3.2 Measures of Dispersion

Discuss limitations of the range as a measure of dispersion.

The range only takes into account the smallest and largest​ values, which does not provide any information about the dispersion of the distribution between those values.

The sum of the deviations about the mean

always equals 0

Standard Deviation (SD)

measures the average difference between each score and the mean of the data set

When comparing two​ populations, the larger the standard​ deviation,

the more dispersion the distribution has.

True or​ False: When comparing two​ populations, the larger the standard​ deviation, the more dispersion the distribution​ has, provided that the variable of interest from the two populations has the same unit of measure.

​True, because the standard deviation describes how​ far, on​ average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical​ value, and​ therefore, more dispersed.