# Answer true or false to each of the statements in parts (a) and (b), and explain

Answer true or false to each of the statements in parts (a) and (b), and explain your reasoning.
a. Two data sets that have identical frequency distributions have identical relative-frequency distributions.
b. Two data sets that have identical relative-frequency distributions have identical frequency distributions.
c. Use your answers to parts (a) and (b) to explain why relativefrequency distributions are better than frequency distributions for comparing two data sets.

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Yusuf Keller
a) Two data sets have identical frequency distributions have identical relative-frequency distributions.
The statement is true as for tabulating the values of relative frequency, it makes the use of the values of the frequency tables. So, the two data set have identical frequency distributions have identical frequency distribution,
Therefore, the given statement is true as for tabulating the values of relative frequency, it makes the use of the values of the frequency tables.
b) Two data sets have identical relative-frequency distributions have identical frequency distributions.
The statement is false as the total number of observations can be different in the two cases. So, if two data sets have identical relative-frequency distributions then they do not have identical frequency distributions
Therefore, the given statement is false as the total number of observations can be different in the two cases.
Step 2
c) Relative frequency distribution is better than frequency distribution for comparing two data sets because the relative frequency always lies between 0 and 1 . Thus, it provide a standard for comparison but this is not so in frequency distribution of data.
Therefore, the Relative frequency distribution is better than frequency distribution for comparing two data sets because the relative frequency always lies between 0 and 1 . Thus, it provides a standard for comparison.