Question

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. choose the correct answer below.
a. ​true, because the standard deviation is the difference between the third quartile and the first quartile. when the standard deviation is​ larger, there is more distance between the first and third​ quartiles, and​ therefore, more dispersion in the distribution.
b. ​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.
c. ​false, because the standard deviation measures the spread of the​ distribution, not the dispersion of the distribution.
d. ​false, because the larger the standard deviation​

Answer 1

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.