Measures of Dispersion Test

Result

Measures of Dispersion Test - 31

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Weekly Quiz Competition

Question 1
1 / -0

The correct relation between variance and standard deviation (S.D) of a variable X is _______.

A
S.D = Var

B
$$S.D =[ Var(X)^{\frac{1}{2}}]$$

C
$$S.D = [Var(x)]^2$$

D
None of the above

Solution

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data.
Variance is the mean of the squares of the deviations from the mean.
Standard deviation is the square root of variance or variance is the square of standard deviation.
S.D = {Var(X)}^1/2
or
Var(X) = (S.D)²
Question 2
1 / -0

In a moderately skewed distribution the arithmetic mean is $$10$$ units and the mode is $$7$$ units, the median is ______.

A
$$9$$

B
$$5$$

C
$$8$$

D
$$6$$
Question 3
1 / -0

Which of the following is a unit less measure of dispersion?

A
Quartile deviation

B
Mean deviation

C
Coefficient of variation

D
Range

Solution

Measure of dispersion is a statistical method to find a specific value from a dispersed series where the extent to which various values of the series tend to disperse from each other or from the average is measured.
Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.
Therefore, Coefficient of variation is a unit less or relative measure of dispersion as variation is the absolute measure of dispersion.
Question 4
1 / -0

Which one of the given measures of dispersion is considered best?

A
Standard deviation

B
Range

C
Mean deviation

D
Coefficient of variation

Solution

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. It is considered as the best and most commonly used measure of dispersion as it is a measure of average of deviations from the average.
Question 5
1 / -0

The quartile deviation from the following observations is
$$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$$

A
$$8$$

B
$$6$$

C
$$10$$

D
$$5$$

Solution

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q₁ and the third quartile is denoted as Q₃ .
In the given series, 10, 15,17,18,20,22,25,28,29,32,34
Q₁= 17 and Q₃=29
Therefore, Quartile deviation = (Q₃-Q₁) /2
= (29-17)/2
= 12/2

= 6
Question 6
1 / -0

From which average sum of deviations is zero?

A
Median

B
Mean

C
Mode

D
None of them
Question 7
1 / -0

The range from the following observations is
$$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$$

A
$$24$$

B
$$20$$

C
$$30$$

D
$$42$$

Solution

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion.
Range = H - L
In the given series, H= 34 and L+ 10
Range = 34-10 = 24.
Question 8
1 / -0

The co-efficient of range from the following observations is
$$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$$

A
$$0.6$$

B
$$0.5$$

C
$$0.55$$

D
None of them

Solution

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion.
Range = H - L
In the given series, H= 34 and L+ 10
Range = 34-10 = 24.
Coefficient of range is found by dividing the range with the sum of highest and lowest value of the series.
Coefficient of range (CR) = R/ (H+L)
=24 / (34+10)
= 24/ 44 = 0.55
Question 9
1 / -0

Which measure of dispersion is most affected by extreme values?

A
Standard deviation

B
Mean deviation

C
Range

D
Quartile deviation

Solution

Range is the most simple and commonly understandable measures of dispersion.Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. Therefore, it is the most affected measures of dispersion by the extreme values of the series.
Question 10
1 / -0

Mean deviation is minimum when deviations are taken from ______.

A
mean

B
median

C
mode

D
zero

Solution

Mean deviation is the arithmetic average of the deviations of the observed values from an average of the observed values.
Mean deviation from the median calculates the arithmetic average of the deviations of the observed values from median of the observed values. Mean deviations is minimum when deviations are taken from median as median is the middle most value of the series and disperse the whole series into minimal value.

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Re-Attempt Weekly Quiz Competition

Measures of Dispersion Test - 31

Result

Measures of Dispersion Test - 31

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SHARING IS CARING

Question 1

S.D = Var

$$S.D =[ Var(X)^{\frac{1}{2}}]$$

$$S.D = [Var(x)]^2$$

None of the above

Solution

Question 2

$$9$$

$$5$$

$$8$$

$$6$$

Question 3

Quartile deviation

Mean deviation

Coefficient of variation

Range

Solution

Question 4

Standard deviation

Range

Mean deviation

Coefficient of variation

Solution

Question 5

$$8$$

$$6$$

$$10$$

$$5$$

Solution

Question 6

Median

Mean

Mode

None of them

Question 7

$$24$$

$$20$$

$$30$$

$$42$$

Solution

Question 8

$$0.6$$

$$0.5$$

$$0.55$$

None of them

Solution

Question 9

Standard deviation

Mean deviation

Range

Quartile deviation

Solution

Question 10

mean

median

mode

zero

Solution

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