M.Sc. (Semester III) Examination Nov/Dec-2018
Statistics
APPLIED STATISTICS
Time: 2½ Hours Max. Marks: 70
Instructions: All Questions carry equal marks.
Figures to the right indicate full marks.
Q.1 Choose the most correct alternative. 14
A rise in prices before Eid is an example of
Seasonal Variation Cyclic Variation
Secular Trend Irregular Variation
The best fitted trend line is one for which sum of squares of residuals or
errors is
1 Maximum
Minimum Negative
In sampling with replacement, a sampling unit can be selected
Only once More than one time
Less than one time Can't say anything
Index numbers are always expressed in
Percentages Ratio
Term of absolute vale All of the above
The relation between Laspeyre's Paasche's and Fisher's indices
is
No relation
F is the arithmetic mean of L and P
F is the geometric mean of L and P
F is the harmonic mean of L and P
Statement Fisher's index number satisfies time reversal test
Statement II: Fisher's index number satisfies factor reversal test
Both statements I and II are true
Only statement I is true
Only statement II is true
Neither statement I nor statement is true
Chance variation in the manufactured product is
Controllable Uncontrollable
Avoidable None of these
The control chart for the number of defectives
p-chart R-chart
c-chart X-bar-chart
A production process is said to be under statistical control for the variables, if
R chart is in control but X-bar chart is not in control
X-bar chart is in control but R chart is not in control
Both chart are under control
Neither X-bar nor R chart is in control
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10) If is the mean and σ is the standard deviation then Shewartz suggested
the control limits as
± σ ± 2σ
± 3σ ± 4σ
11) The study of vital statistics is related with
Population growth
Virility of races
Changing pattern of the population during intercensal period
All of the above
12) The birth or fertility rate depends on
Total population
Total male population
Total female population
Total female population in reproductive age
13) In vital statistics the rates of vital events are measured in
Per hundred Per thousand
Fraction Percentage
14) If NRR<1 then, we say that
Population will be decreasing Population will be increasing
Population will remain constant No conclusion can be drawn
Q.2 Answer the following (any four) 08
What do you mean by Crude birth rate?
What is Specific Death rate?
What is stratified random sampling?
Explain the need of Vital Statistics?
What is meaning of Index Number?
Write notes on (any two) 06
Age specific fertility rate
Chance causes of variation
Crude death rate
Q.3 Answer the following (any two) 08
Explain cost of living index number.
Show that Fisher's price index number lies between Laspeyre's and
Paasches's index number.
Define:
GRR
NRR
Answer the following (any one) 06
For the following data, calculate TFR and ASFR.
Age group of
mother
15-19 20-24 25-29 30-34 35-39 40-44
Women 52 013 54 307 46 990 40 211 30 401 23 496
Births 1884 6371 5362 2901 1170 268
Calculate Laspeyre's price index number for the following and interpret
it.
Commodity A B C Commodity A B C
2005 P0 40 30 80 2009 P1 60 20 40
Q0 20 50 20 Q1 30 10 60
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Q.4 Answer the following (any two) 10
What is time series? Describe in brief its components. Give example of
each component.
Define demerit control chart.
Give a note on Unweighted price and quantity index numbers using
Aggregate method and Average of relatives method.
Answer the following (any one) 04
Define sampling and non-sampling errors.
Write down the tests of Index numbers.
Q.5 Answer the following (any two) 14
Draw X bar and R chart for following data
A2 0.58, D3 D4 2.11)
Sample 1 2 3 4 5 6 7 8 9 10
Mean 12.8 13.1 13.5 12.9 13.2 14.1 12.1 15.5 13.9 14.2
Range 2.1 3.1 3.9 2.1 1.9 3 2.5 2.8 2.5 2
Estimate the trend value of the following time series using progressive
average. Plot the trend values.
Year 1985 1986 1987 1988 1989 1990 1991 1992
Production 86 98 108 106 120 142 148 156
Find x if the ratio of Laspeyre's price index no. to the Paasche's price index
no is 15:14 Hence find Fisher's Price index number using given data (after
funding the x).
Commodity A B Commodity A B
2005 P0 x 2 2009 P1 3 4
Q0 8 6 Q1 6 2