Loyola College Introduction To Statistics Question Papers

Loyola College B.Sc. Corporate Sec. & Business Admin Nov 2012 Introduction To Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – CORPORATE SEC. & BUSINESS ADMIN.

THIRD SEMESTER – NOVEMBER 2012

ST 3105 – INTRODUCTION TO STATISTICS

 

 

Date : 07/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A

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

 

  1. Distinguish between classification and tabulation.
  2. What are the different types of diagrams?
  3. State any two methods of probability sampling.
  4. State merits and demerits of mean
  5. Find the median of the following data:

84 , 91, 72 , 68, 87 ,78,

  1. Define dispersion. What are the measures of dispersion?
  2. 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.
  3. What are the properties of correlation coefficient.
  4. What are the various components of a time series?
  5. State Yule’s coefficient of variation.

                                                                        SECTION – B                                             

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

 

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

(a)   Cluster Sampling   (b) Random sampling.

 

  1. 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.

 

  1. Calculate the harmonic mean for the following :
 x 10 12 14 16 18 20
F 7 9 10 4 3 6

 

  1. 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

 

  1. 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

 

 

 

 

  1. 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)

  1. 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 1stquarter 2ndquarter 3rdquarter 4thquarter
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

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      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)

 

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

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

  1. What are the various measures of dispersion?
  2. You are given that Sk = 0.8, Mean = 40 and Mode = 36 then find Standard deviation.
  3. 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

 

  1. Explain any four methods of graphical representation of data.
  2. 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
  1. 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.

  1. 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
  1. 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
  1. 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.

 

  1. 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.

 

  1. Explain  seasonal indices with an illustration.

                                                      SECTION   C                                   (2 X 20  =  40 Marks)

             Answer any TWO questions

 

  1. (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
I

II

III

 115

113

120

 64

36

49

 90

50

60

( 10 + 10 )

  1. 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

 

 

 

 

  1. (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)

  1. (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

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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)

 

  1. What are the limitations of statistics
  2. State the various methods of collecting primary data.
  3. State any two methods of non-probability sampling.
  4. Distinguish between classification and tabulation.
  5. List the various methods of representing a frequency distribution graphically.
  6. Define quartile deviation.
  7. Positive and negative correlation.
  8. 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.
  9. List the various components of a time series.
  10. Find the regression equation of X on Y from the following data:

E x2 = 164 ,  Ex = 24,  Ey = 44,  Ey 2= 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

 

  1. 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.

  1. 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

 

 

 

 

  1. 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.

 

  1. 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

 

 

 

 

  1. 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.

  1. 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.

 

  1. 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

 

  1. (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.

  1. (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

 

  1. 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

 

 

 

 

 

  1. (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

 

 

 

  1. (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.

 

  1. (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

 

 

 

 

 

 

 

  1. (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

by

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)

  1. Mention the various uses of statistics in Business and Industry.
  2. Distinguish between ‘Census’ and ‘Sampling’ methods of collection of data
  3. What are the different types of bar diagram?
  4. State the different components of time series.
  5. 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.
  6. From the following find out whether the data are consistent or not

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

  1. 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.
  2. The first four central moments of distribution are 0, 2.5, 0.7 and 18.75.  Comment on kurtosis of the distribution.
  3. 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)?
  4. 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)

  1. Distinguish between probability and non-probability sampling.  Examine critically the various types of probability sampling.
  2. 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.
  3. 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

 

  1. 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

 

  1. 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

 

  1. 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

 

 

 

  1. 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

 

  1. 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)

 

  1. 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 –

 

  1. 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.

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

 

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

 

  1. From the data given below find:
  1. The two regression equations
  2. The coefficient of correlation between marks in Economics and Statistics
  3. The most likely marks in Statistics when the marks in Economics are 30
  4. 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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