GU Business Statistics 2014 Question Paper [Gauhati University FYUGP BCom 3rd Sem]

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GAUHATI UNIVERSITY
B.Com. Examination – May/June 2014
BUSINESS STATISTICS

Full Marks: 80
Time: 3 hours
The figures in the margin indicate full marks for the questions

1. Answer the following questions: 1×10=10

(a) Mention one limitation of statistics.
(b) Fill in the blank:
  Simple is a ______ of the population.
(c) Choose the correct answer:
  1) Q₂ = Median
  2) Q₁ = Median
  3) Q₃ = Median
  4) D₁ = Median
(d) If the standard deviation of the series x₁, x₂, …, x₁₀₀ is 7, what is the standard deviation of the series 10x₁, 10x₂, …, 10x₁₀₀?
(e) Choose the correct answer:
  If r = ±1, the two lines of regression are –
  1) Coincident
  2) Parallel
  3) Perpendicular to each other
(f) Fill in the blank:
  Lagrange’s interpolation formula has no ______.
(g) Write whether the following statement is correct or not:
  Base period for an index number should be a year only.
(h) What is the probability of getting two heads when two uniform coins are tossed?
(i) Define random variable.
(j) Mention the two parameters of binomial probability distribution.

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

(a) What are primary data?
(b) Write down the empirical relationship among mean, median and mode.
(c) Two coins are tossed: If X denotes the number of heads obtained, find the probability distribution of X.
(d) What is level of significance?
(e) Define probability distribution of a random variable.

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

(a) Write a note on the importance of statistics in commerce.
(b) Write a note on pie-diagram.
(c) Of a certain distribution, the Karl Pearson’s coefficient of skewness is 0.32, standard deviation is 6.5 and mean is 29.6. Find the mode and the median of the distribution.
(d) Write a note on Karl Pearson’s coefficient of correlation.
(e) From a set of 20 marbles marked 1 to 20, one marble is drawn at random. What is the probability that its number is a multiple of 2 or 5?
(f) What do you mean by statistical quality control? Discuss the causes of variation in quality.

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

Age (in years)	20–30	30–40	40–50	50–60	60–70	70–80	80–90
No. of Persons	3	61	132	153	140	51	2

(b) Mention two advantages of sample survey over census survey.
(3)

5. (a) Calculate the coefficient of correlation between x and y for the following data:
(6)

X	9	8	7	6	5	4	3	2	1
Y	15	16	14	12	10	13	11	8	9

(b) Explain the concept of regression.
(3)

6. (a) What is a time series? Discuss briefly the different components of time series.
(1+5=6)
(b) Write a brief note on the limitations of index numbers.
(4)

7. (a) State the Additive Law of Probability for two mutually exclusive events and explain it with an example.
(2+4=6)
(b) In a business a man 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?
(2+4=6)

8. (a) What is Poisson probability distribution? Mention the properties of this distribution.
(2+4=6)
(b) The probability that the student of a night college will be a graduate is 0.4. Find the probability that one student out of 5 will be a graduate.
(4)

9. (a) Calculate cost of living index number from the following data assigning the given weights:
(4)

Groups of Items	Food	Clothing	Fuel	House Rent	Others
Group Index	150	280	180	300	210
Group Weight	55	10	7	10	18

(b) Write short notes on (any two):
(3×2=6)
i) Interpolation
ii) Null Hypothesis and Alternative Hypothesis

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