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*Tribhuvan University*

*2076*

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*B.B.S.(4yrs.)/First year*

*Business Statistics*

*Full Marks: 100*

*Pass Marks: 35*

*Time: 3hrs.*

*Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicat*e *full marks.*

*Group A*

*Brief Answer Questions [10×2=20]*

*Attempt ALL Questions.*

##### 1* The mean of 200 items was 50 50.Later on it was found that two items were wrongly taken as 92 and 8 instead of 192 and 88.Find the correct mean.*

*2 In a batch of 15 students ,3 students failed in an examination .The marks of passed 12 students were 9,6,7,8,10,9,7,5,7.What was the median mark of all 15 students.*

*3 In a moderately skewed frequency distribution, the mean is 10 and its median is 9 .if the coefficient of variation is 20%.Find the Pearson’s coefficient of skewness of the distribution.*

##### 4* List out the various methods of collecting primary data and secondary data.*

*5 Calculate the lower and upper quartiles from the following marks distribution.*

marks | below 25 | 25-29 | 30-34 | 35-39 | 40-44 | above 44 |

students | 5 | 12 | 22 | 25 | 17 | 9 |

*6 If regression coefficient of Y on X (byx)=-0.61 and regression coefficient X on Y (bxy)=-0.53, calculate the coefficient of correlation and interpret the result.*

*7 The standard deviation of symmetrical distribution is 5.What must be the value of fourth moment about mean in order that the distribution be mesokurtic ?*

*8 A bag contains 20 balls numbered from 1 to 20 .One ball is drawn at random .Find the probability that the number of the drawn ball be multiple of (1) 3 or 7 (2) 3 or 5*

*9 Calculate the price index number from the following data by simple aggregative method. *

commodities | A | B | C | D | E |

price in 2075 | 125 | 105 | 260 | 150 | 250 |

price in 2076 | 125 | 155 | 250 | 160 | 300 |

*10 The following table shows the pay off matrix related to the demand and strategy of a business person. What should be the the decision if he /she uses (1) maximax criterion (2)maximin criterion ?*

Demand | demand | ||

strategy | D1 | D2 | D3 |

S1 | 300 | 100 | 80 |

S2 | 200 | 120 | 60 |

S3 | 80 | 60 | 20 |

*Group B*

*Attempt any FIVE Questions *[5*10=50]

*Descriptive Answer Questions*

##### 11* List the five number summary and prepare a box and whisker plot from the following information .Also comment the nature of frequency distribution.*

class size | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

frequency | 10 | 12 | 25 | 35 | 40 | 50 |

*12 Solve the following system of equations by using determinant method.*

*2x+5y-z=-3 , 4x+3y+2z=1 ,x+2y+3z+-5*

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##### 13* Calculate the Fishers ideal index number for the following data and show that it satisfies*

##### 1 *Time Reversed Test and*

##### *2 Factor Reversed Test *

2018 | 2018 | 2019 | 2019 | |

commodity | price | quantity | price | quantity |

A | 8 | 60 | 12 | 58 |

B | 4 | 110 | 4 | 125 |

C | 6 | 70 | 8 | 70 |

D | 12 | 40 | 14 | 38 |

*14 Fit straight trend by the method of least square to the data given below. Also find the trend values and predict the sales for the year 2022*

year | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 |

sales (000 units) | 15 | 16 | 17 | 16 | 19 | 23 | 25 |

*15 A factory manufactures three types of white sheets papers 1 , 2, 3 and distributes them in two markets A and B .The sales of papers during one year are given below*

PAPERS | PAPERS | PAPERS | |

markets | 1 | 2 | 3 |

A | 12000 | 5000 | 23000 |

B | 14000 | 22000 | 13000 |

*a If the unit sales prices of paper 1, 2 and 3 are RS 5, RS 4, RS 3 respectively ,find the total revenue in each markets with the helps of matrix algebra*

*b If the unit costs of the above papers are RS 3, RS 2 and RS 1 respectively ,find the gross profit*

*16 The following is the net profits of two companies in millions of rupees, find which company shows the greatest consistency in the net profit. justify your answer with statistical evidences.*

company A | 18 | 19 | 23 | 19 | 25 | 23 | 27 |

company B | 17 | 18 | 22 | 23 | 24 | 25 | 25 |

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*Group C*

*Attempt any TWO Questions *[2*15=30]

*Analytical Answer Questions*

*17 A family income and its percentages expenditures on food for 100 families gave the following bivariate frequency distribution. Find out if there exists any relationship between family income and expenditures on food and interpret the results .Also test the significance of the result. Estimate the percentages expenditures on food when family income =Rs 90000*

family income | family income | family income | family income | family income | |

food expenditures% | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |

15 | – | – | – | 3 | 7 |

20 | – | 4 | 9 | 4 | 3 |

25 | 7 | 6 | 12 | 5 | – |

30 | 3 | 10 | 19 | 8 | – |

*18 The following distributrion shows the frequency distribution of weekly expenditures on food of students in certain locality of kathmandu city. Describe the various characteristics features of the frequency distribution .Also comment the nature of the distribution*

Expenditure | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 | 100-120 |

Number of students | 10 | 15 | 28 | 33 | 40 | 35 | 25 | 14 |

*19 What do you mean by linear programming model? A person requires minimum 10,12, and 12 units of chemicals A,B ands C respectively. A liquid product contains 5,2 and 1 units of A,B C per jar .A dry product contains 1,2,3 units of A,B,C per carton. If the liquid product cost RS 30 per jar and dry product cost RS 20 per carton Formulate this problem in linear programming model .How many of each product should be purchased in order to minimize the costs to meet the requirements .Also find the minimum cost.*

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#### “*ASMITA QUESTION BANK QUESTION”*

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