Mathematics
Mathematics
Problem
Thirty hits were recorded with each of two cricket bats. For bat M the mean distance covered was 62 m with a standard deviation of 3 m, while for bat N the mean distance was also 62 m but the standard deviation was 6 m. Which statement correctly compares the consistency of the two bats? a) Both bats are equally consistent because their means are equal. b) Bat M is more consistent than bat N. c) Consistency cannot be judged without knowing the variances. d) Bat N is more consistent than bat M.Intuitive explanation
Standard deviation measures spread—how much individual hits scatter around the mean. Since both bats have the same mean distance (62 m), the bat with the smaller standard deviation is more consistent because its hits cluster more tightly around that average. Bat M's standard deviation of 3 m is half that of bat N's 6 m, so M produces more predictable, reliable distances.
Intuitive explanation
Standard deviation measures spread—how much individual hits scatter around the mean. Since both bats have the same mean distance (62 m), the bat with the smaller standard deviation is more consistent because its hits cluster more tightly around that average. Bat M's standard deviation of 3 m is half that of bat N's 6 m, so M produces more predictable, reliable distances.