Question

the relative - frequency table below displays the proportion of 40 residents in an apartment complex who prefer certain social media sites. which of the following is the corresponding frequency table?

Explanation:

Step1: Calculate total frequency

Total number of residents = 4 + 10+14 + 10+8 + 12+10 + 10+10 + 25+35 + 30=188

Step2: Calculate frequencies for each site

For Upstart: $\frac{4 + 10+8 + 10}{188}=\frac{32}{188}\approx0.17$ (not 0.10)
For Aster: $\frac{10 + 14+12 + 25}{188}=\frac{61}{188}\approx0.32$ (not 0.25)
For Babble: $\frac{14 + 10+10 + 35}{188}=\frac{69}{188}\approx0.37$ (not 0.35)
For Techy: $\frac{12 + 10+10 + 30}{188}=\frac{62}{188}\approx0.33$ (not 0.30)
However, if we assume there is a mistake in data - collection or the way we interpret and we go by the relative - frequency concept where relative frequency = $\frac{\text{Frequency of the category}}{\text{Total frequency}}$ and we consider the data in a more simplistic way (assuming the data is already grouped correctly in the question's context).
The sum of the given relative frequencies 0.10+0.25 + 0.35+0.30 = 1.
We calculate the frequencies for each site based on the total number of residents = 40.
For Upstart: $40\times0.10 = 4$
For Aster: $40\times0.25=10$
For Babble: $40\times0.35 = 14$
For Techy: $40\times0.30=12$
We can reverse - engineer the frequency table from the relative - frequency table.
The frequency table should have values such that when we calculate relative frequencies using the formula $\text{Relative Frequency}=\frac{\text{Frequency}}{\text{Total Frequency}}$, we get the given relative frequencies.
Let's check the sums of frequencies for each site in the original data (assuming we group them correctly).
If we assume the data is about counting preferences of 40 residents.
For Upstart: sum of relevant counts = 4 + 10+8 + 10 = 32 (wrong if total is 40)
If we go by the relative - frequency values given:
For Upstart: Frequency = $40\times0.10=4$
For Aster: Frequency = $40\times0.25 = 10$
For Babble: Frequency = $40\times0.35=14$
For Techy: Frequency = $40\times0.30 = 12$

Answer:

The frequency table with values corresponding to the given relative - frequency table for 40 residents:

Social Media Site	Frequency
Aster	10
Babble	14
Techy	12