00 England Shahid Nazir 159.0 518 17 30.47 Pakistan J.H Kallis 155.1 491 15 32.73 South Africa Z. Khan 170.3 633 18 35.16 India S.I. Mahmood 175.3 685 D.W. Steyn 181.4 734 24 14 19 36.05 England 30.58 South Africa