Question

ACT data for students in 3 school districts has been collected. The mean scores with associated standard deviations are as follows:

District-----Mean------Std Dev
----A------------29------------1
----B------------30------------3
----C------------27------------5

How would you compare the districts? Defend your analysis.

Answer 1

we can compare the ACT data for each district based on the mean and standard deviation

Best ACT data is for district A because it has the lowest standard deviation. This means that most of this district student's will have a score around 29 with very low variation.

Using Empirical rule, we can say that 95% of students for district A will have ACT score between 27 and 31 (2 standard deviation from the mean)

Worst ACT data is for district C because it has the largest standard deviation. This means that most of this district student's will have a score near to 27  with very high amount of variation.

Using Empirical rule, we can say that 95% of students for district C will have ACT score between 17 and 37 (2 standard deviation from the mean)