Measures of Dispersion Test - 2

Measures of dispersion attempt to describe the spread of the data values in a data set. Dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.

It should be based on all the items so as to be more representative of whole series

Absolute measure of dispersion include range, quartile deviation, standard deviation, variance and relative measure of dispersion include coefficient of range, coefficient of quartile deviation, coefficient of standard deviation, coefficient of variance.

It is a absolute measure of dispersion

It is based on the lower quartile Q1 and the upper quartile Q3. The difference Q3−Q1 is called the inter quartile range. The difference  Q3−Q1 divided by 2 is called semi-inter-quartile range or the quartile deviation.

Standard deviation is square root of variance which is also knows as mean square deviation.

The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma). The formula is easy: it is the square root of the Variance. So the square of σ is variance.

Standard Deviation is the positive square root of the mean of squared deviations from mean. So if there are five values x1, x2, x3, x4 and x5, first their mean is calculated. Then deviations of the values from mean are calculated. These deviations are then squared. The mean of these squared deviations is the variance. Positive square root of the variance is the standard deviation.

Variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of (random) numbers are spread out from their average value.The variance is the square of the standard deviation, the second central moment of a distribution, and the co variance of the random variable with itself.