To determine the marginal relative frequency for the people who do not like bar soap, we need to focus on the "Not Bar" row in the provided table.
1. First, identify the total number of people surveyed. From the table, the total number of people surveyed is given in the bottom right cell, which is 400.
2. Next, determine the number of people who do not like bar soap. According to the table, these people are represented in the "Not Bar" row under the "Total" column, which is 100.
3. The marginal relative frequency is the fraction of the people who do not like bar soap from the total number of people surveyed. This is calculated as follows:
[tex]\[
\text{Marginal Relative Frequency} = \frac{\text{Number of people who do not like bar soap}}{\text{Total number of people surveyed}} = \frac{100}{400}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{100}{400} = 0.25
\][/tex]
Thus, the marginal relative frequency for the people who do not like bar soap is 0.25, which corresponds to 25% of the total surveyed population. Therefore, the correct choice from the options provided is [tex]\( \frac{100}{400} \)[/tex].
