Final answer:
The correct operation for calculating relative frequency distributions is dividing the frequency of each category by the total number of observations. This ratio highlights the proportion each category represents in the dataset. Cumulative relative frequency adds up all previous relative frequencies to the current one.
Step-by-step explanation:
The operation that is true regarding relative frequency distributions is c) Dividing the frequency of each category by the total number of observations. This process allows you to determine the relative frequency, which represents the proportion of times a certain value occurs in relation to the total number of observations in a dataset. The formula to find the relative frequency is:
- Relative frequency of a category = (Frequency of the category) / (Total number of observations)
To illustrate, consider a class of 20 students with different hair colors. If 4 students have blonde hair, the relative frequency of the 'blonde hair' category would be 4/20 or 0.20 (20%).
A cumulative relative frequency is found by adding all previous relative frequencies to the current relative frequency. For example, if the first category has a relative frequency of 0.15 and the next category has a relative frequency of 0.25, the cumulative relative frequency for the second category would be 0.15 + 0.25 = 0.40.
It's important when creating a frequency table to include the data, frequencies, relative frequencies, and cumulative relative frequencies to get a comprehensive understanding of the distribution. Relative frequencies can be expressed as fractions, decimals, or percentages.