LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

First SEMESTER – NOVEMBER 2003

ST 1500/ STA 500 STATISTICAL METHODS

07.11.2003 Max: 100 Marks

9.00 – 12.00

section – A

Answer ALL questions (10 ´ 2 = 20 Marks)

Give the definition of statistics according to Croxton and Cowden.
Comment on the following: “ Sample surreys are more advantageous than census”.
Give an example for

(i) Quantitative continuous data (ii) Discrete time series data

Prove that for any two real numbers ‘a’ &’b’ , A.M £M.
Mention any two limitations of geometric mean.
From the following results obtained from a group of observations, find the standard deviation. S(X-5) = 8 ; S(X-5)²= 40; N = 20.

For a moderately skewed unimodal distribution, the A.M. is 200, the C.V.

is 8 and the Karl Pearson’s coefficient of skewness is 0.3. Find the mode

of the distribution.

Given below are the lines of regression of two series X an Y.

5X-6Y + 90 = 0

15X -8Y-130 = 0

Find the values of .

Write the normal equations for fitting a second degree parabola.
Find the remaining class frequencies, given (AB) = 400;

(A) = 800; N=2500; (B) = 1600.

SECTION – B

Answer any FIVE questions. (5 ´8 = 40 Marks)

Explain any four methods of collecting primary data.
Draw a histogram and frequency polygon for the following data.

Variable	Frequency	Variable	Frequency
100-110	11	140-150	33
110-120	28	150-160	20
120-130	36	160-170	8
130-140	49

Also determine the value of mode from the histogram.

Calculate arithmetic mean, median and mode from the following

frequency distribution.

Variable	Frequency	variable	Frequency
10-13	8	25-28	54
13-16	15	28-31	36
16-19	27	31-34	18
19-22	51	34-37	9
22-25	75	37-40	7

The number of workers employed, the mean wages (in Rs.) per month and standard deviation (in Rs.) in each section of a factory are given below. Calculate the mean wages and standard deviation of all the workers taken together.

Section	No. of workers employed	Mean Wages (in Rs.)	Standard deviation (in Rs.)
A	50	1113	60
B	60	1120	70
C	90	1115	80

Calculate Bowley’s coefficient of skewness from the following data.

Variable	frequency
0-10	12
10-20	16
20 -30	26
30- 40	38
40 -50	22
50-60	15
60- 70	7
70 -80	4

Calculate Karl Person’s coefficient of correlation from the following data.

X	44	46	46	48	52	54	54	56	60	60
Y	36	40	42	40	42	44	46	48	50	52

Explain the concept of regression with an example.
The sales of a company for the years 1990 to 1996 are given below:

Year	1990	1991	1992	1993	1994	1995	1996
Sales (in lakhs of rupees)	32	47	65	88	132	190	275

Fit an equation of the from Y = ab^Xfor the above data and estimate the

sales for the year 1997.

SECTION – C

Answer any TWO questions. (2 ´ 20 = 40 Marks)

a) Explain (i) Judgement sampling (ii) Quota sampling and

(iii) Systematic sampling methods with examples.

(i) Draw a blank table to show the distribution of personnel in a

manufacturing concern according to :

Sex: Males and Females.
Salary grade: Below Rs.5,000; Rs.5,000 -10,000;

Rs.10,000 and above.

Years: 1999 and 2000
Age groups: Below 25, 25 and under 40, 40 and above

(ii) Draw a multiple bar diagram for the following data:

Year	Sales (in’000Rs.)	Gross Profit	Net profit
1992	120	40	20
1993	135	45	30
1994	140	55	35
1995	150	60	40

(10+5+5)

a) (i) An incomplete distribution is given below

Variable	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	10	20	f₁	40	f₂	25	15

Given the median value is 35 and the total frequency is 170, find

the missing frequencies f₁ and f_2.

Calculate the value of mode for the following data:

Marks	10	15	20	25	30	35	40
Frequency	8	12	36	35	28	18	9

b) Explain any two measures of dispersion. (7+7+6)
a) The scores of two batsman A and B is 10 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 consistent in scoring.

Calculate the first four central moments and coefficient of skewness from the

following distribution.

Variable	frequency	Variable	Frequency
25-30	2	45-50	25
30-35	8	50-55	16
35-40	18	55-60	7
40-45	27	60-65	2

(10+10)

a) From the following data obtain the two regression equations and calculate

the correlation coefficient.

X	60	62	65	70	72	48	53	73	65	82
Y	68	60	62	80	85	40	52	62	60	81

b) (i) Explain the concept of Kurtosis.

(ii) In a co-educational institution, out of 200 students 150 were boys.

They took an examination and it was found that 120 passed, 10 girls

had failed. Is there any association between gender and success in the

examination? (10+5+5)

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