Question

after constructing an expanded frequency distribution, what should the sum of the relative frequencies be? explain. choose the correct answer below. a. the sum should be n, since in the sum of the frequencies $sum f$, the numerator will be $n = sum f$. b. the sum should be 1, since in the sum of the frequencies $sum f$, the numerator will be $n = sum f$. c. the sum should be 1, since in the sum of the relative frequencies $sum \frac{f}{n}$, the numerator will be $n = sum f$. d. the sum should be n, since in the sum of the relative frequencies $sum \frac{f}{n}$, the numerator will be $n = sum f$.

Explanation:

Step1: Recall relative - frequency formula

The relative frequency of a class is given by $\frac{f}{n}$, where $f$ is the frequency of the class and $n=\sum f$ is the total number of data points (the sum of all frequencies).

Step2: Calculate sum of relative frequencies

The sum of the relative frequencies $\sum\frac{f}{n}$. Since $n = \sum f$ is a constant for the entire data - set, we can factor out $\frac{1}{n}$: $\sum\frac{f}{n}=\frac{1}{n}\sum f$. And we know that $\sum f=n$. So, $\frac{1}{n}\sum f=\frac{1}{n}\times n = 1$.

Answer:

C. The sum should be 1, since in the sum of the relative frequencies $\sum\frac{f}{n}$, the numerator will be $n=\sum f$.