Compare Measures of variation quick check

Answer 1

Measures of variation, such as range, variance, and standard deviation, are used to describe the spread or dispersion of a set of data points.

Range is the simplest measure of variation and is calculated by subtracting the smallest value from the largest value in a data set. It provides a quick way to see how spread out the data is, but it can be greatly affected by outliers.

Variance is a more sophisticated measure of variation that takes into account the average distance of each point from the mean. It involves squaring the differences between each data point and the mean, summing those squared differences, and then dividing by the number of data points. While variance provides a more precise measure of spread, it can be difficult to interpret because it is in square units.

Standard deviation is the square root of the variance and is often preferred as a measure of variation because it is in the same units as the original data. It represents the average distance of each data point from the mean and provides a more intuitive understanding of the spread of the data.

In summary, range is quick and easy to calculate but is sensitive to outliers, variance is a precise measure of spread, and standard deviation is a more commonly used and easily interpretable measure of variation.