LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

YB 08

B.COM/B.B.A – DEGREE EXAMINATION – CORP.SEC.,/BUS.ADMN.

THIRD SEMESTER – April 2009

ST 3105/ST 3102 – INTRODUCTION TO STATISTICS

Date & Time: 17/04/2009 / 1:00 – 4:00 Dept. No. Max. : 100 Marks

SECTION A

Answer ALL questions. (10 × 2 = 20 Marks)

Define statistics and give some application of statistics.
State the various methods of collecting secondary data.
State any two methods of probability sampling.
What are the methods of classification?
State merits and demerits of harmonic mean
Find the value of mean deviation about the mean for the following data:

50, 70, 45, 20, 80, 90, 25, 30, 40, 10.

What are the various measures of dispersion?
You are given that Sk = 0.8, Mean = 40 and Mode = 36 then find Standard deviation.
The first four central moments are 0, 2.5, 0.7 and 18.75. Comment on the skewness and kurtosis of the distribution

10.What are the properties of correlation coefficient?

SECTION B (5 X 8 = 40 Marks)

Answer any FIVE questions

Explain any four methods of graphical representation of data.
The A.M calculated from the following frequency distribution is known to be 67.5 inches.

Find the missing frequency.

Height in inches	60 – 6 2	63 – 65	66 – 68	69 – 71	72 – 74
Frequency	15	54	?	81	24

The Mean marks of 100 students were found to be 40. Later on it was discovered that a

score of 53 was misread as 83. Find the correct mean.

Find the quartile deviation and coefficient of quartile deviation for the following data:

Marks	0-10	10 – 20	20-30	30-40	40-50	50-60
Frequency	8	20	25	30	12	5

Calculate the mean deviation about the Mean for the following data.

Class Interval	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Frequency	8	12	10	8	3	2	7

Ten competitors in a beauty contest are ranked by three judges in the following order:

J1	4	2	3	5	7	1	6	8	10	9
J2	4	1	5	3	6	2	9	10	7	8
J3	2	3	4	5	8	1	7	9	6	10

Use Spearman’s rank correlation method to determine which pair of judges have the nearest approach.

800 candidates of both sex appeared at an examination. The boys out numbered the girls by 15 % of the total. The number of candidates who passed exceed the number failed by 480. Equal number of boys and girls failed in the examination. Prepare a 2×2 table, find the coefficient of association and comment.

Explain seasonal indices with an illustration.

SECTION C (2 X 20 = 40 Marks)

Answer any TWO questions

(a) From the following data find mean, median and mode. Verify the empirical relation.

C.I	3-4	4-5	5-6	6-7	7-8	8-9	9-10
Frequency	83	27	25	50	75	38	18

(b) Find the mean and variance of the combined sample from the following data:

Sample

Mean

Variance

Size

III

115

113

120

( 10 + 10 )

Calculate Skewness and kurtosis for the following distribution and interpret them.

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	5	20	15	45	10	5

(a) The following table gives the aptitude test scores and productivity indices of 10 workers

selected at random.

Aptitude scores(x)	60	62	65	70	72	48	53	73	65
Productivity index(y)	68	60	62	80	85	40	52	62	60

Find the two regression equations and estimate:

(i) the productivity index of a worker whose test score is 92.

(ii) the test score of a worker whose productivity index is 75.

(b) Calculate Karl Pearson`s coefficient of correlation from the following data:

Demand (kg)	85	93	95	105	120	130	150	160
Price (Rs.)	15	18	20	24	30	35	40	50

(10 + 10)

(a ) From the following data calculate the four-year moving average and determine the trend

values. Find the short-term fluctuation.

Year	1958	1959	1960	1961	1962	1963	1964	1965	1966	1967
Value	50.0	36.5	43.0	44.5	38.9	38.1	32.6	41.7	41.1	33.8

(b) Fit a straight line trend through the method of least squares for the following data

and estimate the trend values

Year	1982	1983	1984	1985	1986	1987	1988
Sales	110	115	130	140	145	160	180

(10 + 10)

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