The following points highlight the five types of measures of variability. The types are: 1. Range 2. Standard Deviation 3. Variance 4. Standard Error 5. Coefficient of Variation.
Variability: Type # 1. Range:
Range is the difference between the lowest and the highest values present in the observations in a sample. If there are 20 observations on seed oil content in cotton, the highest value being 25% and the lowest 15%. The range will be 25-15 = 10. Thus, it is a measure of the spread of variation in a sample.
It is the simplest possible measure of variability and its computation is very easy. However, it is very crude measure of variability. It is not capable of further algebraic treatment and cannot be defined rigidly. It is greatly affected by fluctuation of sampling. It does not indicate as to how the data behave in between the highest and the lowest value. It is commonly used as a measure of variability in plant breeding populations.
Dispersion: Type # 2. Standard Deviation:
It is the square root of the arithmetic mean of the squares of the deviations measured from the mean. In other words, it is a square root of the variance. It is the best measure of variation in a population. Thus,
Standard deviation is based on all the observations of a sample and is capable of further algebraic treatment. It is rigidly defined and is less affected by fluctuation of sampling. Its value is always definite. However, it gives more weight to extreme items and less to those which are near to the mean.
Variability: Type # 3. Variance:
Variance is defined as the average of the squared deviation from the mean or it is the square of the standard deviation. It is expressed as the sum of squares of the deviations of all observations of a sample from its mean and divided by degree of freedom (N-1). It is an effective measure of variability which permits partition of variation into various components.
It is estimated by the following formula:
where, ∑, x, x2 and N = summation, an observation, square of an observation, and number of observations, respectively.
Variability: Type # 4. Standard Error:
It is the measure of the mean difference between sample estimate of mean (X) and the population parameter (µ), i.e., it is the measure of uncontrolled variation present in a sample. It is estimated by dividing the estimates of standard deviation by the square root of number of observations in the sample, and is denoted by SE. Thus,
where, SD = standard deviation and N = number of observations.
Variability: Type # 5. Coefficient of Variation:
The standard deviation is an absolute measure of variation and is expressed in terms of the unit of the variable. For example, it would be in rupees for income, in cm for height and in kg or gm. for weight. For the purpose of comparative studies a relative measure of dispersion or variation is required.
Coefficient of variation serves this purpose as it does not have any unit. The ratio of standard deviation of a sample to its mean expressed in percentage is called coefficient of variation. Thus,
Coefficient of Variation (CV) = SD/x X100
This measure was evolved by Karl Pearson. It is very useful for the study of variation in more than one sample or series. A sample in which coefficient of variation is higher would have greater variation than the one in which it is lower. In other words, when the coefficient of variation is high the sample is less consistent or more variable and when it is low the sample is more consistent or less variable.
In plant breeding, phenotypic, genotypic and environmental coefficients of variation are estimated from the corresponding variances, and are used for the assessment of variability. Simple measures of variability can be worked out from both un-replicated and replicated data.