LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS

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.
 Distinguish between Census and sample.
 State the objectives of classification of data.
 Why do we call Arithmetic mean is a good average?
 When do you say a distribution is skewed? Sketch positive and negative skew ness.
 What is curve fitting?
 Write down the normal equations for fitting .
 If for two variable X and Y, correlation coefficient
find the regression co efficient of X onY.
 If two regression lines are and for two variables X and Y, find the mean values of X and Y.
 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?
 State any two characteristics of Yule’s coefficient of Association.
PART – B
(5 x 8 = 40 marks)
Answer any 5 questions.
 Draw ogive curves for the data given below:
Draw Sales
(Rs.000) 
1020  2030  3040  4050  5060  6070  7080 
No. of Shops  3  6  10  15  8  4  2 
 Distinguish between Classification and Tabulation.
 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 
 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 
 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 
 What do you understand by regression? Why there are two regression equations? What are its uses?
 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 
 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.
 a) Calculate mean deviation from median from the following data.
Class Interval:  2025  2530  3040  4045  4550  5055 
Frequency:  6  12  17  30  10  10 
Class Interval:  5560  6070  7080 
Frequency:  8  5  2 
 b) From the prices of shares X and Y given below, state which share is more stable in value
 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.
 Calculate and from the data given below
Marks:  010  1020  2030  3040  4050  5060  6070 
No. of Students:  8  12  20  30  15  10  5 
 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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