# Loyola College B.Sc. Statistics April 2008 Statistical Methods Question Paper PDF Download

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)

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)

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)

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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