Business Statistics Question Paper June 2025 [Dibrugarh University BCOM 4th SEM NEP Syllabus]

Business Statistics Question Paper June 2025
Dibrugarh University BCOM 4^th SEM NEP Syllabus

COMMERCE (Core)

Paper: COM(FIN/MKT/BNI/HRM)

Full Marks: 60 | Time: 2 hours

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

1. Answer any six questions of the following: (2×6=12)

(a) What is the arithmetic mean of 2, 6, 8, 10 and 15?

(b) Write two differences between sample survey and complete enumeration.

(c) If the correlation coefficient between two variables x and y is +1 and byx​=0.5, then find the value of bxy​.

(d) Write two properties of correlation coefficient.

(e) Write the mathematical definition of probability.

(f) If P(A)=1/3, P(B)=1/4 and P(A∩B) = 1/6, then find the value of P(A∪B).

(g) Write the multiplication model of time series analysis.

(h) What do you mean by 'base year' in the construction of index numbers?

2. (a) (i) Prove that for any two values AM≥GM≥HM.

(ii) Calculate median from the following distribution: (4)

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70
No. of Students	20	30	25	45	35	40	15

(iii) Calculate standard deviation for the following distribution: (5)

Marks	0-10	10-20	20-30	30-40	40-50
No. of Students	8	13	16	8	5

OR

(b) (i) Write the advantages of sample survey over complete enumeration. (3)

(ii) Write a note on random sampling and judgemental sampling. (4)

(iii) Write a note on any one of the following: (5)

- Simple random sampling

- Systematic sampling

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

(ii) If the two regression lines are 2x - 3y = 0 and 4y - 5x - 8 = 0, then find the arithmetic mean of x and y. (4)

(iii) Calculate the coefficient of rank correlation from the data given below: (5)

X:	44	33	40	9	16	65	24	18	44	20
Y:	13	10	24	6	15	4	20	9	10	19

OR

(b) (i) What is Karl Pearson's coefficient of correlation? What is its range? (3)

(ii) Prove that Karl Pearson's coefficient of correlation is independent of the change of origin and scale of measurement. (4)

(iii) From the data given below, find the regression equation of y on x: (5)

x:	52	63	45	36	72	65	47	25
y:	62	53	51	25	79	43	60	33

4. (a) (i) If P(A) = 1/2, P(B) = 1/3 and P(AB) = 1/4, then find P(A/B) and P(B/A). (3)

(ii) Find the probability of getting 53 Sundays in a randomly selected leap year. (4)

(iii) Two bags contain 5 white and 3 black balls. Another contains 4 white and 5 black balls. Two balls are selected randomly from any one of the urn. Find the probability that the selected two balls are white. (5)

OR

(b) (i) Write three properties of mathematical expectation. (3)

(ii) From the following data, find the mathematical expectation and variance: (4)

X:	1	2	3
P(X=x):	1/6	1/3	1/2

(iii) Mean and variance of a binomial variate X are 6 and 4. Find the value of n and P. Write the probability distribution of X. (5)

5. (a) (i) Prove that Fisher's index number satisfies time reversal test. (3)

(ii) Discuss the limitations of index numbers. (4)

(iii) Calculate cost of living index number from the data given below: (5)

Group	Index No.	Weight
Clothing	360	40
Food	300	25
Fuel and Lighting	267	7
House Rent	120	8
Others	320	20

OR

(b) (i) Write a short note on seasonal variation in a time series. (3)

(ii) Estimate the trend values by using 3 yearly moving average for the following data: (4)

Year	2011	2012	2013	2014	2015	2016	2017	2018
Sale	60	46	53	54	48	48	42	51

(iii) Using the method of least squares, calculate the trend values for the following data: (5)

Year	2008	2009	2010	2011	2012
Production	100	140	150	180	200

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