GU Business Statistics Question Paper 2024 [Gauhati University FYUGP B.Com 3rd Sem.]

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Gauhati University 

FYUGP BCom 3rd Semester 

Multidisciplinary Course

Business Statistics (MDC030403)

Full Marks: 45

Time: 2 hours

Answer either in English or in Assamese

1. Answer the following as directed: (1×5=5)

(a) Distinguish between univariate and bivariate data.
(b) If A is a certain event in a random experiment, then P(A) = ____ (Fill in the blank)
(c) If r = ±1, then the two lines of regression are:

 (i) Coincident (ii) Parallel (iii) Perpendicular (iv) None of the above
(d) Lockout in a factory for a month is associated with which component of a time series?
(e) What are the different kinds of error associated with tests of significance?

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

(a) Define null hypothesis.
(b) Mention two properties of Karl Pearson’s correlation coefficient.
(c) If A and B are not mutually exclusive events and
 P(A) = ¼, P(B) = ²⁄₅, P(A ∪ B) = ½, find P(A ∩ B).
(d) What do you mean by skewness?
(e) Find the harmonic mean of 2, 3, and 5.

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

(a) AM = 9, GM = 7.2. Find HM and the two numbers.
(b) Find the missing frequency (median = 24):

Class Interval	Frequency
0–10	5
10–20	25
20–30	?
30–40	18
40–50	7

(c) What is time series? Give two examples. What are its components? (1+2+2=5)
(d) Define mathematical probability. Mention drawbacks. (3+2=5)
(e) What is sample survey? Distinguish from census survey. (2+3=5)
(f) What is Poisson distribution? Mention basic features. (2+3=5)
(g) Calculate Karl Pearson’s correlation from:
 x: 1 2 3 4 5 6 7
 y: 3 5 6 8 10 11 13
(h) Given:

	x	y
Mean	36	85
Std. Dev.	11	8

Correlation coefficient = 0.66
Find the regression line of y on x.

4. Answer any one of the following questions: (10 marks)

(a) (i) Define correlation between two variables. Explain types with examples. (2+4=6)
(ii) Given:
 n = 15, x̄ = 25, ȳ = 18
 Σ(x − x̄)² = 136, Σ(y − ȳ)² = 138
 Σ(x − x̄)(y − ȳ) = 122
 Find rₓᵧ (4 marks)

(b) (i) Using 3-yearly moving average, calculate the trend from the following:

Year	Sale (₹ in thousand)	Year	Sale (₹ in thousand)
2001	5	2009	13
2002	7	2010	17
2003	9	2011	19
2004	2	2012	12
2005	11	2013	14
2006	10	2014	12
2007	8	2015	15
2008	12

b)(ii) Write a short note on any one: (3 marks)
 (1) Seasonal variation  (2) Uses of time series analysis

(c) (i) What is the probability that a non-leap year has 53 Saturdays? (4 marks)
(ii) State three properties of normal distribution. (3 marks)
(iii) Two dice are thrown. Find the probability that the sum ≥ 9. (3 marks)

(d) (i) From the data below, calculate mean and variance (3+4=7)

Profit (₹ in lakh)	No. of Companies
20–30	30
30–40	58
40–50	62
50–60	85
60–70	112
70–80	112
80–90	57
90–100	26

(ii) Write a short note on any one: (3 marks)
 (1) Simple random sampling method
 (2) Test of significance
 (3) Scatter diagram

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