**2 TDC BSTAT 4 (DE)**

**2015**

**(July)**

**COMMERCE**

**Paper: 204**

**(Business Statistics)**

**Full Marks: 90**

**Time: 3 hours**

**The figures in the margin indicate full marks for the questions**

1. (i) Which measure of central tendency may be regarded as the best measure? 1x10=10

(ii) Who had designed the formula for the Standard deviation?

(iv) Write the relationship between Karl Pearson’s coefficient of correlation and the two regression coefficients.

(v) What do you mean by price index number?

(vi) Write the full form of C.L.I.

(vii) What is the main variable in a time series?

(viii) Annual rainfall in Assam is decreasing every year – Which component of time series is involved?

(ix) What is the range of the measure of probability?

(x) What do you mean by forecasting?

2. (a) (i) What do you mean by primary data? 2

(ii) What types of precautions are to be taken while collecting secondary data? 3

(iii) Calculate standard deviation for the following data – 5

X: | 105 | 115 | 125 | 135 | 145 | 155 |

Y: | 8 | 10 | 20 | 12 | 7 | 3 |

(iv) Calculate the missing frequency for the following data. (Given arithmetic mean of the series = 24)

Class Interval: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Frequency: | 5 | 25 | ? | 18 | 7 |

Or

(b) (i) when the sample size is small which method should be used to collect data – sampling method/complete enumeration method. 2

(ii) What do you mean by measures of dispersion? 3

(iii) Why standard deviation is regarded as the best measure of dispersion? 5

(iv) Calculate the coefficient of quartile deviation from the data given below – 6

Class Interval: | 30-32 | 32-34 | 34-36 | 36-38 | 38-40 | 40-42 | 42-44 |

Frequency: | 12 | 18 | 16 | 14 | 12 | 8 | 6 |

3. (a) (i) When two variables are said to be correlated? 2

(ii) Discuss why there should be two lines of regression. 3

(iii) If

, , then 5

(iv) Given the two regression equations andfind

(i) means of x and y. (ii) the correlation coefficient between x and y. 6

(b) (i) When there is a positive correlation? 2

(ii) Write the formula for rank correlation coefficient? When is it used? 3

(iii) The rank correlation coefficient between two variables is 2/3 and the sum of the squares of differences between corresponding ranks is 55. Find the number of pairs of items. 5

(iv) Find the regression equation of x and y from the data given below:- 6

X: | 18 | 20 | 22 | 23 | 27 | 28 | 30 |

Y: | 23 | 25 | 27 | 30 | 32 | 31 | 36 |

4. (a) (i) What does index number measure? 2

(ii) Using Layspere’s formula calculate Price Index Number from the data given below: 3

Items | A | B | C | D | E |

Price in base year | 5 | 3 | 4 | 11 | 7 |

Price in current year | 10 | 4 | 6 | 14 | 10 |

Quantity in base year | 50 | 100 | 60 | 30 | 40 |

(iii) From the data given below calculate the cost of Living Index Number – 5

Group | Index | Weights |

Food | 340 | 60 |

Clothing | 310 | 5 |

House Rent | 220 | 8 |

Fuels | 150 | 9 |

Others | 300 | 18 |

(iv) Using the formula data show that Fisher’s index number satisfies time reversal test. 6

Year 2000 | Year 2010 | |||

Items | Price | Quantity | Price | Quantity |

A | 8 | 6 | 12 | 5 |

B | 10 | 5 | 11 | 6 |

C | 7 | 8 | 8 | 5 |

Or

(b) (i) Write any two uses of index numbers. 2

(ii) The wholesale price index of 2012 taking 2005 as base year is 130, - from this what conclusion can you draw about price rise? 3

(iii) Which index number is regarded as the ideal index number and why? 5

(iv) Calculate Fisher’s Price Index number from the data given below –

Base Year | Current Year | |||

Items | Price | Quantity | Price | Quantity |

A | 5 | 50 | 10 | 56 |

B | 3 | 100 | 4 | 120 |

C | 4 | 60 | 6 | 60 |

D | 11 | 30 | 14 | 24 |

E | 7 | 40 | 10 | 36 |

5. (a) (i) What do you mean by a time series? 2

(ii) What do you mean by seasonal variation in a time series? 3

(iii) Calculate trend values by using 3 yearly moving averages – 5

Year: | |||||||

Values: | 18 | 24 | 25 | 20 | 16 | 8 | 2 |

(iv) Using the method of least squares, calculate trend values for the following data – 6

Year: | |||||

Production: | 40 | 20 | 25 | 10 | 5 |

(b) (i) Write the additive model of time series analysis. 2

(ii) Write about the uses of time series analysis. 3

(iii) Write a short note about the least square principle. 5

(iv) Using the method of least squares calculate the trend values for the following data – 6

Year: | 2001 | 2002 | 2003 | 2004 | 2005 |

Value: | 10 | 12 | 8 | 10 | 14 |

6. (a) (i) When two coins are tossed simultaneously, what is the probability of getting one head and one tail? 2

(ii) Prove the addition theorem of probability. 3

(iii) What are the assumptions for business forecasting? 5

(iv) Explain any one method of forecasting. 6

Or

(b) (i) 3 balls are drawn from a box containing 5 white and 4 black balls. What is the probability that all the 3 balls are white. 2

(ii) Find the probability of throwing a total of 8 when 2 dice are thrown together. 3

(iii) Mention the purpose of business forecasting. 5

(iv) Write a note about the time series as a tool of business forecasting? 6