Mels mean on 10 tests for the semester was 89 She complained

12. Mel\'s mean on 10 tests for the semester was 89. She complained to the teacher that she should be given an A because she missed the cutoff of 90 by only a single point. Explain whether it is clear that she really missed an A by only a single point if each test was based on 100 points

Solution

The Mean is nothing but an average of the given variables as per statistics.

Ex : find the mean of: 90, 140, 140, 180, 200, 220

                                                                               
Mean:    90+ 140+ 140+ 180 + 200 + 220 = 161.66
                                        6                             

Now coming to our problem, Mel’s got the mean of 10 tests marks for his semester was 89 and she missed out the grade A.

Now let us assume her marks are all crossed the 90 then she definitely got grade A.

Now let us assume her marks : 90,85,89,91,95,87,88,92,90,89

In the above example five subjects crossed 90 and five subjects below 90

Then find the mean = (90+85+89+91+95+87+88+92+90+89)/10 = 896/10=89.6

                                                900-896=4

Hear the mean is 89.6 and just a difference of 0.4 for 90.But the real fact that she missed the A grade by 4 marks not for 0.4.

Now let us assume the other set of marks : 90,87,89,91,95,89,88,92,90,89

In the above set we have modified two variable (bold) and find the meas

   =(90+87+89+91+95+89+88+92+90+89)/10 = 900/10=90

Here we got 90 as a mean got grade A. so the mean is calculated by all values together but not with a single variables.

Conclusion : so Mel’s got 89 as a mean that means she got an average of her test as 89 out of 100,that means she missed a A grade by 10 marks by the taken of above examples . In some of subjects she may get less marks so that is why she got the 10 marks difference.