The relative frequency table below displays the proportion of residents in an apartment complex who prefer certain social media sites.
| Upstart | Aster | Babble | Techy |
|---|---|---|---|
| 0.10 | 0.25 | 0.35 | ?? |
Which of the following is the missing value?
A. 0.1
B. 0.2
C. 0.3
D. 0.35
Answer (2)
The sum of proportions in a relative frequency table equals 1.
Set up the equation: 0.10 + 0.25 + 0.35 + x = 1 .
Solve for x : x = 1 − 0.10 − 0.25 − 0.35 = 0.30 .
The missing value is 0.3 .
Explanation
Understand the problem and provided data We are given a relative frequency table showing the proportion of residents preferring different social media sites. The sites are Upstart (0.10), Aster (0.25), Babble (0.35), and Techy (unknown). The sum of all proportions in a relative frequency table must equal 1.
Set up the equation Let x be the proportion of residents who prefer Techy. We can set up the equation: 0.10 + 0.25 + 0.35 + x = 1
Solve for x Now, we solve for x :
0.10 + 0.25 + 0.35 + x = 1 0.70 + x = 1 x = 1 − 0.70 x = 0.30
State the final answer Therefore, the missing value for Techy is 0.30.
Examples
In market research, understanding the popularity of different social media platforms among a specific demographic (like residents in an apartment complex) is crucial. This helps businesses tailor their advertising strategies to reach their target audience effectively. By calculating the relative frequencies, companies can determine which platforms are most used and allocate their marketing resources accordingly, maximizing their impact and return on investment. For example, if Techy has a proportion of 0.30, it suggests that 30% of the residents prefer this platform, making it a significant channel for advertising.
The missing value for Techy in the relative frequency table is 0.30. This value is found by ensuring that all proportions in the table sum up to 1. Therefore, the answer is x = 0.30.
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