A cell phone company surveyed 200 random customers on whether they were satisfied with their phone service. They also noted which service plan each customer had. The results are shown in the frequency table below.
Use this table to create a relative frequency table.
\begin{tabular}{|c|c|c|c|}\hline & Plan A & Plan B & Total \\ \hline Satisfied & 104 & 64 & 168 \\ \hline Not Satisfied & 8 & 24 & 32 \\ \hline Total & 112 & 88 & 200 \\ \hline \end{tabular}
Drag each tile to the correct cell in the table.
4\%
16\%
100\%
56\%
$12 \%$
84\%
44\%
32\%
52\%
\begin{tabular}{|c|c|c|} \hline & Plan A & Plan B \\ \hline Total & Satisfied & \\ \hline & & Not satisfied \\ \hline & & \\ \hline \end{tabular}
Answer (1)
Calculate the relative frequency for each cell by dividing the cell frequency by the total number of customers (200).
Convert each relative frequency to a percentage by multiplying by 100.
Populate the relative frequency table with the calculated percentages.
The percentages for each category are: Satisfied, Plan A: 52%; Satisfied, Plan B: 32%; Not Satisfied, Plan A: 4%; Not Satisfied, Plan B: 12%.
Explanation
Understand the problem and provided data We are given a frequency table showing the results of a cell phone company survey of 200 customers. The customers are categorized by service plan (Plan A and Plan B) and satisfaction (Satisfied and Not Satisfied). Our goal is to create a relative frequency table from the given frequency table.
Outline the solution To create a relative frequency table, we need to calculate the relative frequencies for each cell by dividing the cell frequency by the total number of customers (200). Then, we convert each relative frequency to a percentage by multiplying by 100.
Calculate relative frequencies
Calculate the relative frequency for 'Satisfied' with 'Plan A': 200 104 = 0.52 . Converting to percentage: 0.52 × 100 = 52% .
Calculate the relative frequency for 'Satisfied' with 'Plan B': 200 64 = 0.32 . Converting to percentage: 0.32 × 100 = 32% .
Calculate the relative frequency for 'Not Satisfied' with 'Plan A': 200 8 = 0.04 . Converting to percentage: 0.04 × 100 = 4% .
Calculate the relative frequency for 'Not Satisfied' with 'Plan B': 200 24 = 0.12 . Converting to percentage: 0.12 × 100 = 12% .
Calculate the relative frequency for 'Total' with 'Plan A': 200 112 = 0.56 . Converting to percentage: 0.56 × 100 = 56% .
Calculate the relative frequency for 'Total' with 'Plan B': 200 88 = 0.44 . Converting to percentage: 0.44 × 100 = 44% .
Calculate the relative frequency for 'Satisfied' with 'Total': 200 168 = 0.84 . Converting to percentage: 0.84 × 100 = 84% .
Calculate the relative frequency for 'Not Satisfied' with 'Total': 200 32 = 0.16 . Converting to percentage: 0.16 × 100 = 16% .
Calculate the relative frequency for 'Total' with 'Total': 200 200 = 1.0 . Converting to percentage: 1.0 × 100 = 100% .
Present the relative frequency table The relative frequency table is as follows:
Plan A
Plan B
Total
Satisfied
52%
32%
84%
Not Satisfied
4%
12%
16%
Total
56%
44%
100%
State the final answer The percentages for each category are:
Satisfied, Plan A: 52% Satisfied, Plan B: 32% Not Satisfied, Plan A: 4% Not Satisfied, Plan B: 12%
Examples
Relative frequency tables are useful in market research to understand customer satisfaction levels across different product lines or service plans. For example, a company might survey customers to determine satisfaction with different phone plans. The relative frequency table can then highlight which plans have higher satisfaction rates, helping the company make informed decisions about resource allocation and product improvement. If 52% of Plan A customers are satisfied, while only 32% of Plan B customers are, the company might investigate the reasons for this difference to improve Plan B.
