Question

#2 A teacher walks into the room and reports that the average score on the test is 77%. The teacher starts handing back the papers. You notice that almost everyone around you got an F(< 60). You wonder how the average can be 77. Discuss this. (Note: These are the actual scores on the test. There is no curve)

Answer 1

Some times, it is possible to get average score of all students in a class as 77%, even though most of the students around a particular student have got the score less than 60% when there is no curve in the frequecncy graph and the frequency graph shows a line slopes upward. Becuase, the number of students around a particular student who got the score less than 60% may be lesser when compared with the remaining number of students who got score more than 60%. For example, if in a class of 10 students, around a particular student there are 4 students including that particular student have got F, that is the percentage od scores 44%, 56%, 58%, and 42% and the remaining 6 students have got percentage of scores 93%, 96%, 99%, 98%, 95% and 89% in a test.

Then the average of percentages of all 10 students scores is (44%+56%+58%+42%+93%+96%+99%+98%+95%+89%)/10 = (770%)/10 = 77%.