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I B.Com PA , CA EVEN SEM 2016
UNIT I
SECTION A
1
The word statistics have been derived from the Latin
word
(1) Statistik (2) Status (3) Statista
2
Modern statistical devices have been made business
forecasting more
(1) precise and
accurate (2) difficult (3)misunderstanding
3
Statistics does not study
(1) Individual cases (2) Group (3)Average
4
Statistics does not deals with
(1) Qualitative (2) Quantitative (3) Both
5
Statistics is an art as well as
(1) Science (2) Average (3) Theory
6
-----is a measure of central tendancy
(1) Mean (2) Median (3) all these
7
----- is the most commonly used measure of central
tendancy
(1) mean (2) median (3) mode
8
What is the Mean for the following observation ;
3,4,6,7,10
(1) 4 (2) 5 (3) 6
9
Which divides the value of a variable into two equal
parts?
(1) Median (2) Mean (3) Mode
----- is the value of item of a series which occurs most
10 frequently
(1) mean (2) median (3) mode
11
----- is not affected by extreme items
(1) mean (2) median (3) mode
12
Find mode of the following series 2 3 4 3 4 3 5 3 7
(1) 3 (2) 4 (3) 5
In olden days statistics also called ………………
13 (1) science of soldiers (2) science of kings(3) science
of business man
The values which varies with maximum frequency is
14 called
(1) mean (2) median (3) mode
15
----- is a positional average
(1) Mean (2) median (3) mode
16
-----is not a patrician value
(1) Mean (2) median (3) quartiles
----- is the difference between highest and lowest values
17 in a series
(1) Range (2) Mean (3) Dispersion
18
---- are the eyes of Govt. administration
(1) Statistics (2) Economics (3) Politics
19 -----is a figure that represents the whole group
(1) Average (2) Value (3) Data
20
Measures of dispersion are called averages of ----- order
(1) First (2) second (3) Third
21
Standard Deviation was First used by
(1) Karl Pearson (2) Horas Secrist (3)Lorance
22
The most important measure of dispersion
(1) Range (2) Mean deviation (3) Standard deviation
SECTION B
a) What are the limitations of Statistics
b) Write down the Collection of data and explain.
2. a) Write down the objectives of Classification
b) What are the advantages of diagrammatic representation of data?
3. Find arithmetic mean , mode and median from
X:
8
10
12
14
16
18
F:
8
12
18
10
4
16
4. Calculate Mode for
CI: 20-30
30-40 40-50
50-60
60-70 70-80 80-90
F : 15
14
17
22
10
18
14
1.
5. Distinguish between classification and tabulation
6. Find out Harmonic mean from given data
15, 16.9,11, 113.5,14.4,75.5,35,315
7.Find Mean, Median ,Mode
24,32,28,26,30,32
8. Find Harmonic Mean , Geometric Mean
10, 5, 8, 12, 15
9. Find Mean, Median ,Mode
X : 10
20
30
40
50
F : 5
10
7
8
3
10. Find Harmonic Mean , Geometric Mean
X: 10
20
30
40
50
F: 5
10
7
8
3
SECTION C
1. Calculate Mean, Median ,Mode
CI: 20-30
30-40 40-50
50-60
60-70 70-80 80-90
F : 15
14
17
22
10
18
14
2 Find Harmonic Mean , Geometric Mean
Matks : 10-20 20-30 30-40 40-50 50-60
Students:
12
6
15
9
8
3.Find the diference between Classification and Tabulation
4. Find Harmonic Mean , Geometric Mean
Matks : 10-20 20-30 30-40 40-50 50-60
Students:
12
6
15
9
8
5. a. Describe Diagrammatic representation of data
b. Describe Graphical representation of data
UNIT II
1
---- is the half distance between the third and first
quartiles
(1) Q.D (2) M.D (3) S.D
2
The formula of Q.D
(1) (Q3-Q1)/2 (2) (Q2-Q3)/2 (3) (Q2-Q1)/2
3
The most important measure of dispersion
(1) Range (2) Mean deviation (3) Standard deviation
4
Squre of Standard Deviation is known as
(1) Range (2) Variance (3) Quartile
5
For comparing variability in scores of 2 Batsman we can
use
(1) Standard Deviation (2) Mean (3)Co.efficient of
variation
6
Variance = ----(1) (S.D)2 (2) 1/S.D (3) S.D)3
7
In Standard deviation , deviations are taken only from --- values of series
(1) Mean (2) Median (3) Mode
8
Co. Efficient of variation is equal to
(1) (S.D/Mean)*100 (2) (S.D/Range
)*100(3) (Mean/ S.D)* 100
9
----- means lack of symmetry
(1) Skewness (2) Kurtosis (3) Range
10
A distribution is skewed if Mean , Median , Mode are
(1) Equal (2) Not equal (3) Symetric
11
----- is a measure of peakedness
(1) Skewness (2) Kurtosis (3) Range
12
Skewness may be ---(1) + or – (2) Zero (3) Both
Statistical methods are most dangerous tools in the
13 hands of
(1) Expert (2) Inexpert (3) Business man
14 ------ is capable of more algebraic treatment
(1) Direct method (2) arithmetic mean(3) Median
15
Median is a ----- average
(1) Mathematical (2) Positional (3) Both
16
---- is not a mathematical average
(1) A.M (2) mode (3) H.M
17
----- is ill-defined
(1) arithmetic mean (2) Median (3) Mode
18
----- divides the data into 4 equal parts
(1) Quartiles (2) Mean (3) Median
19
Simplest possible measure of dispersion is
(1) Range (2) Q.D (3) M.D
---- cannot be computed in the case of open ended
20 distribution
(1) Range (2) Mean (3) Both
Standard deviation of a series can have minimum value
21 of ----(1) Zero (2) One (3) Two
22
In ---- signs are ignored
(1) S.D (2) Mean (3) Both
----- is defined as the reciprocal of the mean of the
23 reciprocal of these values
(1) H.M (2) G.M (3) A.M
24
------ is used in averaging rates , times etc
(1) H.M (2) G.M (3) A.M
25 Measures of dispersion are statistical devices to measure
the ----- in a series
(1) Variability (2) Convertibility (3)Flexibility
SECTION B
1.Calculate Quartile deviation and its co-efficient from the following data:
Weight(in kg)
:
60
61
62
63
65
70
75
80
No. of Workers :
1
3
5
7
10
3
1
1
2. Explain mean deviation and standard deviation.
3. Calculate the mean deviation about mean for the following data :
Marks
:
40
50
54
60
68
80
No. of Students:
10
18
20
39
15
8
4. Compute: mean deviation about median for the following data
S.No :
1
2
3
4
f
:
3
6
24
28
5. Compute karlpearson co efficient of skewness
25,15,23,40,27,25,23,25,20
6. Calculate Bowleys coefficient skewness
x: 0 1 2 3 4 5 6
y:7 10 16 25 18 11 8
7 If the sum of Q1 and Q3 is 78.2; the difference between Q3 and Q1 is 14.3 and the median
is 35.7, find thecoefficient of skewness.
8. Calculate Karl Pearson’s coefficient of skewness
Class Interval: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency:
6
12
22
48
56
32
18
6
SECTION C
1.. Find out the mean deviation about the mean from the following data:
X
:
10
11
12
13
14
F
:
3
12
18
12
3
2. Find Quartile Deviation
X
:
35
40
45
50
55
60
f
:
12
18
24
16
6
4
3. Calculate the median age for the following:
Age (less than)
:
10
20
30
40
50
60
No. of persons
:
4
16
40
76
96
112
4.. Distinguish between primary data and secondary data.
5. Calculate range and coefficient of range for
CI:
F:
0-9
15
70
120
80
125
10-19 20-29 30-39 40-49 50-59
18
14
15
8
12
6. Calculate Standard Deviation
CI: 0-10
F:
7
10-20 20-30 30-40 40-50 50-60 60-70
18
34
50
35
20
6
7. a)Calculate S. D for
Expenditure :50-100
No. of families: 20
100-150
10
150-200
30
200-250
5
250-300
10
8) Calculate Coefficient of variation for
Marks
:
No. of Students:
0-10 10-20 20-30 30-40 40-50
12
13
21
19
15
9. . Compute Quartile deviation
Marks :1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90
Students: 2
11
30
66
76 58
37
16
4
10) Find out Karl pearson’s coefficient of skewness
Wage :
12
15
20
25
30
40
50
Worker:
10
25
40
70
32
13
10
UNIT III
1
By………. We mean adjusting them making allowance for
changes in the price levels.
(1) changing of index numbers (2)deflating of index
numbers (3) none
2
An index number is a specialized type of
(1) deviation (2) Average (3) variance
Laspeyre’s and ……………… index number formula do not
3 satisfy time reversal test.
(1) Paashe’s (2) Fishers (3) Kelly’s
Cost of living index is known as
4 (1) consumer price index (2) cost price
index (3) both
Consumer price index is used for
5 (1) formulation of price policy (2)product
evaluation (3) both
WPI means
6 (1) wholesale price index (2) world price
index (3) none
7
……………may satisfy time reversal test
(1) Fishers formula (2) Walsche’ (3) All of these
The industrial development of a country is reflected by
8 (1) index of cost of living (2) index of industrial
production (3) weighted price index
9
…………….. index possess upward bias
(1) laspeyre’s (2) fishers (3) Kelly’s
Most frequently used index number formula are
10 (1) fixed weighted formula (2) weighted
formula (3) un weighted formula
Statistical data arranged with respect to time are said to
11 constitute
(1) index number (2) time series (3) S.D
the fluctuations or variations in the value of a time series
exhibited over a period of one year or less are termed as
12
(1) seasonal fluctuations (2) cyclical
variation (3) operational fluctuations
13 Time series is a set of data recorded
(1) periodically (2) At time or space intervals (3) All of
these
14
If the shop of the trend line is positive, it shows
(1) declining (2) rising (3) stagnation
The gross national product value is deflated through
15 (1) price index numbers (2) weighted index
numbers (3) consumer price index numbers
A ………. Consists of long term changes, short term
16 variation, irregular variation etc.
(1) time series (2) index numbers (3)either A or B
The base year for index numbers should be…………..
17 (1) normal period (2) a year only (3) a period at
distant part
In plural sense, statistics means……………
18 (1) statistical methods (2) numerical set of
data (3) science of collection, presentation etc.
19
The sum of deviations taken from mean is ……………..
(1) 0 (2) 1 (3) 2
When an observation in the sata is ……………., then its
20 geometric mean is zero.
(1) 0 (2) 1 (3) 2
Which of the following is an absolute measure of
dispersion
21
(1) co-efficient of variation (2) standard
deviation (3) Co. efficient of quartiles
Standard deviation is always …………….. than mean
22 deviation.
(1) smaller (2) greater (3) lower
23
A time reversal test is satisfied if we use……………..
(1) Mean (2) mode (3) Geometric mean
24
Which of the following is an economic barometer
(1) skewness (2) median (3) index numbers
……………. Is an extension of time reversal test
(1) circular test (2) unit test (3) both
25
SECTION B
1. Find the coefficient of correlation for
Height of Father: 160
162 163 164
Height of son : 150
152 148 149
2. Compute Rank correlation
X:15 20
28
12
40
60
20
Y:40 30
50
30
20
10
30
3. Calculte Pearson’s correlation coefficient
Rainfall:
32
35
31
38
27
Production: 52
67
52
47
41
4 Calculate the coefficient of correlation for
165
154
167
160
168
165
57
63
21
72
80
60
42
55
X:
200
500
400
700
600
300
Y:
10
16
14
20
17
13
5 Find byx and bxy from the data given below
∑ 𝑥 = 24;
∑ 𝑦 = 214;
∑ 𝑥 𝑦 = 306;
∑ 𝑥 2 = 164;
𝑁=4
∑ 𝑦 2 = 576;
SECTION C
1. Compute the co efficient of correlation by concurrent deviation method
Demand:52 63
45
36
72
65
45
25
Supply:62 53
51
25
79
43
60
33
2
.Calculate the Regression of X on Y
x:10 12
13
12
16
y:40 38
43
45
37
3 Calculate 5 yearly moving average
Year:1991 1992 1993 1994 1995
Prod :87
61
92
86
112
4
15
43
1996 1997 1998 1999
101 114 107 121
Find the rank correlation:
X:
1
2
3
4
5
8
10
Y:
9
8
10
12
14
16
15
5 . Calculate rank correlation coefficient for
X:
21
36
42
37
25
Y:
47
40
37
42
43
6. Calculate the two regression equations for the following
X:
10
12
13
12
16
15
Y:
40
38
43
45
37
43
UNIT IV
1)Laspeyre’s and ……………… index number formula do not satisfy time
reversal test.
(1) Paashe’s (2) Fishers (3) Kelly’s
2……………may satisfy time reversal test
(1) Fishers formula (2) Walsche’ (3) All of these]
3Cost of living index is known as
(1) consumer price index (2) cost price index (3) both
4Consumer price index is used for
(1) formulation of price policy (2)product evaluation (3) both
5WPI means……………..
(1) wholesale price index (2) world price index (3) weighted price index
6By………. We mean adjusting them making allowance for changes in the
price levels.
(1) changing of index numbers (2)deflating of index numbers (3)deflationary
index numbers
7An index number is a specialized type of ……………
(1) deviation (2) Average (3) variance
8The industrial development of a country is reflected by
(1) index of cost of living (2) index of industrial production (3) weighted
price index
9…………….. index possess upward bias
(1) laspeyre’s (2) fishers (3) Kelly’s
10Most frequently used index number formula are
(1) fixed weighted formula (2) weighted formula (3) un weighted formula
11Statistical data arranged with respect to time are said to constitute
(1) ndex number (2) time series (3) S.D
12the fluctuations or variations in the value of a time series exhibited over a
period of one year or less are termed as
(1) seasonal fluctuations (2) cyclical variation (3) operational fluctuations
13Time series is a set of data recorded
(1) periodically (2) At time or space intervals (3) All of these
14If the shop of the trend line is positive, it shaws
(1) declining (2) rising (3) stagnation
15The gross national product value is deflated through
(1) price index numbers (2) weighted index numbers (3) consumer price index
numbers
16A ………. Consists of long term changes, short term variation, irregular
variation etc.
(1) time series (2) index numbers (3)either A or B
17The base year for index numbers should be…………..
(1) normal period (2) a year only (3) a period at distant part
18In plural sense, statistics means……………
(1) statistical methods (2) numerical set of data (3) science of collection,
presentation etc.
19The sum of deviations taken from mean is ……………..
(1) 0 (2) 1 (3) 2
20When an observation in the sata is ……………., then its geometric mean is
zero.
(1) 0 (2) 1 (3) 2
21Which of the following is an absolute measure of dispersion
(1) co-efficient of variation (2) standard deviation (3) Co. efficient of quartiles
22Standard deviation is always …………….. than mean deviation.
(1) smaller (2) greater (3) lower
23A time reversal test is satisfied if we use……………..
(1) Mean (2) mode (3) Geometric mean
24Which of the following is an economic barometer
(1) skewness (2) median (3) index numbers
25……………. Is an extension of time reversal test
(1) circular test (2) unit test (3) both
SECTION B and C
1. Using Geometric mean , calculate the cost of living index number for the
year 1990
Commodity
Price 1980 price 1990
weight
Food
60
108
40
Clothing
50
94
17
Fuel
40
65
13
House
125
225
27
Extra
120
240
3
15. a) Explain probability
2. a. Fit a Straight line trend
Year:
1997 1998 1999 2000 2001 2002 2003
Production: 48
50
58
52
45
41
49
3. Show that Fisher’s ideal satisfies both Time and Factor reversal tests,
Commodity
A
B
C
D
E
Price(1990)
6
2
4
10
8
Qty(1990)
50
100
60
30
40
Price(1992)
10
2
6
12
12
Qty(1992)
56
120
60
24
36
4. Using the method of least squares fit a trend for the following data
Year: 1979
1980
1981
1982
1983
Sales: 100
120
140
160
180
5Compute Cost of living index
Items :
Food
Index Number
352
Fuel
10
Clothing
8
Rent
Others
12
15
6. Show that time Reversal and Factor Reversal Test
Commodity
A
B
C
D
Price(1980)
10
7
5
16
Qty(1980)
60
70
80
90
Price(1982)
8
9
11
12
Qty(1982)
20
120
60
24
E
12
20
15
36
UNIT V
……… is the geometric mean of Laspeyre’s and Paashe’s
1 Index number.
(1) Walsche’s Index Number (2) Kelly’s (3)Fishers
From the following which is not a problem in the
construction of Index numbers?
2
(1) understanding of the purpose (2)selection of
price] (3) selection of base
In index number current year quantity is denoted by
3 ……………
(1) p1 (2) p0 (3) q1
ndex numbers may be constructed to reflect percentage
4 changes in
(1) prices (2) wages (3) All of these
5
Mode – 3 median (1) 2 mean (2) 3 mean (3) mean
6 ---- means asymmetry of a distribution
(1) skewness (2) Kurtosis (3) Moments
7
Squares of ---- is known as variance
(1) S.D (2) Q.D (3) M.D
Find range from the following values 23 32 85 32 42 10
8 20 18 28
(1) 70 (2) 75 (3) 85
9
----- is a geometric method of measuring variability
(1) Lorenz Curve (2) Geometric curve (3)Both
Standard deviation of a series can have minimum value
10 of ----(1) 0 (2) 2 (3) 1
11
----- is ill-defined
(1) arithmetic mean (2) Median (3) Mode
Statistical methods are most dangerous tools in the
12 hands of
(1) Expert (2) Inexpert (3) Business man
13
Cyclic variation Occur at intervals of more than ---- year
(1) 1 (2) 2 (3) 3
14
Pie chart is always ………………………
(1) circular (2) freehand (3) both
……………….. percentage of values of a series are less than
15 Q1
(1) 75 (2) 50 (3) 25
16
From the following which is not a kind of index number
(1) price (2) quality (3) value
17
Mean - Mode = 3 (mean – Median)
(1) median (2) mean (3) mode
18
Quartiles can be determined graphically using
(1) ogive (2) Histogram (3) frequency polygon
19
A time series is a set of values arranged in ………………
order.
(1) spatial (2) chronological (3)descending
Which of the following statement is true
(1) Mean is not affected due to sampling
20
fluctuations (2) mean is not affected by extreme
values. (3) Arithmetic mean is not stable
Variation in a time series that occurs due to chance is
21 (1) regular component (2) irregular
component (3) stagnant
……………. Moves like a pendulum of clock and it is never
ending process. [a.
22
(1) free hand curve (2) moving average(3) cyclical
fluctuation
The algebraic sum of deviations of values of a variable
23 from its arithmetic mean is ……………………….
(1) -1 (2) 1 (3) 0
24
When mean = 5, median = 10, mode = ………..
(1) 10 (2) 20 (3) 25
25
2 is a relative measure of …………………….
(1) Skewness (2) variance (3) Kurtosis
UNIT V
1
……… is the geometric mean of Laspeyre’s and Paashe’s
Index number.
(1) Walsche’s Index Number (2) Kelly’s (3)Fishers
2
From the following which is not a problem in the
construction of Index numbers?
(1) understanding of the purpose (2)selection of
price] (3) selection of base
3
In index number current year quantity is denoted by
……………
(1) p1 (2) p0 (3) q1
4
ndex numbers may be constructed to reflect percentage
changes in
(1) prices (2) wages (3) All of these
5
Mode – 3 median (1) 2 mean (2) 3 mean (3) mean
6
---- means asymmetry of a distribution
(1) skewness (2) Kurtosis (3) Moments
7
Squares of ---- is known as variance
(1) S.D (2) Q.D (3) M.D
8
Find range from the following values 23 32 85 32 42 10
20 18 28
(1) 70 (2) 75 (3) 85
9
----- is a geometric method of measuring variability
(1) Lorenz Curve (2) Geometric curve (3)Both
Standard deviation of a series can have minimum value
10 of ----(1) 0 (2) 2 (3) 1
11
----- is ill-defined
(1) arithmetic mean (2) Median (3) Mode
Statistical methods are most dangerous tools in the
12 hands of
(1) Expert (2) Inexpert (3) Business man
13
Cyclic variation Occur at intervals of more than ---- year
(1) 1 (2) 2 (3) 3
14
Pie chart is always ………………………
(1) circular (2) freehand (3) both
……………….. percentage of values of a series are less
15 than Q1
(1) 75 (2) 50 (3) 25
16
From the following which is not a kind of index number
(1) price (2) quality (3) value
17
Mean - Mode = 3 (mean – Median)
(1) median (2) mean (3) mode
18
Quartiles can be determined graphically using
(1) ogive (2) Histogram (3) frequency polygon
A time series is a set of values arranged in ………………
19 order.
(1) spatial (2) chronological (3)descending
Which of the following statement is true
(1) Mean is not affected due to sampling
20
fluctuations (2) mean is not affected by extreme
values. (3) Arithmetic mean is not stable
Variation in a time series that occurs due to chance is
21 (1) regular component (2) irregular
component (3) stagnant
……………. Moves like a pendulum of clock and it is never
ending process. [a.
22
(1) free hand curve (2) moving average(3) cyclical
fluctuation
23
The algebraic sum of deviations of values of a variable
from its arithmetic mean is ……………………….
(1) -1 (2) 1 (3) 0
24
When mean = 5, median = 10, mode = ………..
(1) 10 (2) 20 (3) 25
25
2 is a relative measure of …………………….
(1) Skewness (2) variance (3) Kurtosis
……… is the geometric mean of Laspeyre’s and Paashe’s Index
number.
(1) Walsche’s Index Number (2) Kelly’s (3)Fishers
SECTION B
1 State the addition and multiplication theorem of probability
2.From the following data, interpolate the missing value
Year: 1983 1984 1985 1986 1987
Sales: 72
57
?
81
103
3 What is the chance that a Leap year, selected at random will contain 53
Sundays?
4.Two Unbaised coins are tossed together .Find the Probability of getting tail in
both the coins
5.From a pack of well shuffled playing cards, one card is drawn at random.Find
the probability that it is
a. an ace b. A spade c. A clubs d. An ace or spade