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CBSE Questions for Class 11 Commerce Economics Measures Of Dispersion Quiz 3 - MCQExams.com
CBSE
Class 11 Commerce Economics
Measures Of Dispersion
Quiz 3
Which factory has more variation in wages?
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$$A$$
0%
$$B$$
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Equal Variation
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Cannot be determined.
Explanation
$$(\sigma _A) ^2=64$$ and $$(\sigma _B) ^2=81$$
$$\because S.D=\sqrt {\sigma ^2}$$
$$\therefore S.D_A=8$$ and $$S.D_B=9$$
Since monthly mean wages in two factories are same, and $$ S.D_A < S.D_B$$.
Thus, the factory $$B$$ has more variation in wages.
Ans-Option $$B$$.
The Standard error is denoted by__________.
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$$S_{yx} =$$ S.E. of estimate of y for given x
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$$S_{xy} =$$ S.E. of estimate of x for given y
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both (A) and (B)
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none of the above
Explanation
Standard error is a statistical measure that shows the accuracy by which a sample represents the population. Standard error is denoted by both the equations mentioned in option a and b.
A sampling distribution of means is______________.
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appropriate
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a probability distribution that indicates the likely values the various sample means take on all of the possible samples
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calculated as calculating mean of the population
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all of the above
Explanation
A sampling distribution is the probability distribution of a given statistics based on random samples, it shows the likely values of the various sample means.
The variance of six observations is given as $$16$$ and mean is $$8$$. If each observation is multiplied by $$3$$.
Find the new variance:
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$$155$$
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$$124$$
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$$177$$
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$$144$$
Explanation
Mean, $$u=8$$.
So, $$\dfrac{x_1+x_2...x_6}{6}=8$$.
$$\therefore x_1+x_2...x_6=48$$.
Multiplying the above equation by $$3$$ on both the sides we get,
$$3x_1+3x_2...3x_6=48\times 3$$
$$\therefore u'=\dfrac{3x_1+3x_2....3x_6}{6}=\dfrac{48 \times 3}{6}$$
$$\therefore u'=24$$
Thus, new mean, $$u'=24$$.
$$\therefore$$ New variance, $$\sigma ^2=\dfrac{(3x_1)^2+...(3x_6)^2}{6}-(24)^2$$
$$\therefore \sigma ^2=9\times \dfrac{(x_1)^2+....(x_6)^2}{6}-576$$
$$\therefore \sigma ^2=9\times \dfrac{480}{16}-576$$
$$\therefore \sigma ^2=720-576$$
$$\therefore \sigma ^2=144$$
Thus, New Variance is $$144$$.
Ans-Option $$D$$
Inter Quartile Range =
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Difference between the upper and lower quartiles
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Q(3) - Q(1)
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Both A and B
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Q(2)-Q(1)
Which of the following is true with respect to range?
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Higher value of Range implies higher dispersion and vice-versa
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Range is unduly affected by extreme values.
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It is not based on all the values.
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All of these
Mean deviation of $$6, 8, 12, 15, 10, 9$$ through mean is:
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$$10$$
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$$2.33$$
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$$2$$
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None of these
Explanation
$$\overline { x } =\cfrac { 6+8+12+15+10+9 }{ 6 } =\cfrac { 60 }{ 6 } $$
$$ \overline { x } = 10$$
Mean deviation about mean $$= \cfrac { 1 }{ 6 } \left[ \left| 6-10 \right| +\left| 8-10 \right| +\left| 12-10 \right| +\left| 15-10 \right| +\left| 10-10 \right| +\left| 9-10 \right| \right]$$
$$ = \cfrac { 1 }{ 6 } (14)$$
$$ = 2.33$$
Find the Coefficient of Variation of Factory $$A$$.
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$$0.22857 \%$$
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$$0.25758 \%$$
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$$0.39462 \%$$
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$$0.82547 \%$$
Explanation
Coefficient of Variation, $$C.V=\dfrac{S.D}{Mean} \times 100 \%$$
So, $$C.V_A=\dfrac{S.D_A}{Mean_A} \times 100 \%$$
$$\therefore C.V_A=\dfrac{\sqrt {64}}{3500} \times 100 \%$$.
$$\therefore C.V_A=0.22857 \%$$.
Ans-Option $$A$$.
Which of the following is true?
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Quartile Deviation can generally be calculated for open-ended distributions
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It is unduly affected by extreme values
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Both A and B
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None of these
_________ is the most commonly used relative measure of
dispersion.
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Coefficient of Mean Deviation
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Coefficient of Range
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Coefficient of Quartile Deviation
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Coefficient of Variation
Relative counterpart of Quartile Deviation is _______.
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inter quartile deviation
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coefficient of quartile deviation
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coefficient of range
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none of these
What are the
Weaknesses of absolute measures of dispersion?
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Absolute measures may give misleading ideas about the extent of variation specially when the averages differ significantly
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They give the answer in the units in which original values are expressed
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Both A and B
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None of these
Quartile Deviation =
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Half of the Inter-Quartile Range
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[ Q(3) - Q(1) ] / 2
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Both A and B
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Q(3) - Q(1)
Two measures
which are based upon deviation of the
values from their average are _______ and _______.
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range, quartile deviation
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mean deviation, quartile deviation
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mean deviation, standard deviation
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standard deviation, quartile deviation
If Range is an absolute measure, its relative counterpart is _________.
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inter quartile range
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quartile range
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coefficient of range
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none of these
Coefficient of Range =
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L-S
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(L + S)/ (L - S)
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L-S / 2
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(L - S)/ (L + S)
Coefficient of Variation =
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0%
SD / Mean * 100
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SD / Median *100
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SD / Range *100
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SD / QD *100
Dispersion measures ______________.
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the scatterness of a set of observations
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the concentration of a set of observations
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Both (A) and (B)
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Neither (A) nor (B)
According to _______, "Dispersion is the measure of extent to which individual items vary".
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A.L. Bowley
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Spiegel
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Simpson and Kafka
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L.R. Connor
The objectives and significance of dispersion are _______________.
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to test the reliability of an average
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to compare the extent of variability in two or more distributions
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to facilitate the computation of other statistical measures
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All of above
_________ means the variation or scattering or deviation of the different values of a variable from their average.
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Mean
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Median
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Dispersion
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Mode
Find the value of $$4(512)^{-1/9}$$___.
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3
0%
1
0%
2
0%
None
According to ________, "The degree to which numerical data tend to spread about an average value is called the variation or dispersion of the data".
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A.L. Bowley
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Spiegel
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Simpson and Kafka
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L.R. Connor
The most commonly used measure of dispersion is the _______________.
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range
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standard deviation
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coefficient of variation
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quartile deviation
Lorenz Curve uses which of the following?
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Class upper limits
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Class lower limits
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Class mid points
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None of these
Line joining Co-ordinate
(0, 0) with (100,100) is called _______.
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Lorenz Curve
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Line of equal distribution
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Both A and B
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None
When it comes to comparing two or more distributions we consider.
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Absolute measures of dispersion
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Relative measures of dispersion
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Both (A) and (B)
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Either (A) or (B)
$$Rs. 2,000$$ is invested at annual rate of interest of $$10$$%. What is the amount after two years if compounding is done monthly?
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$$2,420$$
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$$2,431$$
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$$2,436.80$$
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$$2,440.58$$
Explanation
For monthly compounding
$$n = 12\times 2 = 24, i = 0.1/12 = 0.00833$$
$$A_{24} = 2000 (1 + 0.00833)^{24}$$
$$= 2,000\times 1.22029$$
$$= Rs. 2,440.58$$.
What percentage of value is less than $$4th$$ decile?
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$$50\%$$
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$$70\%$$
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$$40\%$$
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None of the above
What percentage of value is greater than $$3^{rd}$$ quartile?
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$$75$$ per cent
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$$50$$ per cent
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$$25$$ per cent
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$$0$$ per cent
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