Loyola College B.Com Corporate & Secretaryship Nov 2009 Introduction To Statistics Question Paper PDF Download

Define dispersion. What are the measures of dispersion?
The average rainfall of a city from Monday to Saturday is 0.3 inches. Due to heavy rainfall on Sunday the average rainfall of the week increased to 0.5 inches. Find the rainfall on Sunday.
What are the properties of correlation coefficient.
What are the various components of a time series?
State Yule’s coefficient of variation.

SECTION – B

Answer any FIVE questions: (5 X 8 = 40 Marks)

What are the limitations of statistics?
Write short notes of the following:

(a) Cluster Sampling (b) Random sampling.

The mean of 200 items is 60.Later on it was discovered that one of the observation with value 182 was wrongly taken as 82 . Find the correct mean.

Calculate the harmonic mean for the following :

x	10	12	14	16	18	20
F	7	9	10	4	3	6

Compute mean deviation abut median from the following data:

X	0-10	10-20	20-30	30-40	40-50	50-60	60-70
F	8	12	17	14	9	7	4

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

Demand (kg)	95	96	98	110	115	125	130	140
Price (Rs.)	25	26	23	27	30	33	35	40

Calculate the trend values for the following data using 3 yearly moving average

Year	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010
Sales	26	27	29	32	35	38	35	34	30	32

18.Out of 900 persons, 300 were literates and 400 had travelled beyond the limits of their district.100 of

the literates were among those who had not travelled. Is there any relationship between literacy and

travelling?

SECTION – C (2 X 20 = 40 Marks)

Answer any TWO questions

19.(a) Draw a histogram and frequency polygon on the basis of the following data:

Mid value	18	25	32	39	46	53	60
Frequency	10	15	32	42	26	12	9

(10)

19.(b) Calculate the mean, median and mode from the following data and verify the empirical relationship.

C.I	1-10	11-20	21-30	31-40	41-50	51-60	61-70	71-80	81-90	91-100
F	5	9	12	15	10	9	7	5	6	4

(10)

20.(a) The scores of two players A and B in 12 rounds are given below:

A	84	87	80	85	88	87	89	98	95	94	92	91
B	87	84	80	90	85	94	96	82	85	84	86	81

(10)

Identify the better player and the more consistent player. (10)

20.(b) From the following data compute Bowley’s coefficient of skewness.

Marks	40 – 50	50 – 60	60 -70	70 – 80	80 – 90
No.of students	20	25	28	23	15

(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	10	15	20	27	14	12

(20)

22.(a) Fit a straight line trend for the following data by the method of least squares. Also estimate the trend value for the Year 2005.

Year	1996	1997	1998	1999	2000	2001
Production	12	10	14	15	16	20

(10)

22.(b) Calculate the seasonal indices from the following data using the simple average method.

Year	1^stquarter	2^ndquarter	3^rdquarter	4^thquarter
1974	72	68	80	70
1975	76	70	82	74
1976	74	66	84	80
1977	76	74	84	78
1978	78	74	86	82

(10)

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Loyola College B.Com Corporate & Secretaryship April 2009 Introduction To Statistics Question Paper PDF Download

October 23, 2017 by 01 prakash

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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Loyola College B.Com Nov 2008 Introduction To Statistics Question Paper PDF Download

October 20, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Com., B.B.A. DEGREE EXAMINATION – COMMERCE & COR.SECR.

BA 05

THIRD SEMESTER – November 2008

ST 3105 / ST 3102 – INTRODUCTION TO STATISTICS

Date : 11-11-08 Dept. No. Max. : 100 Marks

Time : 9:00 – 12:00

SECTION A

Answer ALL questions. (10 x 2 = 20 marks)

What are the limitations of statistics
State the various methods of collecting primary data.
State any two methods of non-probability sampling.
Distinguish between classification and tabulation.
List the various methods of representing a frequency distribution graphically.
Define quartile deviation.
Positive and negative correlation.
Pearson’s coefficient of skewness is – 0.7 and the value of the median and standard deviation are 12.8 and 6 respectively. Determine the value of the mean.
List the various components of a time series.
Find the regression equation of X on Y from the following data:

E x² = 164 , Ex = 24, Ey = 44, Ey²= 574 and Exy =306, N = 10

Find the value of X when Y = 6.

SECTION B (5 X 8 = 40 Marks)

Answer any FIVE questions

Below is given the frequency distribution of marks in mathematics obtained by 100 students in a class

Marks	20 – 29	30 – 39	40 – 49	50 – 59	60 – 69	70 – 79	80 – 89	90 -100
No.of students	7	11	24	32	9	14	2	1

Draw the Ogives( “ less than “ and “ more than” type) for this distribution and use it to determine the

Median.

Compute the geometric mean from the data given below:

Marks	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
No.of students	8	12	18	8	6

The following are some particular of the distribution of weights of boys and girls in a clas.

Boys Girls

Number 100 50

Mean weight 60 kg 45 kg

Variance 9 4

Find the standard deviation of the combined data.

Find 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

The marks obtained by the students in statistics and accounts are as following

Statistics	60	62	68	76	72	42	35	78	30	90
Accounts	50	66	58	74	60	40	28	64	38	88

Compute the ranks for the two subjects and find the coefficient of correlation of ranks.

16.The following table gives age ( X ) in years of cars and annual maintenance cost Y (In hundred Rs.)

X	1	3	5	7	9
Y	15	18	21	23	22

Estimate the maintenance cost for a 4 – year old car after finding the regression equation.

200 candidates appeared for a competitive examination and 60 of them succeeded. 35 received

special coaching and out of them 20 candidates succeeded. Prepare a 2×2 contingency table and

using Yule’s coefficient, discuss whether special coaching is effective or not.

Explain briefly the various methods of determining trend in the analysis of time series. Explain the

Merits and demerits of each method.

SECTION C (2 X 20 = 40 Marks)

Answer any TWO questions

(a) The scores of two players A and B in 12 rounds are given below:

X	74	75	78	72	78	77	79	81	79	76	72	71
Y	87	84	80	88	89	85	86	82	82	79	86	80

Identify the better player and the more consistent player.

(b) From the following data compute Bowley’s coefficient of skewness.

Income(Rs.)	Below 200	200 -400	400 – 600	600 – 800	800 – 1000	1000 above
No.of pearsons	25	40	85	75	16	16

Calculate Skewness and kurtosis for the following distribution

Class Interval	1 – 5	6 – 10	11 – 15	16 – 20	21 – 25	26 – 30	31 – 35
Frequency	3	4	68	30	10	6	2

(a) Calculate the correlation coefficient between X and Y from the following data:

X	61	72	73	63	84	80	66	76
Y	40	52	49	43	61	58	42	58

(b) In a laboratory experiment on correlation research study, the equation of the two regression

lines Were found to be 2x – y + 1 = 0 and 3x – 2y +7 = 0. Find the mean of X and Y. Also

worked the Values of the regression coefficient of correlation between the two variables x and y.

(a ) Calculate seasonal indices by the ratio to moving average method from the following data.

Wheat Prices ( in rupees quintal )

Quarter /Year	1972	1973	1974	1975
I	75	86	90	100
II	60	65	72	78
III	54	63	66	72
IV	59	80	85	93

(b) Fit a straight line trend equation by the method of least square and estimate the trend values

Year	1961	1962	1963	1964	1965	1966	1967	1968
Value	80	90	92	83	94	99	92	104

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Loyola College B.B.A. Business Administration April 2008 Introduction To Statistics Question Paper PDF Download

October 13, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

NO 8

B.B.A & B.Com. DEGREE EXAMINATION – BUS.ADMIN. & CORP.

THIRD SEMESTER – APRIL 2008

ST 3105/ 3102 – INTRODUCTION TO STATISTICS

Date : 07-05-08 Dept. No. Max. : 100 Marks

Time : 9:00 – 12:00

SECTION- A

Answer all the questions (10×2=20 marks)

Mention the various uses of statistics in Business and Industry.
Distinguish between ‘Census’ and ‘Sampling’ methods of collection of data
What are the different types of bar diagram?
State the different components of time series.
The mean heights of 25 male workers in a factory is 61 inches and mean height of 35 female workers in the same factory is 58 inches. Find the combined mean height of 60 workers in the factory.
From the following find out whether the data are consistent or not

(A) =100, (B) = 150, (AB) = 60, N = 500

The arithmetic mean of a group of 75 observations is 27. It was later discovered that one observation was wrongly read as 43 instead of the correct value 53. Calculate correct mean.
The first four central moments of distribution are 0, 2.5, 0.7 and 18.75. Comment on kurtosis of the distribution.
An automobile driver travels from plain to hill station 100 Km distance at an average speed of 30 km per hour. He then makes the return trip at average speed of 20 km per hour. What is his average speed over the entire distance (200 km)?
If the upper quartile of a series is 40 and lower quartile is 15, find out the value of quartile deviation and coefficient of quartile deviation.

SECTION – B

Answer any five questions (5×8=40 marks)

Distinguish between probability and non-probability sampling. Examine critically the various types of probability sampling.
In order to ascertain if the marriage has any effect on the examination results of students, 1,000 students were selected at random. There were Hindus, Muslims & Christians of the 1000 students, 375 were married. Of the married students, 167 passed and of the unmarried students, 203 failed. Find Yule’s coefficient of association between marriage and failure of students in the examination.
Draw ogive by less than and more than methods for the following and determine the median graphically:

Marks	0-6	6-12	12-18	18-24	24-30	30-36
No. of students	4	8	15	20	12	6

Obtain the Spearman’s rank correlation coefficient between the variables X and Y from the following pairs of observed values.

X	50	55	65	50	55	60	50	65	70	75
Y	110	110	115	125	140	115	130	120	115	160

Fit a straight line trend by the method of least squares to the following data:

Year	1990	1991	1992	1993	1994	1995	1996	1997
Sales (‘000)	38	40	65	72	69	67	95	104

Estimate the sales for the year 2000

Calculate Karl Pearson’s coefficient of skewness:

Variable	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency	5	6	11	21	35	30	22	11

Compute mode using grouping and analysis table from the following frequency distribution of marks at a test in English.

Marks	5	10	15	20	25	30	35	40	45	50
No. of students	20	43	75	76	72	45	39	9	8	6

Find out the mean deviation from the median for the following data:

Age (years)	4-6	6-8	8-10	10-12	12-14	14-16	16-18
No. of Students	30	90	120	150	80	60	20

SECTION – C

Answer any two questions (2×20=40 marks)

Calculate Karl Pearson’s coefficient of correlation from the following data:

X Y	200-300	300-400	400-500	500-600	600-700
10-15	–	–	–	3	7
15-20	–	4	9	4	3
20-25	7	6	12	5	–
25-30	3	10	19	8	–

The scores of two batsman A and B in ten 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 more consistent in scoring.

Find the seasonal variation by the ratio-to-trend method from the data given below:

Year	1^st quarter	2nd quarter	3rd quarter	4th quarter
2001	86	95	96	99
2002	96	102	104	110
2003	103	108	106	107

From the data given below find:

The two regression equations
The coefficient of correlation between marks in Economics and Statistics
The most likely marks in Statistics when the marks in Economics are 30
The most likely marks in Economics when the marks in Statistics are 35

Marks in Economics	25	28	35	32	31	36	29	38	34	32
Marks in Statistics	43	46	49	41	36	32	31	30	33	39

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