Statistics deals with data collected for specific purposes. We can make decisions about the data by analysing and interpreting it.
Mean (arithmetic mean), median and mode are three measures of central tendency. A measure of central tendency gives us 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: Range, Quartile deviation, mean deviation, variance, standard deviation are measures of dispersion.
Range = Maximum Value - Minimum Value
The range of data gives us a rough idea of variability or scatter but does not tell about the dispersion of the data from a measure of central tendency. The important measures of dispersion, which depend upon the deviations of the observations from a central tendency are mean deviation and standard deviation.
Mean deviation may be obtained from any measure of central tendency. However, mean deviation from mean and median are commonly used in statistical studies.
Continuous frequency distribution: A continuous frequency distribution is a series in which the data are classified into different class-intervals without gaps along with their respective frequencies. While calculating the mean of a continuous frequency distribution, we had made the assumption that the frequency in each class is centred at its mid-point.
While calculating mean deviation about mean or median, the absolute values of the deviations were taken. The absolute values were taken to give meaning to the mean deviation, otherwise the deviations may cancel among themselves. Another way to overcome this difficulty which arose due to the signs of deviations, is to take squares of all the deviations. Mean of the squares of the deviations from mean is called the variance and is denoted by σ2 (read as sigma square).
The proper measure of dispersion about the mean of a set of observations is expressed as positive square-root of the variance and is called standard deviation.