Question

Exercise 2

The following data represent the mutual fund prices reported at the end of the week for selected 42 nationally sold funds.

10        17        15        18        22        19        10        17        18        25        11        13        35        28

27        29        39        31        35        33        22        24        28        35        45        50        47        38

41        31        21        11        49        38        35        25        33        42        27        15        28        34

1. Organize the data.
2. Present the data.

Exercise 3

Twenty MBA students have got the following marks out of 100 in three courses in the first semester.

Course	Marks out of 100
Marketing	79	85	92	95	77	82	85	88	90	92
	82	92	93	84	80	90	88	87	80	75
Quantitative Methods	91	80	75	64	50	83	75	91	88	79
	92	73	78	81	82	76	85	80	75	90
International Business	90	88	87	80	75	83	75	91	88	79
	88	91	90	77	76	82	92	93	84	80

1. Organize the above data in meaningful form.
2. Present the data.
3. Analyze and compare performance of students in three courses.

Exercise 4

A random sample of 8 MBA students from two sections of same batch are selected from of a B-School. The marks scored by these students are given below;

            

Section A	60	50	76	87	90	57	68	77
Section B	50	78	84	62	75	53	73	90

On the basis of sample statistic find out (show working),

1. Which section is more consistent?                                                           
2. Which section’s overall performance is better and why?

Answer 1

Exercise 2 :

Mutual Fund No	MF prices
1	10
2	17
3	15
4	18
5	22
6	19
7	10
8	17
9	18
10	25
11	11
12	13
13	35
14	28
15	27
16	29
17	39
18	31
19	35
20	33
21	22
22	24
23	28
24	35
25	45
26	50
27	47
28	38
29	41
30	31
31	21
32	11
33	49
34	38
35	35
36	25
37	33
38	42
39	27
40	15
41	28
42	34

The following are the summary statistics of the MF prices of the 42 Mutual funds :

MF prices
Mean	27.9
Standard Error	1.7
Median	28.0
Mode	35.0
Standard Deviation	11.1
Sample Variance	122.7
Kurtosis	-0.8
Skewness	0.2
Range	40.0
Minimum	10.0
Maximum	50.0
Sum	1171.0
Count	42.0

Here, we can see that Mean is 27.9 and Standard Deviation is 11.1 . Thus coefficient of variation is 0.3972. Mean is almost equal to Median , which shows that the distribution is near to normal. Also, the minimum is 10 & maximum is 50 , which fall within 2 standard deviations of mean. It also indicates that the distribution is normal.

2.

Student no	Marketing	Quantitative Methods	International Business
1	79	91	90
2	85	80	88
3	92	75	87
4	95	64	80
5	77	50	75
6	82	83	83
7	85	75	75
8	88	91	91
9	90	88	88
10	92	79	79
11	82	92	88
12	92	73	91
13	93	78	90
14	84	81	77
15	80	82	76
16	90	76	82
17	88	85	92
18	87	80	93
19	80	75	84
20	75	90	80

From the above three scatter plots, we can see that there is not much variation in the student's score across the subjects.

The descriptive summary statistics is shown below :

Marketing		Quantitative Methods		International Business
Mean	85.8	Mean	79.4	Mean	84.5
Standard Error	1.3	Standard Error	2.2	Standard Error	1.4
Median	86.0	Median	80.0	Median	85.5
Mode	92.0	Mode	75.0	Mode	88.0
Standard Deviation	5.8	Standard Deviation	10.0	Standard Deviation	6.1
Sample Variance	33.6	Sample Variance	99.1	Sample Variance	37.1
Kurtosis	-1.0	Kurtosis	3.0	Kurtosis	-1.4
Skewness	-0.2	Skewness	-1.3	Skewness	-0.2
Range	20.0	Range	42.0	Range	18.0
Minimum	75.0	Minimum	50.0	Minimum	75.0
Maximum	95.0	Maximum	92.0	Maximum	93.0
Sum	1716.0	Sum	1588.0	Sum	1689.0
Count	20.0	Count	20.0	Count	20.0

The findings are :

1. On an average, students scored more in Marketing as compared to any other subject.

2. in Quantitative method, the range of students score and the variation in score is highest as compared to any other subject.

3. In all the 3 subjects , the mean is close to median, which implies that the distribution is pretty much normal in all the three cases.

Exercise 4 :

Section A	Section B
60	50
50	78
76	84
87	62
90	75
57	53
68	73
77	90

The descriptive statistics are shown below:

Section A		Section B
Mean	70.6	Mean	70.6
Standard Error	5.1	Standard Error	5.1
Median	72.0	Median	74.0
Mode	#N/A	Mode	#N/A
Standard Deviation	14.4	Standard Deviation	14.4
Sample Variance	206.3	Sample Variance	206.3
Kurtosis	-1.3	Kurtosis	-1.2
Skewness	0.0	Skewness	-0.3
Range	40.0	Range	40.0
Minimum	50.0	Minimum	50.0
Maximum	90.0	Maximum	90.0
Sum	565	Sum	565
Count	8	Count	8

i. In this case, we can see that both the mean and the standard deviations are same. The minimum & maximum values are also same, but in Section A, Median is 72 & in section B, Median is 74 & the mean is 70.6 in both the cases. It implies that Section B's distribution is more skewed to the left as compared to Section A. This is also implied from the Skewness metric in both the sections.

Thus , Section A is more consistent as compared to Section B.

ii. Section B overall performance is good as more people have scored higher scores as compared to Section A.