In this article we will discuss about the meaning and co-efficient of Variance.
Meaning of Variance:
It is very useful measure of dispersions which is commonly used for population data. The arithmetic mean of the squares of deviations obtained from the mean is referred to as variance. It is based on standard deviation and the square of the standard deviation is termed as variance.
Co-Efficient of Variation:
Co-efficient of variation is a relative term which measures the relative magnitudes of variations present in observations and is related to the magnitude of their arithmetic mean. Since the standard deviation is independent measure of dispersion obtained from a single series of data, the comparison of variability of two different series of data is not possible directly by standard deviations.
To make it possible Karl Pearson used co-efficient of variation. Co-efficient of variation is defined as the ratio of standard deviation to arithmetic mean and is expressed in percentage. Co-efficient of variation or CV (%) = σ /x × 100, where σ = standard deviation of a series x = arithmetic mean of series.
Thus, when standard deviation of a series is compared to arithmetic mean of the series in terms of percentage, we get co-efficient of variation. It expresses the relative variability of each data series. The co-efficient of variation can be used to compare the homogeneity, consistency and stability of data of two or more series.
The data series with high value of co-efficient of variation is said to be unstable and the series with low values of co-efficient of variation are stable and they show good degree of homogeneity of data.
Example:
Compare the relative variability of two samples with the following data:
Example:
Calculate standard deviation, variance and co-efficient of variation form the following classified data regarding number of pods per plant recorded on 50 plants in a plot.
