**TDC BSTAT 4 (DE)**

**2016**

**(July)**

**COMMERCE**

**Paper: 204**

**(Business Statistics)**

**Full Marks: 90**

**Time: 3 hours**

The figures in the margin indicate full marks for the questions

1. Answer all the questions: 1x10=10

- Fill up the blanks: A sample is a representative ____ of the population.

- Which is the best measure of dispersion?
- Define a price Index Number.
- When does Spearman’s Rank Correlation Coefficient used?
- Which is the main variable in a time series?
- Write the additive model of time series analysis.
- What do you mean by business forecasting?
- What is the range of the value of probability?
- If , what should be the value of

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

(ii) If mean and median of a moderately skewed distribution are 36.1 and 35.0 respectively, what should be the value of mode? 3

(iii) Calculate median and mode of the following distribution – 5

Class Interval: | 20-24 | 24-28 | 28-32 | 32-36 | 36-40 |

Frequency: | 20 | 45 | 36 | 18 | 1 |

(iv) Calculate the coefficient of variation from the following data – 6

X: | 30 | 32 | 34 | 36 | 38 | 40 | 42 |

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

Or

(b) (i) Calculate the value of mode and median of 2, 3, 3, 4, 4, 5, 3, 7, 7, 8 and 5. 2

(ii) Prove for any two values - . 3

(iii) The mean monthly salary of 1,000 employees of a company is Rs. 5,000. If the mean monthly salary of the male and female employees of the company is Rs. 5,200 and Rs. 4,200 respectively, find the number of male employees of the company.

(iv) Calculate the value of standard deviation for the data given below – 6

C.I.: | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 |

F: | 12 | 13 | 10 | 18 | 15 | 12 |

3. (a) (i) Prove the relationship between coefficients of regression and the coefficient of correlation. 2

(ii) Discuss the differences between regression and correlation. 3

(iii) Calculate spearman’s coefficient of rank correlation from the following data – 5

X: | 5 | 8 | 12 | 20 | 16 | 40 | 35 | 26 |

Y: | 8 | 12 | 6 | 4 | 10 | 25 | 16 | 19 |

(iv) Given

and, calculate the value of correlation coefficient. 6

Or

(b) (i) Write why dot diagrams are used. 2

(ii) What is Karl Pearson’s Coefficient of Correlation? What is its range? 3

(iii) The sum of squares of differences between the ranks of two variables is 231 and the coefficient of rank correlation is – 0.4. Find the number of pairs of items. 5

(iv) Calculate coefficient of correlation for the data given below – 6

X: | 104 | 111 | 104 | 114 | 118 | 117 | 105 | 108 | 100 | 106 |

Y: | 57 | 55 | 47 | 45 | 45 | 50 | 64 | 63 | 62 | 66 |

4. (a) (i) What do you mean by wholesale price index number? 2

(ii) Prove that Fisher’s Index Number satisfies factor reversal test. 3

(iii) Using Paasche’s formula calculate quantity index number from the data given below: 5

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 |

(iv) Find Fisher’s Price Index Number from the data given below – 6

Quantity | Price | |||

Items | Base year | Current year | Base year | Current year |

A | 10 | 12 | 12 | 15 |

B | 5 | 10 | 8 | 12 |

C | 12 | 15 | 10 | 12 |

D | 3 | 10 | 15 | 20 |

Or

(b) (i) Write about the uses of cost of living index number. 2

(ii) Write a short note on time reversal test. 3

(iii) Why Fisher’s Index Number is regarded as an ideal index number? 5

(iv) Calculate cost of living index from the data given below and hence calculate how the dearness allowance of an employee should be increased to keep the level of cost of living stable – 6

Items | Weight | Price of base year | Price of current year |

Food Rent Clothing Fuel Others | 35 20 15 10 20 | 250 60 80 50 200 | 270 80 100 50 250 |

5. (a) (i) Write the multiplicative model used in time series analysis. 2

(ii) Discuss the graphic method of time series analysis. 3

(iii) Calculate trend values by using the method of 3-yearly moving averages – 5

(Year): | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 |

(Production): | 75 | 83 | 109 | 129 | 134 | 148 | 156 |

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

(Year): | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 |

(Number): | 56 | 55 | 51 | 47 | 42 | 38 | 35 |

Or

(b) (i) If the annual trend equation of production of a factory be, what is the monthly trend of production? 2

(ii) Write a short note on moving averages. 3

(iii) Calculate 3-yearly moving average for the data given below –

(Year): | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 |

(Value): | 28 | 38 | 46 | 40 | 56 | 70 | 60 |

(iv) Using the method of least squares find the trend line equation. 6

(Year): | 2011 | 2012 | 2013 | 2014 | 2015 |

(Production): | 10 | 12 | 8 | 10 | 14 |

6. (a) (i) Define probability. 2

(ii) In a single toss of two coins find the probability of getting two heads. 3

(iii) Write a short note on “long term forecasting” and “short term forecasting”. 5

(iv) What is business forecasting? Discuss the limitations of statistical forecasting. 6

Or

(b) (i) Define independent variable. 2

(ii) Four persons in a group of 20 are graduates. If a 4 persons are selected at random what is the probability that all are graduates? 3

(iii) What are the assumptions of forecasting? 5

(iv) Write in details about any one method of business forecasting. 6