Question

Question 2

Emma	60
Noah	75
Olivia	95
Mason	80
Liam	65
Sophia	82
Isabella	75
Ethan	98
James	93
Charlotte	87

2a. What is the mean of the mid-term test scores?

Mean =        = 60+75+95+80+65+82+75+98+93+87= 810/10= 81

              

2b. What is the standard deviation of the mid-term test scores?

Names	Score	Deviations from Mean(X-Mean)	Squared Deviations
Emma	60	-21	441
Noah	75	-6	36
Olivia	95	14	196
Mason	80	-1	1
Liam	65	-16	256
Sophia	82	1	1
Isalbella	75	-6	36
Ethan	98	17	289
James	93	12	144
Charlotte	87	6	36
Total		0.00	1436.00

Standard Deviation Formula

                                                         

SD = Total / (N-1) = 1436.00/ 10-1= 1436.00/9= 159.56

SD = 12.63

2c. What is the coefficient of variance for the mid-term tests scores?  

Coefficient of Variation = SD/Mean = 12.63/ 81= 15.59%

Question 3

Consider the following scores on a final exam.

Emma	85
Noah	90
Olivia	95
Mason	87
Liam	88
Sophia	94
Isabella	92
Ethan	95
James	92
Charlotte	91

3a. What is the mean test score?

Mean = Mean =        = 85+90+95+87+88+94+92+95+92+91= 909/ 10= 90.9

              

3b. What is the standard deviation of the test scores?

Names	Scores	Deviations from Mean(X-Mean)	Squared Deviations
Emma	85	-5.9	34.81
Noah	90	-0.9	0.81
Olivia	95	4.1	16.81
Mason	87	-3.9	15.21
Liam	88	-2.9	8.41
Sophia	94	3.1	9.61
Isalbella	92	1.1	1.21
Ethan	95	4.1	16.81
James	92	1.1	1.21
Charlottee	91	0.1	0.01
Total		0.01	104.09

Standard Deviation Formula

SD = Squared Root Total / (N-1) = 104.9/9 = 11.66

SD= 3.41

Coefficient of Variation is given by:

CV- SD/ Mean *100 = 3.75%

Please help me answer the question below using the information above.

3c. Compare the standard deviation and coefficient of variance from the Mid-Term Exam (problem 2) to the standard deviation and coefficient of variance from the Final Exam. What does this tell you about the scores on the mid-term compared to the final?

Answer 1

Please find the answer below. Don't hesitate to give a "thumbs up" for the answer in case you're satisfied with it.

3c.

SD of 1st table = 12.63
COV of 1st table = 15.59%

SD of 2nd table = 3.41
COV of 2nd table = 3.75%

Compare 1st and 2nd SDs : 1st is way more than 2nd, indicating standard deviation of Mid-term exams is way more than 2nd. It means that scores vary more for Midterm exams than for Final exams. But this is in absolute terms.

To compare better, we must take the COV(coefficient of variation). For 1st table it is 15.59% , way more than 2nd table ( 3.75%), indicating that
even in relative terms Final exam scores have less variation than the Mid-term scores