Measures of Variability

Variability refers to how spread out or dispersed a set of data values is. Measures of variability provide information about the amount of variation or diversity within a dataset. It helps to understand the extent to which individual data points differ from the central tendency.

Range

Range is the simplest measure of variability and represents the difference between the largest and smallest values in a dataset. It provides an overall sense of the spread of the data, but it is highly influenced by outliers.

Interquartile Range (IQR)

Interquartile Range (IQR) is a measure of variability that is not affected by extreme values or outliers. It is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1). The IQR provides a robust measure of dispersion for skewed or non-normally distributed data.

Variance

Variance is a measure of the average squared deviation from the mean. It quantifies the spread of data by calculating the average of the squared differences between each data point and the mean. Variance considers the entire dataset, making it sensitive to outliers or values far from the mean.

Standard Deviation

Standard Deviation is a widely used measure of variability that provides information about the dispersion of data around the mean. It is calculated as the square root of the variance. The standard deviation is particularly useful for interpreting normally distributed data and is widely used in statistical analysis.

Coefficient of Variation (CV)

Coefficient of Variation (CV) is a relative measure of variability that represents the standard deviation as a percentage of the mean. It allows for comparison of the variability between datasets with different units of measurement or scales. CV is often used in fields such as economics and finance.