If a teacher is grading on a curve, the median is 78 and the standard deviation is 9.6, how do i find out the ranges for grades? ex, an A is the top 15% of the curve. I know it has to do with the z score and that is the # of standard deviations the score is from the median, but i am totally confused how to use this information to get the grade ranges.

Question

If a teacher is grading on a curve, the median is 78 and the standard deviation is 9.6, how do i find out the ranges for grades?  ex, an A is the top 15% of the curve.  I know it has to do with the z score and that is the # of standard deviations the score is from the median, but i am totally confused how to use this information to get the grade ranges.

PsyDAG · Answer

Unless the curve is normal, the median and mean may not be the same and you cannot calculate the percentages with a Z score.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.15) and its Z score. Insert data inot above equation.