Measurements of spread are summary statistics that describe the variability or dispersion of a dataset. The three most commonly used measures of spread in statistics are:
Range: The range is the difference between the maximum and minimum values in a dataset. It provides a measure of the total spread of the data but is sensitive to extreme values.
Variance: The variance is the average of the squared differences between each data point and the mean of the dataset. It provides a measure of the spread of the data around the mean and is used to calculate other measures such as the standard deviation.
Standard deviation: The standard deviation is the square root of the variance. It provides a measure of the spread of the data around the mean and is often used to describe the typical amount of deviation from the mean. A smaller standard deviation indicates that the data points are clustered closely around the mean, while a larger standard deviation indicates that the data points are more spread out.
Other commonly used measures of spread include the interquartile range (IQR), which is the difference between the 75th percentile and the 25th percentile, and the coefficient of variation, which is the standard deviation divided by the mean expressed as a percentage.
The choice of which measure of spread to use depends on the characteristics of the dataset and the research question being addressed. For example, the range may be more appropriate for datasets with extreme values, while the standard deviation may be more appropriate for datasets with a normal distribution.