Half of the Inter-Quartile Range

MCQ Questions for Class 11 Commerce Economics Measures Of Dispersion Quiz 3

Which factory has more variation in wages?

0%
$A$
0%
$B$
0%
Equal Variation
0%
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__________.

0%
$S_{yx} =$ S.E. of estimate of y for given x
0%
$S_{xy} =$ S.E. of estimate of x for given y
0%
both (A) and (B)
0%
none of the above

A sampling distribution of means is______________.

0%
appropriate
0%
a probability distribution that indicates the likely values the various sample means take on all of the possible samples
0%
calculated as calculating mean of the population
0%
all of the above

The variance of six observations is given as

$16$ and mean is

$8$ . If each observation is multiplied by

$3$ .
Find the new variance:

0%
$155$
0%
$124$
0%
$177$
0%
$144$

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 =

0%
Difference between the upper and lower quartiles
0%
Q(3) - Q(1)
0%
Both A and B
0%
Q(2)-Q(1)

Which of the following is true with respect to range?

0%
Higher value of Range implies higher dispersion and vice-versa
0%
Range is unduly affected by extreme values.
0%
It is not based on all the values.
0%
All of these

Mean deviation of

$6, 8, 12, 15, 10, 9$ through mean is:

0%
$10$
0%
$2.33$
0%
$2$
0%
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

$A$ .

0%
$0.22857 \%$
0%
$0.25758 \%$
0%
$0.39462 \%$
0%
$0.82547 \%$

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?

0%
Quartile Deviation can generally be calculated for open-ended distributions
0%
It is unduly affected by extreme values
0%
Both A and B
0%
None of these

_________ is the most commonly used relative measure of dispersion.

0%
Coefficient of Mean Deviation
0%
Coefficient of Range
0%
Coefficient of Quartile Deviation
0%
Coefficient of Variation

Relative counterpart of Quartile Deviation is _______.

0%
inter quartile deviation
0%
coefficient of quartile deviation
0%
coefficient of range
0%
none of these

What are the Weaknesses of absolute measures of dispersion?

0%
Absolute measures may give misleading ideas about the extent of variation specially when the averages differ significantly
0%
They give the answer in the units in which original values are expressed
0%
Both A and B
0%
None of these

Quartile Deviation =

0%
Half of the Inter-Quartile Range
0%
[ Q(3) - Q(1) ] / 2
0%
Both A and B
0%
Q(3) - Q(1)

Two measures which are based upon deviation of the values from their average are _______ and _______.

0%
range, quartile deviation
0%
mean deviation, quartile deviation
0%
mean deviation, standard deviation
0%
standard deviation, quartile deviation

If Range is an absolute measure, its relative counterpart is _________.

0%
inter quartile range
0%
quartile range
0%
coefficient of range
0%
none of these

Coefficient of Range =

0%
L-S
0%
(L + S)/ (L - S)
0%
L-S / 2
0%
(L - S)/ (L + S)

Coefficient of Variation =

0%
SD / Mean * 100
0%
SD / Median *100
0%
SD / Range *100
0%
SD / QD *100

Dispersion measures ______________.

0%
the scatterness of a set of observations
0%
the concentration of a set of observations
0%
Both (A) and (B)
0%
Neither (A) nor (B)

According to _______, "Dispersion is the measure of extent to which individual items vary".

0%
A.L. Bowley
0%
Spiegel
0%
Simpson and Kafka
0%
L.R. Connor

The objectives and significance of dispersion are _______________.

0%
to test the reliability of an average
0%
to compare the extent of variability in two or more distributions
0%
to facilitate the computation of other statistical measures
0%
All of above

_________ means the variation or scattering or deviation of the different values of a variable from their average.

0%
Mean
0%
Median
0%
Dispersion
0%
Mode

Find the value of

$4(512)^{-1/9}$ ___.

0%
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".

0%
A.L. Bowley
0%
Spiegel
0%
Simpson and Kafka
0%
L.R. Connor

The most commonly used measure of dispersion is the _______________.

0%
range
0%
standard deviation
0%
coefficient of variation
0%
quartile deviation

Lorenz Curve uses which of the following?

0%
Class upper limits
0%
Class lower limits
0%
Class mid points
0%
None of these

Line joining Co-ordinate (0, 0) with (100,100) is called _______.

0%
Lorenz Curve
0%
Line of equal distribution
0%
Both A and B
0%
None

When it comes to comparing two or more distributions we consider.

0%
Absolute measures of dispersion
0%
Relative measures of dispersion
0%
Both (A) and (B)
0%
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?

0%
$2,420$
0%
$2,431$
0%
$2,436.80$
0%
$2,440.58$

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?

0%
$50\%$
0%
$70\%$
0%
$40\%$
0%
None of the above

What percentage of value is greater than

$3^{rd}$ quartile?

0%
$75$ per cent
0%
$50$ per cent
0%
$25$ per cent
0%
$0$ per cent

CBSE Questions for Class 11 Commerce Economics Measures Of Dispersion Quiz 3 - MCQExams.com

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Practice Class 11 Commerce Economics Quiz Questions and Answers

CBSE Questions for Class 11 Commerce Economics Measures Of Dispersion Quiz 3 - MCQExams.com

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Practice Class 11 Commerce Economics Quiz Questions and Answers

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