Explanation
Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data.
Standard deviation = { (sum of the squares of the observations/ number of observations ) – (sum of observations/ number of observations ) } ½
= { (1444) –(18.4) } ½
= (1425.6) ½
= 37.75
Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.
Coefficient of variation = ( standard deviation / mean )x 100
= ( 37.75/ 18.4)x100
= 20.51
Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. Standard deviation is not affected by the increase of decrease of observations in the series.
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
Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. If each value of the series is multiplied by 2, then the overall standard deviation will also be doubled as standard deviation is affected by the multiplication and division of the values.
Therefore, Coefficient of variation is a unit less or relative measure of dispersion as variation is the absolute measure of dispersion.
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 .
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