MEASURES OF VARIABILITY

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MEASURES OF VARIABILITY

Range
The range is the most obvious measure of dispersion and is the difference between the lowest and highest values in a dataset
Standard Deviation
The standard deviation is a measure that summarizes the amount by which every value within a dataset varies from the mean. The standard deviation is simply the square root of the variance.
For datasets that have a normal distribution the standard deviation can be used to determine the proportion of values that lie within a particular range of the mean value. For such distributions it is always the case that 68% of values are less than one standard deviation (ISD) away from the mean value, that 95% of values are less than two standard deviations.(2SD) away from the mean and that 99% of values are less than three standard deviations (3SD) away from the mean. 
Quartile Deviation
The quartile deviation is a measure that indicates the extent to which the central 50% of values within the dataset are dispersed In the same way that the median divides a dataset into two halves, it can be further divided into quarters by identifying the upper and lower quartiles. 
The lower quartile is found one quarter of the way along a dataset when the values have been arranged in order of magnitude; the upper quartile is found three quarters along the dataset. Therefore, the upper quartile lies half way between the median and the highest value in the dataset whilst the lower quartile lies halfway between the median and the lowest value in the dataset. The quartile deviation is found by subtracting the lower quartile from the upper quartile and the answer is divided by two.

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