Mathematics
Mathematics
Problem
A coach is comparing the scoring consistency of two cricket players in five consecutive matches. Player A (runs): 48, 52, 55, 45, 50 Player B (runs): 20, 100, 15, 90, 25 a. (i) Calculate the range of runs for each player. b. (ii) Compute the standard deviation of runs for each player (show all working). c. (iii) Using the numerical results of parts (i) and (ii), advise the coach which player is more consistent. Support your answer with clear reasoning based on both measures.Intuitive explanation
The key here is variance and standard deviation—measures of how spread out a player's scores are around their average. Both players might have similar mean scores, but one will be much more consistent than the other. Calculate the average for each, then measure how far their individual scores typically deviate from that average. The player with the smaller spread is more reliable, which matters more in cricket than raw average alone.
Intuitive explanation
The key here is variance and standard deviation—measures of how spread out a player's scores are around their average. Both players might have similar mean scores, but one will be much more consistent than the other. Calculate the average for each, then measure how far their individual scores typically deviate from that average. The player with the smaller spread is more reliable, which matters more in cricket than raw average alone.