Question

In your own words, discuss measures of variability as they are associated with frequencies.

Include a discussion of variance and standard deviation. What is the difference between the two and how can they be used to explain the same distribution.

Answer 1

By measure of variability we mean we mean a summary statistic that measures the amount of dispersion in a dataset.it describes how far away the data points fall from the center. A low dispersion indicates a low measure of variability which means the data are well organised that is the data are clustered around the mean while a high value of dispersion indicates that the data points are spread far awar from the mean. Measures of dispersion are standard deviation, variance, mean deviation about mean etc.

Variance (s²) & standard deviation (s) are most commonly used measure of variability. By variance we mean a measure of how much a data is spread. It is calculated as the average squared deviation of each number from the mean of a data set. By taking the square root of the variance we get the units used in the original scale and this is the standard deviation.

The difference are

1.Variance is nothing but the average of the squares of the deviations,Unlike, standard deviation is the square root of the numerical value obtained while calculating variance.

2. Variance is the It is the average of squared deviations while standard deviation is the root mean square deviation.

3. Variance is expressed in Squared units but standard deviation is expressed in same units as the values in the set of data.

To use :

variance is defined as the measure of variability that represents how far members of a distribution are spread out. It finds out the average degree to which each observation varies from the mean.

Standard deviation is a measure that quantifies the amount of dispersion of the observations in a distribution.