B.Com. II (Semester IV) (CGPA) Examination, 2018
busines statistics
Day and Date Friday, 14-12-2018 Total Marks 70
Time 10.30 a.m. to 1.00 p.m. .00 .m. to .00 p.m.
N.B. All questions are compulsory.
Each question carries equal marks.
Figures to the right indicate full marks.
Use of soundless calculators is allowed.
Graph papers will be supplied on request.1
Figures to the right indicate full marks.
1. Choose the most appropriate alternative amongst the given for each question 14
If two events A and B cannot occur simultaneously, then they are called as
Independent events Mutually exclusive events
Equally likely events None of these
II) Probability of an impossible event is equal to
0 1 0.5 None of these
III) Variance of a Binomial distribution is given by
np nq npq None of these
None of these
Mean deviation in normal distribution with mean m and S.D. is given by
None of these
VI) Normal curve is a
U shaped V shaped Bell shaped None of these
VII) Variations due to use of substandard raw material is a cause.
Natural Assignable Tolerable None of these
VIII) A control chart was devised by
Hungarian Karl Pearson
Walter A. Schwartz None of these
IX) Control limits of C-chart are based on
Binomial distribution Normal distribution
Poisson distribution None of these
A Index number may be defined as a designed to measure
the change in the level of a phenomenon in relation to a characteristic like
time, locality etc.
A.M. Geometric mean
Specialised average None of these
XI) In Paache's price Index Number what is used as weight
Quantity in base year Price in current year
Quantity in current year None of these
XII) Fisher's Ideal Index number is a square root of Laspeyre's
Index Number and Paache's Index number.
Product of Summation of
Division of None of these
XIII) More demand for umbrella in rainy season is an example of
Secular trend Seasonal variation
Irregular variation None of these
XIV) Increase in an industrial production is an example of
Secular trend Seasonal variation
Cyclic variation None of these
2. State the additive and multiplicative laws of probability. 7
For a binomial distribution mean is 3 and variance is 3/2. Find all the
constants of it. Also find P[X 4]. 7
3. The following figures give the number of defects found in 1000 items of
cotton piece goods inspected every day in a certain month. 7
10, 19, 16, 20, 12,
14, 8.
Draw the c-chart and comment on it.
Explain in detail progressive averages method. Following are the infant
mortality rates in a region from 1922 to 1931. Find the progressive averages
from the following 7
Year 1922 23 24 25 26 27 28 29 30 31
Infant mortality 77, 69, 75, 75, 70, 70, 65, 74, 60, 66
4. Attempt any one of the following 14
What are the components of time series Explain each of these in brief.
Calculate 5-yearly moving averages for the following time series. Plot the
actual and trend values on the same graph paper.
Year 1 2 3 4 5 6 7 8 9 10
Values 78, 67, 107, 142, 152, 155, 160, 177, 155, 163
Define Laspeyre's, Paache's and Fisher's index numbers. Calculate
Laspeyre's, Paache's and Fisher's price index numbers from the following
data treating 1933 as a base year.
Commodity 1933 1934
Prize Quantity Prize Quantity
Wheat 170 562 72 632
Rice 192 535 70 756
Sugar 195 639 95 926
Ghee 187 128 92 255
Fuel 185 542 92 632
Gold 150 217 180 314
5. Attempt any one of the following 14
Define normal distribution. Also define standard normal variate. State mean
and variance of SNV. State various properties of normal curve.
What is a control chart On what principle control limits of control chart
are based. Give the construction of X and R-charts.
For the following data construct X and R-charts and comment on the findings.
Sample No. 1 2 3 4 5 6 7 8 9 10
Mean X 11.2, 11.8, 10.8, 11.6, 11.0, 9.6, 10.4, 9.6, 10.6, 10.0
Range R 9
(Given, for n Az 0.58, D3 D4 2.11)