* Definition :

We definition it by too many wayswe can say thatVariability is the extent to which data point in a statistical distribution or we can say it as the measurement of the spread of data set

where the conditions of the measurement are stablelike :, temperature,length , etc.

*Measures of Variability:

1) Range :

the difference between the biggest and the smallest value in the series of observations

It is also the simplest way we can use to measure the variability and can be calculated according to the following equation :- Range = X max – X Min

Where ,X max = the maximum value in the observationX min = the minimum value in the observation

The main disadvantage of the range is that it depends only on the two

outlying values of the observations and does not take into consideration the

other values in the series of observations .

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2) Standard Deviation:

The standard deviation is the square root of the variance and could be calculated according to the formula

standard deviation has the advantages that it takes into consideration all the values in the series of observations and its value is expressed in the same units as the mean

*the best way to measure the variation in the population is SD

* standard deviation is considered the ideal measure for variability.

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3) Variance:

The variance is defined as the mean deviation of the values from their mean or it is the square of the standard deviation

The variance takes into consideration all the values in the series ofobservations and does not ignore the sign but the main disadvantage isthat it is expressed in squared units and so cannot be added to orsubtracted from the mean value

* the effective way we can use to measure of the variability

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4) Standard Error:

We can use it for accuracy measurement with the simple

From descriptive statistics

as small as the standard error as big as the progressive or the more representative will it be in the sample overall

*inversely proportional to the sample size << the more big the sample size the more small you get error >>

* part from descriptive statistics

The more we have data involved in the mean calculations the few the error tends to be when we have a small error the data is more progressive or we can say the morerepresentative near to the real mean ( the true one )

But when you get a large error maybe the data have some notable irregularities

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5) Coefficient of Variation:

is used to compare the biological variability between two sets of observations independent on the units of measurements

The coefficient of variation is calculated according to the following formula :

it is a statistical measure of data points of the whole data around the mean .present the standard deviation to the mean, and the ratio between them

and it is very useful in comparing the variation degree from one data to another one

even if the mean are completely different from one another

Karl Pearson. Evolved the measure * Sometimes, we need to compare two different data sets that have different units.

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*Importance:

wee can use it in too many major and fields such as :

(1) Business:

(2) In Economics:

(3) In Mathematics:

(4) In Banking:

(5) In State Management (Administration):

(6) In Accounting and Auditing:

(7) In Natural and Social Sciences:

(8) In Astronomy: