Question

	liquid	not liquid	total
bar	200	100	300
not bar	80	20	100
total	280	120	400

which is the marginal relative frequency for the people who do not like bar soap?
\\(\frac{100}{400}\\)
\\(\frac{120}{400}\\)
\\(\frac{280}{400}\\)
\\(\frac{300}{400}\\)

Explanation:

Step1: Identify relevant totals

Find the total number of people who do not like bar soap (row "Not Bar" total) and the overall total number of people.
Row total for "Not Bar" = 100, Overall total = 400

Step2: Calculate marginal relative frequency

Divide the "Not Bar" total by the overall total.
$\text{Marginal relative frequency} = \frac{100}{400}$

Answer:

$\frac{100}{400}$ (Option 1: $\frac{100}{400}$)