Question

Thomas has a mean exam score of 72 with a standard deviation of 5, and Mike has a mean exam score of 85 with a standard deviation of 21. Who is more consistent in test performance?

Answer 1

We know that smaller the standard deviation, more reliable is result and larger the standrad deviation, less reliable is result.

So, in this case, Thomas standard deviation is 5 and Mike standard deviation is 21, this means that Thomas is more consistent with the performance because he has low fluctuation in the exam score.

Suppose there will be one standard deviation move possible, then

Thomas's lowest and highest exam score are (72-5) and (72+5) =67 and 77

Mike's lowest and highest exam score are (85-21) and (85+21) = 64 and 106

So, we can see that Thomas score is more reliable and consistent as compared to Mike score due to low variation.