Braxton Pugh

2020-12-25

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.

SoosteethicU

Skilled2020-12-26Added 102 answers

a) The frequency of the class is defined as the total number of observations in the class, and the relative frequency of the class is defined as the ratio of the class frequency to the total number of observations in the class. The claim that two data sets with the same frequency distribution also have the same relative frequency distribution is thus true.

b) The distinction is that relative frequency of each class is multiplied by 100 to determine the proportion (percentage). If the percentage of a class is expressed as a decimal value, however, it is relative frequency of the class. According to the assertion, the ratio of the relative frequency distribution will equal the total of the two frequency distributions. Because doubling one distribution yields the entire value of the other, for instance, if the percentage of two distributions is 5, 4, 1, and 10, 8, 2, their values will differ even if they have the same relative frequency distribution. The claim that two data sets with the same relative frequency distribution also have the same frequency distribution is false.

c) Based on the findings of parts a and b, it can be seen that data sets with the same number of observations use the frequency or relative frequency distribution. In contrast, the relative frequency distribution is the best option if the data set contains a range of observation counts since the total of each set's relative frequencies equals one, making it simple and clear to compare the relative frequency distribution with other distributions. Therefore, relative frequency distribution is preferable than frequency distribution when comparing two data sets.

Vasquez

Expert2023-05-14Added 669 answers

user_27qwe

Skilled2023-05-14Added 375 answers

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