A relative frequency table is made from data in a frequency table.
Frequency Table
\begin{tabular}{|c|c|c|c|}
\hline & U & V & Total \\
\hline S & 5 & 8 & 13 \\
\hline T & 4 & 2 & 6 \\
\hline Total & 9 & 10 & 19 \\
\hline
\end{tabular}
Relative Frequency Table
\begin{tabular}{|c|c|c|c|}
\hline & U & V & Total \\
\hline & $\ldots$ & $\ldots$ & $\ldots$ \\
\hline
\end{tabular}
What is the value of $k$ in the relative frequency table?
Round the answer to the nearest percent.
A. $2 \%$
B. $11\%$
C. $20 \%$
D. $33 \%
Answer (2)
The value of k in the relative frequency table, calculated from the frequency of S and U, is approximately 26%. Among the given options, the closest value is 20%. Therefore, the correct answer is 20%.
;
Calculate the relative frequency of S and U: 19 5 .
Convert the fraction to a percentage: 19 5 × 100 ≈ 26.32% .
Round the percentage to the nearest percent: 26% .
Choose the closest option from the given choices: 33% .
Explanation
Understand the problem and provided data We are given a frequency table and asked to find the relative frequency of the cell where S and U intersect. The frequency table provides the counts for different categories, and we need to convert the frequency of S and U into a relative frequency, which is a percentage of the total observations.
Calculate the relative frequency The frequency of S and U is 5. The total number of observations is 19. To find the relative frequency, we divide the frequency of S and U by the total number of observations: 19 5
Convert to percentage To express this fraction as a percentage, we multiply by 100: 19 5 × 100
Round to the nearest percent Now, we calculate the value and round to the nearest percent. 19 5 × 100 ≈ 26.315789... Rounding this to the nearest percent gives us 26%.
Determine the final answer Therefore, the value of k in the relative frequency table, rounded to the nearest percent, is 26%. Among the given options, the closest value is 20% or 33% . However, since we calculated 26%, we need to re-evaluate the question. The question asks for the value of k, which represents the relative frequency of S and U. We calculated this to be approximately 26%. The options provided are 2%, 11%, 20%, and 33%. It seems there might be a typo in the options, or the question is slightly misleading. However, based on our calculation, 26% is the correct relative frequency. Since we must choose from the given options, and 26% is closer to 33% than 20%, we choose 33% as the closest answer.
Examples
Relative frequency tables are used in many real-world scenarios, such as analyzing survey data, understanding market trends, or assessing the distribution of grades in a classroom. For example, if a survey of 100 people shows that 60 prefer coffee over tea, the relative frequency of coffee drinkers is 60%. This information can help businesses make informed decisions about product offerings and marketing strategies.
