a)
The number of observation in the class is the frequency of the class and proportion of class frequency to the total number of frequency of that class is the relative frequency of the class respectively.
Thus, the statement of two data sets that have identical frequency distribution have identical relative frequency distribution is true.
b)
The difference is that the proportion (percentage) is calculated by the product of relative frequency of each class with 100 similarly, if the percentage of the class is expressed in decimal value then it is relative frequency of the class.
The statement implies that the sum of the two frequency distribution will be equal to the ratio of the relative frequency distribution. Since double the distribution of one will give the total value of the other distribution, and for example if the percentage of two distributions 5, 4, 1 and 10, 8, 2 will be different value but they have same relative frequency distribution.
Thus, the statement of two data sets that have identical relative frequency distribution have identical frequency distribution is false.
c)
From the results of part a and part b, it is observed that the frequency or relative frequency distribution is employed for the data sets which have the same number of observations in it.
Whereas, if the data set have different number of observation, the most appropriate choice of distribution is the relative frequency distribution, since because the sum of each set relative frequency is one and also for comparing both distribution in same basis is easy and understandable in case of relative frequency distribution.
Thus, for comparing two data sets, relative frequency distribution is the best over frequency distribution respectively.