Answer
The relative frequencies should add up to $1$.
Work Step by Step
Look at the following example.
In a basket, there were $10$ peaches. After counting, I found that
- $2$ are too ripe to be eaten (so we can call this category 'inedible-too ripe').
- $7$ are just ripe enough to be able to eat ('edible' category).
- $1$ is still unripe ('inedible-unripe' category).
1) Now we calculate the relative frequency of each category of data, which is the frequency divided by the sum of all frequencies (here it means the total number of peaches):
- Inedible-too ripe category: $\frac{2}{10}=0.2$
- Edible category: $\frac{7}{10}=0.7$
- Inedible-unripe category: $\frac{1}{10}=0.1$
2) Now we add up all the relative frequencies:
$$0.2+0.7+0.1=1$$
Therefore, the relative frequencies add up to $1$.
This is reasonable since each category takes over a distribution of the number of occurrences. This means that if they are all summed up together, they would equal the total number of occurrences, or in the above example, $\frac{10}{10}=1$.
