Mr. Capuano, an art teacher, surveyed his students to find out whether they are satisfied with his classes. He also noted which class each student had taken.
Oil-painting
Satisfied: 17
Not satisfied: 3
Sculpture
Satisfied: 25
Not satisfied: 5
Art Classes
\begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} Oil \ Painting \end{tabular} & Sculpture & Total \\ \hline Satisfied & $34 \%$ & & $84 \%$ \\ \hline$\ldots \ldots$ & & & \\ \hline \end{tabular}
What is the value of $x$ in the relative frequency table for the survey results? Round the answer to the nearest percent.
$3 \%$
$6 \%$
$8 \%$
$15 \%
Answer (2)
Calculate the total number of students surveyed: 50 .
Determine the number of students taking Oil-painting and not satisfied: 3 .
Calculate the percentage: 50 3 = 6% .
The value of x is 6% .
Explanation
Understand the problem We are given a survey of art students, with data on satisfaction levels in Oil-painting and Sculpture classes. The goal is to find the value of x in the relative frequency table, which represents the percentage of students who took Oil-painting and were not satisfied.
Calculate total students in Oil-painting First, calculate the total number of students surveyed for Oil-painting: 17 + 3 = 20 .
Calculate total students in Sculpture Next, calculate the total number of students surveyed for Sculpture: 25 + 5 = 30 .
Calculate total students surveyed Then, calculate the total number of students surveyed: 20 + 30 = 50 .
Calculate percentage of Oil-painting students Now, calculate the percentage of students taking Oil-painting: 50 20 = 0.4 = 40% .
Calculate percentage of Sculpture students Calculate the percentage of students taking Sculpture: 50 30 = 0.6 = 60% .
Calculate percentage of satisfied students Calculate the percentage of satisfied students: 50 17 + 25 = 50 42 = 0.84 = 84% (given).
Calculate percentage of not satisfied students Calculate the percentage of not satisfied students: 50 3 + 5 = 50 8 = 0.16 = 16% .
Calculate the value of x The value of x is the percentage of 'Oil Painting' and 'Not satisfied'. We know that the number of 'Oil Painting' and 'Not satisfied' is 3. So, x = 50 3 = 0.06 = 6% .
State the final answer Therefore, the value of x in the relative frequency table for the survey results, rounded to the nearest percent, is 6% .
Examples
Understanding relative frequencies is crucial in many real-world scenarios. For example, in market research, companies use surveys to determine customer satisfaction with their products. By analyzing the relative frequencies of satisfied and dissatisfied customers, they can identify areas for improvement and make data-driven decisions to enhance their products and services. This helps in optimizing business strategies and improving overall customer experience.
The value of x in the relative frequency table for the survey results is 6% . This represents the percentage of students who took Oil-painting and were not satisfied. The calculation was based on the total number of students surveyed and the count of those not satisfied in the Oil-painting class.
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