LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc., B.Com. DEGREE EXAMINATION
SUPPLEMENTARY EXAMINATION – JUNE 2008
ST 3105 / 3102 - INTRODUCTION TO STATISTICS
Date : 27-06-08
Time : 9:00 - 12:00
Dept. No.
Max. : 100 Marks
SECTION A
Answer ALL questions.
(10 x 2 =20 marks)
1. What are the main steps involved in a sample survey?
2. What are the various methods of collecting primary data?
3. State the empirical relationship between mean, median and mode.
4. What are the advantages of diagrammatic and graphic presentation of data?
5. What are the different types of bar diagram?
6. Distinguish between simple and multiple correlations.
7. What is coefficient of variation? What purpose does it serve?
8. Give any two relative measures of skewness.
9. What is meant by regression analysis?
10. Give suitable examples for seasonal and random variations?
SECTION B
Answer any FIVE questions.
(5 x 8 =40 marks)
11. Explain the different types of sampling methods.
12. Draw a suitable bar diagram for the following data.
1994 95 96 97 98 99 00 01 02 03
Year
Tax (Rs.Crores) 282 271 533 716 273 431 488 514 615 1287
13. Calculate Mean deviation and coefficient of mean deviation from the following data.
Height (cms) 158 159 160 161 162 163 164 165 166
8
No. of persons 15 20 32 35 33 22 20 10
14. Calculate coefficient of correlation for the following data and interpret the results.
X
Y
100
30
200
50
300
60
400
80
500
100
600
110
700
130
15. Calculate Bowleys coefficient of skewness.
Variable 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
16
26
38
22
15
7
4
Frequency 12
16. Calculate trend by 4 year moving average method for the following data.
1996 97 98 99 00 01 02 03 04 05 06
Year
Productivity 614 615 652 678 681 655 717 719 708 779 757
1
17. Explain all the components of time series.
18. Find the association between A and B for the following data by applying Yule’s method:
(i)
(AB) = 5, (A) = 40, (B) = 45, N = 240.
(ii)
(AB) = 2, (A) = 34, (B) = 22, N = 234.
SECTION C
Answer any TWO questions.
(2 x 20 =40 marks)
19. Consider the following data:
Daily income(Rs.) 0-200 200-400 400-600 600-800 800-1000 1000-1200
80
165
230
80
32
13
No of persons
(i)
(ii)
Draw a histogram and superimpose the corresponding frequency polygon.
Find median and mode.
20. From the prices of shares of companies Repco and Delto, find out which is more stable in value
using coefficient of variation.
Repco 35 54 52 53 56 58 52 50 51 49
Delto 108 107 105 105 106 107 104 103 104 101
21. The quantity of raw materials purchased by a company at the specified prices during the 12
months of 2005 is given:
Month Price/Kg Quantity/Kg Month Price/Kg Quantity/Kg
Jan
96
250
July
112
220
Feb
110
200
Aug
112
220
Mar
100
250
Sept
108
200
Apr
90
280
Oct
116
210
May
86
300
Nov
86
300
June
92
300
Dec
92
250
(i)
(ii)
(iii)
Find the two regression equations based on the above data.
Estimate the approximate quantity likely to be purchased if the price shoots upto Rs. 124
per Kg.
Using the regression coefficients obtain the correlation coefficient.
22. Find seasonal variations by ratio-to-trend method from the data given below:
Year 1 Quarter 2 Quarter 3 Quarter 4 Quarter
30
40
36
34
1999
34
52
50
44
2000
40
58
54
48
2001
54
76
68
62
2002
80
92
86
82
2003
☺☺☺☺☺☺☺ ALL THE BEST ☺☺☺☺☺☺☺
2