class average

Question

There are two math classes. Class A has an average mark of 74% and a standard deviation of 10%. Class B has an average mark of 80% and a standard deviation of 2%. Which class would most likely have the highest individual score in the class? Justify your answer.

Answer 1

Subtle question. On the surface of it, 80 is obviously higher than 74, but the standard deviation is minuscule for B compared to A. Given the fact that the vast majority of all data is between ±3 standard deviations, A should range from:

74 - 3*10   to 74 + 3*10

44              to            104

 

...while B would only run from:

80 - 3*2      to 80 + 3*2

  74            to           86

Looked at empirically, we would expect A to reach far higher.