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 relative frequencies ∑(f / n), the numerator will be n = ∑f. b. the sum should be 1, since in the sum of the relative frequencies ∑(f / n), the numerator will be n = ∑f. c. the sum should be 1, since in the sum of the frequencies ∑f, the numerator will be n = ∑f. d. the sum should be n, since in the sum of the frequencies ∑f, the numerator will be n = ∑f.

Explanation:

Step1: Recall relative - frequency formula

The formula for relative frequency of a class is $\frac{f}{n}$, where $f$ is the frequency of the class and $n=\sum f$ (total frequency).

Step2: Sum of relative - frequencies

When we sum up all the relative frequencies $\sum\frac{f}{n}$, since $n = \sum f$, we have $\sum\frac{f}{n}=\frac{\sum f}{n}$. Substituting $n=\sum f$ into the formula, we get $\frac{\sum f}{\sum f}=1$.

Answer:

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