A data set consists of integer values. If the value 7 has relative frequency 2/11, which statement must be true?
A) The data set contains 11 values.
B) The data set contains 22 values.
C) At least two of the data values are equal to 7.
D) The mode of the data set is 7.

Question

Quizplus · Accepted Answer

The relative frequency of a value is the number of times that value appears divided by the total number of observations in the data set. If the relative frequency of 7 is 2/11, it means that 7 appears $2/11 \times \text{total number of observations}$ times. Since you can't have a fraction of an occurrence, this means at least 2 occurrences of 7 are in the data set, making option C correct. Options A and B make specific claims about the total number of values in the data set, which cannot be determined from the given relative frequency alone. Option D assumes 7 is the mode, which is not necessarily true without knowing the frequency of other values in the data set.

A Data Set Consists of Integer Values