##### Question

In: Statistics and Probability

# in a relative frequency distribution, what should the relative frequencies add up to?

in a relative frequency distribution, what should the relative frequencies add up to?

## Solutions

##### Expert Solution

In a relative frequency distribution the relative frequencies always add up to 1 .

explanation:

relative frequency = frequency of that class / total frequency.

example :

let, there are three classes with number of students $$a, b, c .$$

total number of students $$(n)=a+b+c$$

the relative frequency of the three classes are $$\mathrm{a} / \mathrm{n}, \mathrm{b} / \mathrm{n}, \mathrm{c} / \mathrm{n}$$ respectively. $$[\mathrm{n}=\mathrm{a}+\mathrm{b}+\mathrm{c}]$$

then the sum of the relative frequencies are:

$$=\frac{a}{n}+\frac{b}{n}+\frac{c}{n}=\frac{a+b+c}{n}=\frac{a+b+c}{a+b+c}=1$$

hence, it is proved .