Similarities and Differences of Proportion, Mean, and Standard Deviation.Variance

The three population characteristics differ primarily by their definitions. For instance, population proportion is a fraction of a set of people with a specific characteristic to the whole population. In contrast, mean is the sum of the total number of people in a population divided by the numeric value of the total population. Also, Standard Deviation or variance are measures of the distribution of a data set in a population from the mean of the data set.

A population mean is similar to the standard deviation in that both concern a specific data set in relation to the whole population. Both can be represented in a binomial distribution, for which the conditions must be satisfied. In contracts, mean concerns the whole population, not an explicit data set. Nevertheless, both mean and standard deviation or variance present some similarities. For instance, they have one critical value in a data set – the mean, from which the variance would spread. They also concern combining all values of a data set, to produce a measure (characteristic) of a population. However, I think this relationship is sophisticated since a change in a population’s data set would cause a shift to the mean of the data set, and a spread of the variance.

Additionally, the three characteristics are sampled. Mean is the average value of a data set (sample) in a population, while proportion illustrates the relationship of each sample with the whole population. Standard deviation uses chi-square to select independent samples, which is used in the sampling distribution.