# Business Statistics Question Paper' 2020 | B.Com 3rd Sem | Dibrugarh University

## 3 SEM TDC BUST (CBCS) GE 3032 0 2 0(Held in April–May, 2021)COMMERCE(Generic Elective)Paper: GE–303(Business Statistics)Full Marks: 80Pass Marks: 32Time: 3 hours

The figures in the margin indicate full marks for the questions 1. Answer any eight questions: 2x8=16

1. Calculate AM from the following data: 10, 20, 15, 18, 30.

2. Define mutually exclusive events.

3. What are the probabilities of an impossible event and a certain event?

4. Mention the two properties of correlation coefficient.

5. If the correlation coefficient between two variables and is and , then find the value of 6. Define price index number and quantity index number.

7. What do you mean by cost of living index number?

8. Write the main objectives of time series analysis.

9. What do you mean by seasonal variations in time series analysis?

10. Define parameter.

11. In what situations stratified sampling is used to draw a sample from a population?

2. (a) (1) Prove that for any two non-zero numbers . 3

(2) Find standard deviation and coefficient for variation from the following series: 6

 Class Interval: 5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 Frequency: 8 12 15 9 6

Or

(b) (1) Why is standard deviation considered to be the best measures of dispersion? 3

(2) Calculate median from the following distribution: 6

 Marks: 0 -10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 No. of Students: 4 6 10 15 12 6

3. (a) (1) Two coins are tossed simultaneously. Find the probability of getting same face on both the coins. 3

(2) A problem is given to three students A, B and C. The probability of solving the problem by A, B and C are 1/2, 1/3 and 1/4 respectively. Find the probability that the problem will be solved. 5

(3) A random variable X has the following probability distribution: : 1 2 3 4 5 6 7 :       Find the value of and . 3+2=5

Or

(b) (1) Find the probability that a leap year selected at random will contain 53 Sundays. 3

(2) A random variable X has the following probability distribution: : 1 4 7 : 1/4 1/2 1/4

Find . 3

(3) A binomial variable X has mean 6 and variance 4. Find the probability distribution of X.       3

(4) A normal variate X has a mean 50 and standard deviation 5. Find the probability that X lies between 40 and 60. 4

4. (a) (1) Prove that coefficient of correlation is the geometric mean of the two regression coefficients.         3

(2) If the two regression equations are and , what should be the means of and ?    4

(3) Find the correlation coefficient from the data given below: 6 : 105 120 95 150 130 : 100 115 110 135 115

Or

(b) (1) What is meant by correlation? Distinguish between positive, negative and zero correlations. 3

(2) Calculate the coefficient of rank correlation from the data given below: 5 : 92 89 86 87 83 71 77 63 53 50 : 86 83 77 91 68 52 85 82 57 57

(3) Derive the regression line of X and Y from the following data: 5   5. (a) (1) What are NSE SENSEX and NSE NIFTY? 3

(2) From the data given below, prove that Fisher index number satisfies time reversal test: 5

 Items    A 4 20 6 10 B 3 15 5 23 C 2 25 3 15 D 5 10 4 40

(3) The following table gives the index number of different groups of items with their respective weights for 2020 (base year 2010):

 Group Group Index No. Weight Food 525 40 Closing 325 16 Fuel 240 15 Rent 180 20 Others 200 9

Calculate the overall cost of living index number and interpret the results. 4+1=5

Or

(b) (1) Write the three uses of cost of living index number. 3

(2) Prove that Fisher index number satisfies time reversal test and factor reversal test. 5

(3) Find the price index number from the following data using Paasche and Laspeyres index: 5

 Base Year Current Year Item Price Quantity Price Quantity A 6 50 6 72 B 7 84 10 80 C 10 80 12 96 D 4 20 5 30

6. (a) (1) Write the two models used for studying time series analysis. 3

(2) From the data given below, find the straight line trend by using the method of least squares:

 Year: 1968 1969 1970 1971 1972 1973 1974 1975 1976 Value: 80 90 92 83 94 99 92 110 100

Also estimate the value for the year 1980. 8

Or

(b) (1) What are the components of time series? Discuss any one of them. 2+3=5

(2) Calculate the seasonal index for the following data by using the method of simple average (assuming that the trend is absent): 6

 Year    1991 72 68 80 70 1992 76 70 82 74 1993 74 66 84 80 1994 76 74 84 78 1995 78 74 86 82

7. (a) What is simple random sampling? Explain lottery method used to draw a simple random sample from a population. 5

Or

(b) What do you mean by the standard error of a statistic? A random sample of size 100 has mean 15, the population variance is 25. Find the interval estimate of the population mean with confidence level of (1) 99% and (2) 95%.   2+3=5

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