Accurate Group of Institutions, Greater Noida
Master of Business Administration (MBA)
Subject Name: Business Statistics and Analytics (Code KMBN 104)
Important Questions -Statistics
Unit- 1
SECTION A
Question 1 Define statistics. Question 2
What is skewness?
Question 3 Define Inferential Statistics
Question 4 Find out the quartile deviation for the following Series:
Question 5 Calculate Mode from the following data:
SECTION B
Question 6 What do you understand by Statistics? Explain the importance of statistics concerning
business and industry.
Question 7 Explain the difference between Mean deviation and Standard deviation.
Question 8 Calculate the mean deviation from the median and its coefficient for the given
series:
Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency 17 16 18 22 17 13 11
Question 9 Write short notes on quartiles, Deciles, and percentiles. Question 10
Calculate the mode for the following data by grouping method:
Wages 100-200 200-300 300-400 400-500 500-600
Frequency 15 18 30 20 17
SECTION C
Question 11: Define statistics. Explain the objectives and scope of statistics.
Question 12: Calculate the Mean Deviation coefficient from the following data and
interpret the result:
Question 13: What is the coefficient of variation? How this can be calculated in different
Methods.
Question 14 “Statistics is a method of decision-making in the face of uncertainty based on
numerical data and calculated risks.” Explain with suitable illustrations.
Question 15: Calculate the standard deviation for the given series:
Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency 6 8 15 7 3 0 1
UNIT 2
SECTION -A
1. What do you mean by trend analysis?
2. Give any two merits of the free hand method.
3. How to write the equation of the least square method?
4. Define time-series analysis and explain its significance in business forecasting.
5. What do you understand by index numbers?
SECTION -B
6. The following figures relate to the profits of a commercial concern for 8 years
Find the trend of profits by the method of three yearly moving averages.
7. What do you mean by splicing?
8. What are the fixed base and chain base index numbers? What are the methods used in
their conversions?
9. Distinguish between time reversal and factor reversal tests.
SECTION -C
10. Differentiate between Laspeyres and Paasches Index formulae.
11. Calculate price index number for 2005 by (a) Laspeyre’s (b) Paasche’s method
12. Using Fisher’s Ideal Formula, compute the price index number for 1999 with 1996 as
the base year, given the following:
13. Explain the various models of the time series.
UNIT 3
SECTION A
1. Explain the difference between causation and correlation.
2. Why are there two regression lines?
3. How would you interpret a correlation coefficient of -0.5?
4. Write a short note of Positive and Negative correlation correlation.
5. Using the free hand or graphic method, fit the straight-line trend to the following time
series:
Years 199 199 199 199 199 199 200 200 200 200
4 5 6 7 8 9 0 1 2 3
Maize 35 55 40 85 135 110 130 150 130 120
productio
n (lakh
tonnes)
SECTION: B
6. Ten entries are submitted for the competition. Three judges study each entry and list
the ten in rank order. Their rankings are as follows:
Entry: A B C D E F G H I J
Judge J1: 9 3 7 5 1 6 2 4 10 8
Judge J2: 9 1 10 4 3 8 5 2 7 6
Judge J3: 6 3 8 7 2 4 1 5 9 10
Calculate the appropriate rank correlation to help you answer the following questions:
i. Which pair of judges agrees the most?
ii. Which pair of judges disagree the most?
7. In partially destroyed laboratory records of an analysis of correlation data, the
following results are only legible. (Variance of x=9) Regression equations
8x−10y+66=0 and 40x−18y=214.
Find values of (i) xˉ and yˉ. (ii) Correlation coefficient between x and y. (iii) S.D. of y.
8. What is the difference between correlation and regression write in detail.
9. Write the advantages and disadvantages of Karl Pearson's correlation coefficient.
10. From the given data, obtain the two regression lines:
X 45 48 50 55 65 70 75 72 80 85
y 25 30 35 30 40 50 45 55 60 65
Section C
11. Distinguish between time reversal and factor reversal tests.
12. How is hypothesis testing applied to assess the significance of Karl Pearson's
correlation coefficient?
13. If the calculated r is 0.62 and the sample size is 30, perform a hypothesis test to
determine if the correlation is significant at the 5% level.
14. Compare and contrast simple linear regression with multiple regression.
15. Provide an example of a real-world situation where multiple regression would be
more appropriate than simple linear regression.
UNIT-4
Very short questions
1) Define probability. What is the probability of getting more than 10 in a single throw
of two dice?
2) Explain the theory of probability.
3) Write a short note on conditional probability.
4) A bag contains 8 red,10 blue, and 12 black balls. If one ball is drawn at random find
the probability that it is black.
5) What is the probability that a leap year selected at random will contain 53 Sundays?
6) Explain the theory of probability.
Short Questions
7) What are the fundamental rules of counting?
8) Define probability. What is the probability of getting more than 10 in a single throw
of two dice?
9) What are the characteristics of probability function P(A)?
10) Give two applications of Bayes, theorem.
11) What is the Poisson Distribution?
12) What is binomial Distribution? Explain the assumptions and properties of binomial
distribution.
Long Questions
13) Define the following terms
Events Mutually & Exhaustive events
Mutually exclusive events & Equally likely events
Algebra of events & Independent and Dependent Event
14) Describe the addition and multiplication rules of probability with an example for
each.
15) Describe briefly the importance of normal distribution in business decision-making.
What are its chief properties?
16) A can hit a target 3 times in 5 shots, B 2 times in 5 shots, and c 3 times in 4 shots.
They fire a volley. What is the probability of hitting 2 shots?
17) A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the
probability that they are of the same color.
18) A box contains 10 bulbs, of which just three are defective. If a random sample of five
bulbs is drawn, find the probability that the sample contains exactly one defective
bulb.
19) A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls.
One bag is selected at random. From the selected bag, one ball is drawn. Find the
probability that the ball drawn is red.
20) A talent test was conducted on 5000 students in a school in which the mean score was
found to be 65 and the standard deviation was 15. If the population is assumed to be
normal, how many students have scored:
a) less than 50 marks?
b) between 60-70 marks?
c)more than 75 marks?
UNIT- 5
Very Short Questions
1) What do you mean by hypothesis testing?
2) Describe the Chi-square test.
3) Give the assumptions of the parametric test.
4) Define business analytics.
5) What is the alternative hypothesis?
Short Questions
6) What is a hypothesis? Explain how hypothesis testing is useful to management.
7) What is a sampling distribution, and what are the uses of sampling distribution?
8) What are the applications of business analytics?
9) Is the severity of the drug problem in high school is same for boys and girls? 85 boys
and 70 girls were questioned and 34 boys and 14 girls admitted to have tried some
sort of drug. What can be concluded at the 0.05 level?
10) A large organization produces electric bulbs in each of its two factories. It is
suspected that the efficiency in the factories is not alike, so a test is carried out for
ascertaining the variability of the life of the bulbs produced by each factory. The
results are as follows:
Factory A Factory B
No. of bulbs in sample 100 (n1) 200 (n2)
Average life 1100 (x1) 900 (x2)
Standard deviation 240(s1) 220 (s2)
From the above information, determine whether the difference between the variability
of life of bulbs from each sample is significant (take 1% level of significance).
Long Questions
11) A certain drug is claimed to be effective in curing colds. In an experiment on 500
persons with cold. half of them were given the drug and half of them were given sugar
pills. The patient's reactions to the drugs are recorded in the following table:
Treatment Helpful Reaction No effect
Drug 150 30 70
Sugar pills 130 40 80
Based on the data, can it be concluded that there is a significant difference in the
effect of drug and sugar pills. ( %² at df 25%=5.99 )
12) Describe the various tools of business analytics.
13) Write a detailed note on type-I and type-II errors while testing the hypothesis. Also,
explain one tailed and two tailed tests.
14) Explain the basic concepts of testing of hypothesis.
15) Difference between parametric and non- parametric tests.
16) Discuss the application of Chi- square test.
