Statistics deals with data collected for specific purposes. A measure of central tendency gives a rough idea where data points are centred. But, in order to make better interpretation from the data, we should also have an idea how the data are scattered or how much they are bunched around a measure of central tendency.
Measures of Dispersion
The dispersion or scatter in a data is measured on the basis of the observations and the types of the measure of central tendency. Range, Quartile deviation, mean deviation, variance, standard deviation are measures of dispersion.
Range = Maximum Value - Minimum Value
The range of data gives a rough idea of variability or scatter but does not tell about the dispersion of the data from a measure of central tendency.
Mean deviation about a central value 'a' is the mean of the absolute values of the deviations of the observations from 'a'. Mean deviation from mean and median are commonly used in statistical studies.
Mean deviation for ungrouped data
Calculate the measure of central tendency about which you are to find the mean deviation. Let it be 'a'. Find the absolute values of the deviations from a. Then, find the mean of the absolute values of the deviations.
Mean deviation for grouped data
Data can be grouped into two ways - Discrete frequency distribution and Continuous frequency distribution. While calculating the mean of a continuous frequency distribution, make an assumption that the frequency in each class is centred at its mid-point.
Variance and Standard Deviation
Mean of the squares of the deviations from mean is called the variance and is denoted by σ2. Positive square-root of the variance and is called standard deviation.