GU Business Statistics Question Paper 2021 (Held in 2022) | Gauhati University B.Com 3rd Sem CBCS Pattern

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Gauhati University B.Com 3rd Sem CBCS Pattern Business Statistics
4 (SEM-3/CBCS) HG 1/HG 2
2021 (Held in 2022)
COMMERCE (Honours Generic) 
OPTION – A
Paper: COM-HG-3016
(Business Statistics) 
Full Marks: 80
Time: Three hours

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

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Answer Questions Nos. 1, 2, 3 and any four from the rest.

1. (a) Select the correct answer: 1×4=4

1. Sum of the squares of deviations of the given set of observations from their arithmetic means is
   
   

1. Maximum.
   
   

2. Minimum.
   
   

3. Zero.
   
   

4. None of the above.
   
   

2. Standard deviation is dependent on the change of
   
   

1. Origin.
   
   

2. Scale.
   
   

3. Origin and scale.
   
   

4. None of the above.
   
   

3. Seasonal variations are
   
   

1. Short-term variations.
   
   

2. Long-term variations.
   
   

3. Sudden variations.
   
   

4. Cyclical variations.
   
   

4. Coefficient of variations is calculated by the formula
   
   

1. .
   
   

2. .
   
   

3. .
   
   

4. .
   
   

(b) Fill in the blanks: 1×3=3

1. An index number is a special type of _______.
   
   

2. Correlation coefficient is _______ of two regression coefficients.
   
   

3. If A and B are mutually exclusive events, _______.
   
   

(c) Write True or False: 1×2=2

1. An average alone is sufficient to understand the basic characteristics of a frequency distribution.
   
   

2. Mean of binomial distribution is always greater than variance.
   
   

(d) What do you mean by sample? 1

2. Answer the following questions: 2×5=10

1. What is estimation?
   
   

2. Write two properties of correlation coefficient.
   
   

3. Two regression coefficients in a distribution are calculated as – 1.89 and – 0.52. Is it possible? Justify your answer.
   
   

4. Find the E(X) for the following probability distribution of X:
   
   

5. Define skewness.
   
   

3. Answer any four of the following questions: 5×4=20

1. What is sample survey? Write the advantages and disadvantages of sample survey.
   
   

2. Prove that the expectation of a random variable x is equal to the arithmetic mean.
   
   

3. Discuss briefly various problems involved in the construction of index numbers.
   
   

4. Given the two regression equations as follows: and . Find the correlation coefficient between x and y.
   
   

5. State the additive law of probability and explain it with an example.
   
   

6. What do you mean by correlation between two variables? Mention different types of correlation.
   
   

4. (a) A study of 100 companies gives the following information: 

Profit  (Rs. in crore):	0-10	10-20	20-30	30-40	40-50	50-60
Number  of companies:	8	12	20	30	20	10

Calculate mean and standard deviation of the profit earned. 3+3=6

(b) Mention the desirable properties of a good measure of dispersion. 4

5. (a) Find the coefficient of correlation between X and Y from the following data: 6

X:	10	6	9	10	12	13	11	9
Y:	9	4	6	9	11	13	8	4

(b) What is a regression line? What purpose does it serve? When are the two regression lines identical?    2+1+1=4

6. (a) What is a binomial probability distribution? Mention the properties of this distribution. 2+4=6

(b) In a business a person can make a profit of Rs. 2,00,000 with a probability of 0.4 or have a loss of Rs. 1,00,000 with a probability of 0.6. What is his expected profit? 4

7. (a) Write the probability density function of a normal distribution. Under what conditions a binomial distribution tends to a normal distribution? 3+2=5

(b) If 5% of electric bulbs manufactured by a company are defective, find the probability that in a sample of 100 bulbs (1) 3 bulbs will be defective and (2) none will be defective. (Given) 5

8. (a) What is time series? Explain various components of time series. 6

(b) Calculate Fisher’s price index number from the data given below: 4

Commodity	Price per unit (Rs. )	Quantities (Quintal)
	2015	2020	2015	2020
A B C D E	6 2 4 10 8	10 2 6 12 1	50 100 60 30 40	56 120 60 24 36

9. (a) What is estimator? Write the characteristics of a good estimator. 2+4=6

(b) Explain null hypothesis and alternative hypothesis. 4

10. (a) Write the definitions of arithmetic mean, median and mode. Mention one use of each of these three measures.  6

(b) Given below the mean, median and standard deviation of two distributions. Determine which distribution is more skewed. 4

1. Mean = 22
   
   

Median = 24

Standard deviation = 10

2. Mean = 22
   
   

Median = 25

Standard deviation = 12

11. (a) What is cost of living index number? Discuss the importance of cost of living index number. 5

(b) A can hit a target thrice in 5 shots, B twice in 5 shots and C thrice in 4 shots. They fire a volley. What is the probability that A and B can hit the target and C cannot hit? 5

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