GU Business Statistics 2013 Question Paper [Gauhati University FYUGP BCom 3rd Sem]

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Gauhati University
B.Com Examination
Business Statistics 2013
Full Marks: 80
Pass Marks: 24
Time: 3 Hours

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

a) State whether the profit margins of a company during the last eight years constitute statistical data or not. (1)
b) Fill in the blank: Data collected for the first time are called ________. (1)
c) Which of the following relations is not true? (1)
 1) Q₂ = Median
 2) P₅₀ = Median
 3) D₅ = Median
 4) D₅₀ = Median
d) What is the relationship between the standard deviation of the following two series? (1)
 Series 1: 10, 20, 30, 40, 50, 80, 120
 Series 2: 1, 2, 3, 4, 5, 8, 12
e) Select the correct answer: If the correlation between x and y is negative, then the regression coefficient of x on y is (1)
 a) Positive
 b) Negative
 c) Not certain
f) Fill in the blank: The independent variable values in interpolation and extrapolation are termed as ________. (1)
g) Fill in the blank: Cost of living index numbers are also known as ________. (1)
h) Select the correct answer: The component of time series associated with the sale of wool and umbrella is (1)
a) Secular trend
b) Irregular variations

2.a) Mention two situations in which census survey is a must. (2)
b) What do you mean by Kurtosis? (2)
c) Find E(X) for the following probability distribution of X: (2)

X	0	1	2	3
P	1/8	3/8	3/8	1/8

d) What is type I error? (2)
e) Mention two properties of correlation coefficient. (2)

3. (Answer any four parts)

a) Write a note on the limitations of statistics. (5×4=20)
b) Explain briefly the use of diagrams in presenting statistical data.
c) Determine mode for the following distribution:

Marks	1–5	6–10	11–15	16–20	21–25	26–30	31–35	36–40	41–45
No. of Students	7	10	18	32	24	18	10	5	1

d) What is Skewness? Explain the different types of Skewness.
e) If A, B, and C are mutually exclusive and exhaustive events, and P(A) = 1/2 P(B) and P(B) = 2/3 P(C), find P(A), P(B), and P(C).
f) What is a control chart? Explain the reason for 3σ control limits for a control chart.

4.a) Calculate mean and standard deviation for the following distribution: (3+4=7)

Profit (Rs. in lakh)	20–30	30–40	40–50	50–60	60–70	70–80	80–90	90–100
No. of Companies	30	58	62	50	112	112	57	26

b) Differentiate between primary and secondary data. (3)

5.a) What do you mean by correlation between two variables? Mention the different types of correlation. (2+2=4)
b) The following data are about sales and advertisement expenditure of a firm:

	Sales (Rs. in crores)	Advt. Exp. (Rs. in crores)
Mean	40	6
Standard deviation	10	1.5
r = 0.9

Estimate the likely sales for the proposed advertisement expenditure of Rs. 10 crores. (3)

1. What would be the advertisement expenditure if the firm fixes a sales target of 60 crores of rupees? (3)

6. Write a brief note on the usefulness of index numbers. (4)

7.a) What is a binomial probability distribution? Mention the properties of this distribution. (2+4=6)
b) If 5% of electric bulbs manufactured by a company are defective, find the probability that in a sample of 100 bulbs:
 1) None is defective
 2) 5 bulbs are defective
(Given: e⁻⁵ = 0.007)

8.a) What is index number? Write down the formulae of Laspeyre’s, Paache’s, and Fisher’s index numbers. (1+3=4)
b) Write short notes on: (3×2=6)
 1) Level of significance
2) Usefulness of interpolation in Commerce

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