LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

NO 8

B.B.A & B.Com. DEGREE EXAMINATION – BUS.ADMIN. & CORP.

THIRD SEMESTER – APRIL 2008

ST 3105/ 3102 – INTRODUCTION TO STATISTICS

 

 

 

Date : 07-05-08                  Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

 

SECTION- A

Answer all the questions                                                                              (10×2=20 marks)

1. Mention the various uses of statistics in Business and Industry.
2. Distinguish between ‘Census’ and ‘Sampling’ methods of collection of data
3. What are the different types of bar diagram?
4. State the different components of time series.
5. The mean heights of 25 male workers in a factory is 61 inches and mean height of 35 female workers in the same factory is 58 inches.  Find the combined mean height of 60 workers in the factory.
6. From the following find out whether the data are consistent or not

(A) =100, (B) = 150, (AB) = 60, N = 500

1. The arithmetic mean of a group of 75 observations is 27.  It was later discovered that one observation was wrongly read as 43 instead of the correct value 53.  Calculate correct mean.
2. The first four central moments of distribution are 0, 2.5, 0.7 and 18.75.  Comment on kurtosis of the distribution.
3. An automobile driver travels from plain to hill station 100 Km distance at an average speed of 30 km per hour.  He then makes the return trip at average speed of 20 km per hour.  What is his average speed over the entire distance (200 km)?
4. If the upper quartile of a series is 40 and lower quartile is 15, find out the value of quartile deviation and coefficient of quartile deviation.

 

SECTION – B

Answer any five questions                                                                              (5×8=40 marks)

1. Distinguish between probability and non-probability sampling.  Examine critically the various types of probability sampling.
2. In order to ascertain if the marriage has any effect on the examination results of students, 1,000 students were selected at random.  There were Hindus, Muslims & Christians of the 1000 students, 375 were married.  Of the married students, 167 passed and of the unmarried students, 203 failed.  Find Yule’s coefficient of association between marriage and failure of students in the examination.
3. Draw ogive by less than and more than methods for the following and determine the median graphically:

 

Marks	0-6	6-12	12-18	18-24	24-30	30-36
No. of students	4	8	15	20	12	6

 

1. Obtain the Spearman’s rank correlation coefficient between the variables X and Y from the following pairs of observed values.

 

X	50	55	65	50	55	60	50	65	70	75
Y	110	110	115	125	140	115	130	120	115	160

 

1. Fit a straight line trend by the method of least squares to the following data:

 

Year	1990	1991	1992	1993	1994	1995	1996	1997
Sales (‘000)	38	40	65	72	69	67	95	104

      Estimate the sales for the year 2000

 

1. Calculate Karl Pearson’s coefficient of skewness:

 

Variable	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	5	6	11	21	35	30	22	11

 

 

 

1. Compute mode using grouping and analysis table from the following frequency distribution of marks at a test in English.

 

Marks	5	10	15	20	25	30	35	40	45	50
No. of students	20	43	75	76	72	45	39	9	8	6

 

1. Find out the mean deviation from the median for the following data:

 

Age (years)	4-6	6-8	8-10	10-12	12-14	14-16	16-18
No. of Students	30	90	120	150	80	60	20

 

 

SECTION – C

Answer any two questions                                                                  (2×20=40 marks)

 

1. Calculate Karl Pearson’s coefficient of correlation from the following data:

 

X   Y	200-300	300-400	400-500	500-600	600-700
10-15	–	–	–	3	7
15-20	–	4	9	4	3
20-25	7	6	12	5	–
25-30	3	10	19	8	–

 

1. The scores of two batsman A and B in ten innings during a certain season are:

 

A	32	28	47	63	71	39	10	60	96	14
B	19	31	48	53	67	90	10	62	40	80

 

Find which of the two batsmen is more consistent in scoring.

1. Find the seasonal variation by the ratio-to-trend method from the data given below:

 

Year	1st quarter	2nd quarter	3rd quarter	4th quarter
2001	86	95	96	99
2002	96	102	104	110
2003	103	108	106	107

 

1. From the data given below find:

1. The two regression equations
2. The coefficient of correlation between marks in Economics and Statistics
3. The most likely marks in Statistics when the marks in Economics are 30
4. The most likely marks in Economics when the marks in Statistics are 35

 

Marks in Economics	25	28	35	32	31	36	29	38	34	32
Marks in Statistics	43	46	49	41	36	32	31	30	33	39

 

 

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