Question

What is Variation? ( Stats for criminal justice )

Answer 1

the variation is another name of dispersion in statistics. The various measures of variation or dispersion are standard deviation, variance, interquartile range, and range.

The standard deviation measures the dispersion in true units. However, the variance measures the dispersion in square units. sd = sqrt(variance) ; variance = sum(Xi-Xbar)^2/(n-1). In the case of a variable following a normal distribution, the standard deviation is considered as the best measure of dispersion. A low value of standard deviation indicates that the mean is a reliable measure of Central tendency. A high value of standard deviation indicates that mean is not a reliable measure of Central tendency.

Considering a scenario of criminal justice, the variable total number of crimes corresponding to various cities in the United States is an area of interest. A low value of standard deviation for the total number of crimes would indicate, mean is a reliable measure of Central tendency for this variable. hypothetically, I can say that the average number of crimes in a city of the United States is 30,000 per year. This value of 30000 is considered to be reliable with the low value of standard deviation as 3003 only.