Business Statistics

St. Joseph’s College of Commerce B.Com. 2014 IV Sem Business Statistics Question Paper PDF Download

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  1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – APRIL 2014

B.COM (TRAVEL & TOURISM) – IV SEMESTER

BUSINESS STATISTICS

Time: 3 Hrs.                                                                                                                                              Max. Marks : 100

SECTION – A

  1. Answer ALL the Each carries 2 marks.                (10 x 2 =20)

 

  1. Mention the differences between  the two types of class intervals.
  2. A reporter has an average speed of taking 160 words per minute. A typed page takes an average of 200 words . How many sheets of paper will be needed to type out the speech that lasted half an hour assuming that typing is done on both sides of
  3. Differentiate between absolute measure of dispersion and relative measure of dispersion. Give examples.
  4. Define regression. Why the regression lines cannot be used interchangeably. Is it possible to have only one regression line?
  5. State the empirical relation between Mean, Median and Mode. If Mean=120, Mode=135  a moderately asymmetrical distribution, what would be its most probable median value?
  6. Calculate mean, median and mode of the following numbers

3, 2, 0, 4, 2, 4, 5, 4, 6, 5

  1. What are Pictograms and Cartograms?
  2. Why are index numbers called economic barometers?
  3. Fisher’s index number is the ideal index number- give reasons.
  4. What do you mean by irregular variations in Time series?

SECTION- B

II   Answer any FOUR questions. Each carries 5 marks.                                               (4 x 5 = 20)

 

  1. A study conducted for 500 tourists in India revealed the following data regarding the favorite tourist place. The Four tourist spots considered were beaches & Resorts , Historical places, Religious places and Heritage Hotels. Among the respondents 150 were foreigners and the rest were Indians. The number of tourists who liked beachs & resorts and Historical Places were 25% each. The number of people who liked religious places is 50 more than the people who liked Beaches & resorts. 49 Indians liked Heritage hotels and Foreigners who liked beaches & Resorts and  Historical places are 60 and 33 respectively.  Present the above data in an appropriate table.
  2. The following table shows religiosity and death anxiety  scores of 10 people. High score implies greater religiosity or greater death anxiety resp.  Find  correlation coefficient using con-current deviation method. What does the statistics indicate?

 

Religiosity 4 3 11 5 9 6 14 9 10
Death Anxiety 38 42 29 31 28 15 24 17 19

 

  1. Apply 3 yearly moving averages method and determine the trend for the following data.
Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Sales

(in lakhs)

 500 520 550 470 510 540 560 570 590 610
  1. The following information is obtained through a middle class family budget enquiry of Bombay. Calculate consumer price index number by family budget method. What changes have taken place in 2010 compared to 2006?

 

Items Food Rent Clothing Fuel Miscellaneous
% Expenditure 35 15 20 10 20
Price (Rs)  2006 150 50 100 20 60
Price (Rs) 2010 174 60 125 25 90

 

  1. Write a short note on importance of Index numbers.

 

  1. Explain the different positional averages and their uses.

 

SECTION- C

III)   Answer any THREE questions. Each carries 15  marks.                                         ( 3×15 =  45)

 

  1. The following table shows annual profits ( Rs. In crore) of two investment companies  A and B during the given five years. Find the mean and  standard deviation of profits for both the companies A and B. Which company is better?  Which company ensures consistent profit?
Year

Company

 2009 2010 2011 2012 2013
A 70 60 70 60 70
B 60 50 60 80 80

                      

  1. a) The following results are given. The co-efficient of correlation between X and Y is

r= +0.66. Find the two regression lines and estimate the value of X when Y=75.

  X Y
Arithmetic Mean 36 85
 Standard deviation 11 8

 

  1. b) Identify the regression equations and find the means of variables X and Y and the correlation co-efficient   2Y – X – 50 =0,  3Y – 2X – 10=0

(8 +7)

  1. a) From the following data fit a straight line trend through the method of least square. Calculate the trend values.
Year 2005 2006 2007 2008 2009 2010 2011 2012
Expenditure

(Rs. In ‘000)

 43 49 54 62 71 75 78 80

 

  1. b) Calculate Arithmetic mean by step deviation method
Production

In tonnes

 0-

100

 100-

200

 200-

300

 300-

400

 400-

500

 500-

600

 600-

700

 700-

800

 800-

900

 900-

1000
No of

factories

 7 15 10 9 10 12 8 13 9 7

(8+7)

  1. For the following data calculate Laspeyre’s, Paasche’s and Fisher’s Index Numbers. Also prove that Fisher’s Index number satisfies Time Reversal Test and Factor Reversal Test.
Commodity 2005 2012
Price

(Rs)

 Quantity

(Kg)

 Price

(Rs)

 Quantity

(Kg)
I 6 50 10 56
II 2 100 2 120
III 4 60 6 60
IV 10 30 12 24
V 8 40 12 36

 

  1. a ) Present the following data using sub divided bar diagram and percentage bar diagram.
Subject No. of Students
2010-11 2011-12 2012-13
Science 240 280 340
Humanities 560 610 570
Commercw 220 280 370

 

  1. b) Prepare Histogram for the following data and find mode graphically. Also support the value using calculation method.
Wages

(Rs)

 325-350 350-375 375-400 400-425 425-450
Frequency 30 45 75 60 35

(8 + 7)

 

 

 

 

 

 

SECTION- D

  1. IV) Compulsory Question                                                     (1x 15 =  15)

 

  1. A tour operator during a survey asks three families to rank the ten different places visited in Rajasthan in the order of their preference. The data is presented in the table below. Use the method of Rank Correlation  to determine to what extent the families match in their choices?  Interpret the result.

 

Places A B C D E F G H I J
Family I 1 6 5 10 3 2 4 9 7 8
Family II 3 5 8 4 7 10 2 1 6 9
Family III 6 4 9 8 1 2 3 10 5 7

 

 

 

 

 

St. Joseph’s College of Commerce Business Statistics Question Paper PDF Download

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REG NO:

St. Joseph’s college of Commerce (AUTONOMOUS)
END SEMESTER EXAMINATION – march / APRIL 2016
B.COM(T.T.) – IV SEMESTER
C2 12 403: BUSINESS STATISTICS
Duration: 3 Hours                                                                                             Max. Marks: 100
SECTION – A
I) Answer ALL the questions.  Each carries 2 marks.                                        (10×2=20)
  1. Statistics is a useful subject for people working in every walk of life.  Substantiate.
  2. Which measure of central tendency is usually regarded as the best, why?
  3. Explain weighted average.  When should it be applied instead of a simple average?
  4. What is coefficient of dispersion?  What purpose does it serve?
  5. Explain the different types of correlation as explained by Karl Pearson.
  6. What is regression?  How is it different from correlation?
  7. Mention two uses of Index Numbers.
  8. Explain two diagrammatic representations of data with figures.
  9. State briefly the importance of time series analysis in business.
  10. Discuss the limitations of Statistics.
SECTION – B
II) Answer any FOUR questions.  Each carries 5 marks.                                      (4×5=20)
  11. Explain the functions of Statistics.
  12. 150 candidates appeared for a written examination.  Their scores out of 100, are given below, calculate the mean score of these candidates.

Scores No. of candidates
0-10

10-20

20-30

30-40

40-50

50-60

60-70

70-80

80-90

 8

15

17

28

25

24

18

9

6

 
  13. Export earnings of companies are mentioned in the following table:

Earnings (Rs. crores):  5–10    10–15    15–20    20–25    25–30    30-35    35-40

No. of companies:         25        28         32         21           17         14         8

Calculate Range and its Coefficient.

 
  14. A student calculates the value of r as 0.7 when the value of n is 5 and concludes that r is highly significant.  Is he correct?  Also calculate the limits for the population coefficient correlation.

 
   

15.

  

From the following data, construct price index number using simple aggregative method.

Commodities Base year Prices

Rs.

 Current year Prices

Rs.
Milk

Wheat

Apple

House Rent

 11

15

30

3,500

 12.50

16

35

4,500
  16. Fit a trend by the method of semi averages to the following data:

Year:                             2003    2004    2005    2006    2007    2008    2009    2010

Output (in units):          70        65        82       85        93         90        96      100
SECTION – C
III) Answer any THREE questions.  Each carries 15 marks.                                (3×15=45)                                                                                                
  17. From the following income distribution, draw a histogram and locate the mode.  Also verify it through calculations.

Income No. of Employees
0 – 100

100 – 200

200 – 300

300 – 400

400 – 500

500 – 600

600 – 700

 12

25

38

45

32

17

14
  18. Complete the following distribution, if its median is 2600 and the total frequencies is 1500:

Size 1000-

1500

 1500-

2000

 2000-

2500

 2500-

3000

 3000-

4000

 4000-

5000

 5000-

6000
Frequencies 120 ? 400 500 ? 50 20
  19. Calculate Spearman’s Rank correlation co-efficient between Advisement cost and Sales from the following data:

Advertisement cost (‘000s) Sales (in lakhs of Rs.)
39 47
65 53
62 58
90 86
82 62
75 68
25 60
98 91
36 51
78 84
   

 

 

20.

  

 

 

Given below are the data relating to interest rate on housing loan and the amount of housing loan advanced by a bank.

 

Years Rate of Interest (% p.a.) Amount of Housing Loan (in Rs. Crores)
2004 14 3
2005 13 8
2006 11 20
2007 10 35
2008 7 40
2009 5 44
2010 4 50

 

Compute the regression equation of X on Y and Y on X from the above data and estimate the housing loan amount if the rate of interest is reduced to 6%.

 
  21. From the following table calculate the coefficient of correlation by Karl Pearson’s method.

X 6 2 10 4 8
Y 9 11 5 8 7
 

SECTION – D
IV) Case Study – Compulsory question.                                                                (1×15=15)                                                                                           
  22. Share prices of two companies A Ltd. and B Ltd. are recorded as follows:

 

A Ltd. 12 13 15 14 14 14 13 17
B Ltd. 113 114 113 115 117 114 112 114

 

Use standard deviation to find which company’s share prices are more variable?

 

 

 

 

 

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St. Joseph’s College of Commerce II Sem Business Statistics Question Paper PDF Download

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REG NO:

ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – MARCH/APRIL 2016
B.COM (T.T.)– II SEMESTER
C2 15 AR 203 :BUSINESS STATISTICS
Duration: 3 Hours                                                                                    Max. Marks: 100
SECTION – A
I) Answer ALL the questions.  Each carries 2 marks.                                 (10×2=20)
  1. Give the meaning of Statistics.
  2. Three students in a group of 9 failed in the examination. Six students who passed got the marks as 55, 40, 82, 61, 80, and 53. Find the Median.
  3. Define Index Number.
  4. Mention the four components of Times Series.
  5. The average rainfall for a week excluding Sunday was 0.5”. Due to heavy rain on Sunday, the average rain for the week was 1.5. How much rainfall was there on Sunday?
  6. State any two differences between Correlation and Regression Analysis.
  7. What are the different methods of constructing Price Index Numbers?
  8. Explain with a help of scatter diagram perfect negative and positive correlation.
  9. Find the range and coefficient of range from the following:

X 22 24 26 28 30 32 40 42
  10. Mention any two basic functions of MS-Excel.
SECTION – B
II) Answer any FOUR questions.  Each carries 5 marks.                              (4×5=20)
  11. Prepare a frequency distribution of the marks obtained by 50 students in an examination with width of each class interval as 10. Use exclusive method of classification:

57 44 80 75 00 18 45 14 04 64
72 51 69 34 22 83 70 20 57 28
96 56 50 47 10 34 61 66 80 46
22 10 84 50 47 73 42 33 48 65
10 34 66 53 75 90 58 46 39 69
  12. Define Statistics and explain its characteristics in detail.
  13. Calculate the trend values by the method of 4-yearly moving averages:

Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Sales

(Rs)

 464 515 518 467 502 540 557 571 586 612

Sales are given in Lakhs of rupees.

 
  14. Compute the cost of living index number using both the Aggregate Expenditure Method and Family Budget Method from the following information:

 

 

 

Commodity Unit Consumption in Base Year Price in Base Year Price in Current Year
Wheat 200 20 24
Rice 50 30 35
Pulses 50 40 45
Ghee 20 200 300
Sugar 40 25 30
Oil 50 100 120
Fuel 60 50 62.5
Clothing 40 500 600
  15. Compute Spearman’s rank correlation for the following observation:

Candidate 1 2 3 4 5 6 7 8
Judge X 20 22 28 23 30 31 21 24
Judge Y 28 24 22 25 26 27 32 30

Marks are awarded out of 35.

 
  16. The Shareholders Research Centre of India has conducted recently a research-study on price behavior of three leading industrial shares A, B and C for the period 2011 to 2016. The results are published in the Quarterly Journal:

Share Average Price Standard Deviation Current Selling Price
A 18.2 5.4 36.00
B 22.5 4.5 34.75
C 24.0 6.0 39.00

The above figures are given in Rs.

(a) Find Coefficient of Variation & state which share appears to be more stable in value?

(b) If you are the holder of all the three shares, which one would you like to dispose of at present, and why?
    

 SECTION – C
III) Answer any THREE questions.  Each carries 15 marks.                           (3×15=45)                                                                                                
  17.

 

 

 

 

 

 

 Find the standard deviation and coefficient of variation from the following data: (use step deviation method)

 

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No. of Students 12 18 35 42 50 45 20 8

 
  18.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 (a)The following table gives the distribution of items of production and also the relatively defective items among them, according to size groups. Find the correlation coefficient between size and percentage of defective items and its probable error. (Use Karl Pearson’s Assumed Mean Method)

Size-group 15-16 16-17 17-18 18-19 19-20 20-21
No. of Items 200 270 340 360 400 300
No. of Defective Items 150 162 170 180 180 114

 

(b)Using the following data construct Fisher’s Ideal Index and show that it satisfies Factor Reversal test and Time Reversal test:

 

Commodity

 Price (in Rs.) per unit Number of units
Base Year Current Year Base Year Current Year
A 6 8 10 12
B 10 10 5 8
C 5 7 8 10
D 15 20 12 15
E 20 25 15 10

(8+7)
  19. (a)Draw a histogram using graph for the following distribution and find the modal wage. Also check the value by direct calculation.

Daily wages (in Rs.) 200-220 220-240 240-260 260 -280 280-300 300-320 320-340
No. of workers 60 140 110 150 120 100 90

 

(b)“Statistical tools are very helpful in numerous troubles of various fields such as agricultural production, population, industrial growth, sociology, psychology, administration, natural science, etc. Universal application of statistics does not mean that it is free from limitations”. – In the light of this statement briefly discuss the limitations of Statistics.

                                                                                                              (10 +5)
  20. (a) Calculate the value of Mode for the following data (use Grouping Method):

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

 

(b) A computer while calculating the correlation coefficient between two variables X and Y from 25 pairs of observations obtained the following results:

n = 25;  ∑X = 125; ∑X2 = 650; ∑Y = 100; ∑Y2= 460; ∑XY = 508

It was however, discovered at the time of checking that he had copied down two pairs as:

X Y
6 14
8 6

While the correct values were:

X Y
8 12
6 8

Obtain the correct value of coefficient of correlation using assumed mean method.                                                                                            (8+7)

 

 

 
  21. Below are given the annual production (in thousand tonnes) of a fertilizer factory:

 

Year 2010 2011 2012 2013 2014 2015 2016
Production 70 75 90 91 95 98 100

(a) Fit a straight line trend by the method of least squares and depict the trend line on the graph.

(b) Estimate the trend value of production for the year 2017.

 
              SECTION – D

 
IV Case Study – Compulsory question.                                                           (1×15=15)                                                                                           
  22. From the data given below find:

(a) The two regression equations.

(b) The coefficient of correlation between marks in Economics and Statistics.

(c) The most likely marks in Statistics when the marks in Economics are 30.

 

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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