No.	CGPA	Background	Specialisation	Work Experience	Age (in years)
1	3.24	Commerce	Finance	2	23
2	3.14	Commerce	Finance	1	21
3	3.72	Commerce	Finance	2	23
4	3.06	Commerce	Finance	4	21
5	3.14	Commerce	Finance	2	22
6	3.14	Commerce	Finance	2	23
7	3.06	Commerce	Finance	0	22
8	3.17	Commerce	Finance	3	21
9	2.97	Commerce	Finance	2	22
10	3.14	Commerce	Finance	4	23
11	3.69	Commerce	Finance	2	24
12	2.85	Commerce	Finance	4	25
13	2.92	Commerce	Marketing	2	23
14	2.79	Commerce	Marketing	3	25
15	3.22	Commerce	Marketing	3	22
16	2.87	Commerce	Marketing	5	22
17	3.14	Commerce	Marketing	1	22
18	3.17	Commerce	Marketing	4	23
19	3.22	Economics	Finance	1	26
20	2.58	Economics	Finance	2	25
21	3.36	Economics	Finance	1	22
22	3.17	Economics	Marketing	3	21
23	2.59	Economics	Marketing	5	24
24	2.97	Engineer	Human Resources	4	31
25	2.92	Engineer	Marketing	5	23
26	3.03	Engineer	Marketing	4	23
27	2.79	Engineer	Marketing	2	25
28	2.77	Engineer	Marketing	3	23
29	2.97	Engineer	Marketing	21	25
30	3.11	Engineer	Marketing	3	27
31	3.33	Engineer	Marketing	1	24
32	2.65	Engineer	Marketing	2	23
33	3.14	Engineer	Marketing	2	24
34	2.97	Engineer	Marketing	3	23
35	3.39	Engineer	Marketing	4	24
36	3.08	Engineer	Marketing	3	23
37	3.3	Engineer	Marketing	3	27
38	2.94	Engineer	Marketing	3	24
39	3.25	Engineer	Marketing	2	23
40	3.14	Engineer	System	3	23
41	3.36	Engineer	System	2	26
42	2.95	Information	Finance	2	24
43	2.98	Technology	Finance	5	23
44	2.82	Information	Marketing	3	24
45	2.98	Information	Marketing	3	26
46	3.33	Information	Marketing	2	24
47	2.96	Information	Marketing	4	27
48	3.67	Information	System	3	25
49	3.22	Science	Finance	1	25
50	3.14	Science	Finance	3	22
51	3.17	Science	Finance	2	26
52	3.25	Science	Human Resources	0	21
53	3. 10	Science	Marketing	2	22
54	2.85	Science	Marketing	5	24
55	3.25	Science	Marketing	2	22

1. At one of the Management Institutes, a sample of 55 second Year MBA students was selected, and information gathered relating to their age, background of graduation, work experience prior to joining MBA, CGPA score at the end of First Year, and area of specialization. The collected data is mentioned above-

(a) Present the above data with the help of tables, charts and graphs.

(b) Calculate the measures of location and dispersion of CGPA, age and work experience for all backgrounds and specializations. Combine these measures, wherever possible, for all the backgrounds and specializations separately. Discuss the findings.

(c) Study and comment on correlations between CGPA and age for students of all backgrounds viz. commerce, science etc.,

(d) Summarize your findings and present a managerial report.

2. An investor is concerned with the market return for the coming year, where the market return is defined as the percentage gain ( or loss, if negative) over the year. The investor believes there are five possible scenarios for the national economy in the coming year- rapid expansions, moderate expansions, no growth, moderate contractions and serious contraction. Furthermore, she has used all of the information available to her to estimate that the market returns for these scenarios are, respectively 23%, 18%,15%,9% and 3% .Also she has assessed the probabilities of these outcomes are 0.12, 0.40,0.25, 0.15 and 0.08. Use this information to describe the probability distribution of the market return. Calculate, average return, standard deviation and variance of the probability distribution of the market return for the coming year and comment.

3. The personnel department of ZTel, a large communication company, is reconsidering its hiring policy. Each applicant for a job must take a standard exam and the hire or no hire decision depends at least in part on the result of the exam. The scores of all applicants have been examined closely. They are approximately normally distributed with mean 525 and standard deviation 55.

The current hiring policy occurs in two phase. The first phase separates all applicants into three categories: automatic accepts, automatic rejects and maybe. The automatic accepts are those whose test scores are 600 or above. The automatic rejects are those whose test scores are 425 and above. All other applicants ( the maybes) are passed on to the second phase where their previous job experience, special talents, and other factors are used as hiring criterial. The personnel manager at ZTel wants to calculate the percentage of applicants who are automatic accepts or rejects, given the current standards. She also wants to know how to change the standards to automatically reject 10% of all applicants and automatically accept 15% of all applicants.

4.An American consumer organization is currently examining the relationship among several variables including gasoline mileage as measured by miles per gallon; the horsepower of the car's engine and the weight of the car (in pounds). A sample of 50 recent car models was selected and the results recorded. (provided in below table)

MPG	Horsepower	Weight
43.1	48	1985
19.9	110	3365
19.2	105	3535
17.7	165	3445
18.1	139	3205
20.3	103	2830
21.5	115	3245
16.9	155	4360
15.5	142	4054
18.5	150	3940
27.2	71	3190
41.5	76	2144
46.6	65	2110
23.7	100	2420
27.2	84	2490
39.1	58	1755
28	88	2605
24	92	2865
20.2	139	3570
20.5	95	3155
28	90	2678
34.7	63	2215
36.1	66	1800
35.7	80	1915
20.2	85	2965
23.9	90	3420
29.9	65	2380
30.4	67	3250
36	74	1980
22.6	110	2800
36.4	67	2950
27.5	95	2560
33.7	75	2210
44.6	67	1850
32.9	100	2615
38	67	1965
24.2	120	2930
38.1	60	1968
39.4	70	2070
25.4	116	2900
31.3	75	2542
34.1	68	1985
34	88	2395
31	82	2720
27.4	80	2670
22.3	88	2890
28	79	2625
17.6	85	3465
34.4	65	3465
20.6	105	3380

(a) Using the sample dataattached, calculate the sample meanand standard deviationfor the variables: -

1. Miles per gallon (MPG)

2. Horsepower

3. Weight (in pounds)

(b) Is there any evidence of skewness in the data sets? Which data set displays greatest skewness?

(c) Using the sample data on MPG, calculate the sample proportionof vehicles whose fuel economy exceeds 37 mpg and its corresponding standard deviation.

(d) Indicate all possible relationship between the variables and comment on it. (You may use scatter diagram or Karl Pearson's correlation coefficient)

(e) Using the complete data set and using simple ordinary least squares regression formulaedevelop twomodels to explain the behavior of gasoline mileage (Miles per gallon) as a function of their-

(i) Horsepower

(ii) Weight

Which model best describes the behavior of gasoline mileage? Explain your reasons here.