LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 1

FIRST SEMESTER – APRIL 2008

ST 1500 – STATISTICAL METHODS

 

 

 

Date : 03/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

                                                                                    (10 x 2 = 20 marks)

Answer ALL the questions.

 

1. Distinguish between Census and sample.
2. State the objectives of classification of data.
3. Why do we call Arithmetic mean is a good average?
4. When do you say a distribution is skewed? Sketch positive and negative skew ness.
5. What is curve fitting?
6. Write down the normal equations for fitting .
7. If for two variable X and Y, correlation coefficient

find the regression co efficient of X onY.

1. If two regression lines are  and  for two variables X and Y, find the mean values of X and Y.
2. In a report on consumers preference, it was given that out of 500 persons surveyed 410 preferred variety A, 380 preferred variety B and 270 persons liked both. Are the data consistent?
3. State any two characteristics of Yule’s coefficient of Association.

 

PART – B

                                                                                                (5 x 8 = 40 marks)                 

Answer any 5 questions.      

 

1. Draw  ogive curves for the data given below:

Draw Sales (Rs.000)	10-20	20-30	30-40	40-50	50-60	60-70	70-80
No. of Shops	3	6	10	15	8	4	2

 

1. Distinguish between Classification and Tabulation.

 

1. Calculate Karl Pearson’s Co efficient of Skewness for the data given below. On the basis of mean, median and standard deviation.

Wages:	5	6	7	8	9	10	11	12
Workers:	25	45	65	100	30	75	40	50

 

1. Bring out the relationship between to the following data:

x:	0	1	2	3	4
y:	1	1.8	1.3	2.5	2.3

 

1. Fit a parabola of second degree to the following data

x:	0	1	2	3	4
y:	1	1.8	1.3	2.5	2.3

 

1. What do you understand by regression? Why there are two regression equations? What are its uses?
2. From the following data, calculate the coefficient of rank correlation between X and Y

X:	36	56	20	65	42	33	44	50	15	60
Y:	50	35	70	25	58	75	60	45	80	38

 

1. 1660 candidates appeared for a competitive examination. 422 were successful, 256 had attended a coaching class, and of these 150 came out successful. Estimate the utility of the coaching classes.

 

PART – C

                                                (2 x 20 = 40 marks)

Answer any TWO questions.

 

1. a) Calculate mean deviation from median from the following data.

Class Interval:	20-25	25-30	30-40	40-45	45-50	50-55
Frequency:	6	12	17	30	10	10

 

Class Interval:	55-60	60-70	70-80
Frequency:	8	5	2

 

1. b) From the prices of shares X and Y given below, state which share is more stable in value

 

1.  It is known that the readings for x and y given below should follow a law of the form , where a and b are constants

x:	1	2	3	4	5	6	7	8
y:	5.43	6.28	8.23	10.32	12.63	14.86	17.27	19.51

use the method of least squares to find the best values of a and b.

 

1. Calculate and from the data given below

Marks:	0-10	10-20	20-30	30-40	40-50	50-60	60-70
No. of Students:	8	12	20	30	15	10	5

 

1. Calculate the two regression equations Y on X and X on Y and correlation coefficient     .

Price (Rs):	10	12	13	12	16	15
Amount Demanded	40	38	43	45	37	43

Also estimate the likely demand when the price is Rs.20.

 

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