To address the problem of finding the marginal relative frequency for the people who do not like bar soap, let's break down the solution step-by-step:
1. Understanding Marginal Relative Frequency:
Marginal relative frequency is the ratio of the total number of occurrences of an event to the total number of observations.
2. Identify the Total Number of Observations:
From the table, we see that the total number of people surveyed is 400. This information is located in the cell at the intersection of the "Total" row and the "Total" column.
3. Identify the Number of People Who Do Not Like Bar Soap:
The table shows that under the row "Not Bar" (for those who do not like bar soap), the total count is 100. This is found at the intersection of the "Not Bar" row and the "Total" column.
4. Calculate the Marginal Relative Frequency:
The marginal relative frequency for people who do not like bar soap is computed as the ratio of the number of people who do not like bar soap to the total number of people surveyed. This can be expressed as:
[tex]\[
\text{Marginal Relative Frequency} = \frac{\text{Number of people who do not like bar soap}}{\text{Total number of people surveyed}}
\][/tex]
5. Substitute the Known Values and Simplify the Fraction:
Plugging in the values we identified:
[tex]\[
\text{Marginal Relative Frequency} = \frac{100}{400} = 0.25
\][/tex]
Therefore, the correct answer is [tex]\(\frac{100}{400}\)[/tex], which simplifies to 0.25.
