Final answer:
A marginal relative frequency is the ratio of the frequency of a category to the total number in a two-way table, which helps analyze data in one of the margins, like the proportion of women in a sampled population. It's calculated by dividing the category count by the total sample count. An example in a sample of 100 would have a relative frequency of 0.05 if an event occurred 5 times.
Step-by-step explanation:
A marginal relative frequency is used in the analysis of two-way tables. It refers to the proportion of a total count that falls within a particular category at the margins of the table. To calculate a marginal relative frequency, you can focus on just one variable. For example, if a two-way table shows that 20 out of a total of 50 people sampled are women, then the marginal relative frequency for women is 20/50 or 0.40. The table's margins provide the sums of each row and column, and these sums are used to determine the marginal relative frequencies.
To illustrate further, imagine a scenario where a sample size is 100 and we want to determine the relative frequency distribution. If an event occurred 5 times, the relative frequency would be the frequency (5) divided by the total number of outcomes (100), giving us 5/100 or 0.05. This process is repeated for each event to build a full relative frequency distribution.