suppose that students from your high school took a standardized test. the results of this test showed a mean score of 80 with a standard deviation of 25. what

Question

Suppose that students from your high school took a standardized test. The results of this test showed a mean score of 80 with a standard deviation of 25. What would this  tell you about the students performance on the standardized test?

Answer 1

Lucy,

 

Presumably the maximum score on the test is 100.  If so, then a symmetrical Normal distribution that would fit into the (0, 100) range would have a mean of 50, and a standard deviation of (100-50)/3 = 16.7.

 

Given that the mean on this test moved up a lot from 50 to 80 implies many or most people got high scores above 80.

 

But given that the standard deviation (or the spread of the distribution) increased from 16.7 to 25 (about 50%) means that there must have been a significant number of very low scores because the cramped ceiling at the top where 100 is just  (mean 80 + 0.8 σ ) would not contribute much to the calculated standard deviation of 25 because deviations from the 80 mean are squared and added.  An extreme minus 3.0 σ grade would represent a 5 score out of 100!