Tag: measures of dispersion and skewness
Questions Related to measures of dispersion and skewness
Which measure of dispersion is most affected by extreme values?
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Standard deviation
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Mean deviation
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Range
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Quartile deviation
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.
Semi inter-quartile deviation is given by the formula _______.
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$Q _3 - Q _1$
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$\frac{Q _3 - Q _1}{8}$
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$\frac{(Q _3 - Q _1)}{2}$
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$\frac{(Q _3 - Q _1)}{4}$
Semi inter-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 .
Semi inter-quartile deviation = (Q3-Q1) /2
= (29-17)/2
= 12/2
= 6
Which measure of dispersion ensures lowest degree of reliability?
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Range
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Mean deviation
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Quartile deviation
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Standard deviation
Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most affected measures of dispersion by the extreme values of the series therefore it has the lowest degree of reliability.
The co-efficient of range from the following observations is
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$
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$0.6$
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$0.5$
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$0.55$
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None of them
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.
The co-efficient of quartile deviation from the following observations is
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$
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$0.26$
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$0.16$
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$0.06$
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$0.36$
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 .
The coefficient of quartile deviation is found by dividing the difference between the first quartile and the third quartile by the sum between the first quartile and the third quartile.
In the given series, 10, 15,17,18,20,22,25,28,29,32,34.
Q1= 17 and Q3=29
Coefficient of quartile deviation =(Q3-Q1)/ (Q3+Q1)
= (29-17)/ (29+17)
= 12/46 = 0.26
The variance of $1, 2, 4, 5$ and x is $2$, then x is _____.
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$3$
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$6$
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$1$
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$2$
Which measure of dispersion is least affected by extreme values?
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Range
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Mean deviation
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Standard deviation
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Quartile deviation
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 . Therefore, quartile deviation is not affected by the extreme values of the series.
Sum of squares of the deviations is minimum when deviations are taken from ________.
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mean
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median
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mode
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zero
The quartile deviation from the following observations is
$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$
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$8$
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$6$
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$10$
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$5$
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
Given the following set of data, what is the range 12 23 34 54 21 8 9 67:
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55
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59
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8
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56
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. Therefore, it is the most affected measures of dispersion by the extreme values of the series.
Range = H - L
In the given series, H= 67 and L= 12
Range = 67 -12 = 55 .