Answered

A relative frequency table is made from data in a frequency table.



\begin{table}

\captionsetup{labelformat=empty}

\caption{Frequency Table}


GHTotal

E		121123

F		14822

Total		261945




\end{table}



\begin{table}

\captionsetup{labelformat=empty}

\caption{Relative Frequency Table}


GHTotal

E		$y$24\%51\%

F		31\%18\%49\%

Total		58\%42\%100\%




\end{table}



What is the value of $y$ in the relative frequency table? Round the answer to the nearest percent.


A52%
B27%

Verified Answer :

  • Identify the frequency of (E, G) as 12 and the total count as 45.
  • Apply the relative frequency formula: \(\frac{12}{45} \times 100\%\).
  • Perform the division and multiplication: \(0.2666... \times 100\% \approx 26.66...\% \).
  • Round the result to the nearest percent to get \(\boxed{27\%}\).

Explanation

  1. Analyze the data and identify the relevant frequencies

To determine the value of \(y\) in the relative frequency table, we need to calculate the relative frequency of the intersection of row E and column G. The relative frequency is defined as the ratio of a specific frequency to the total number of data points, usually expressed as a percentage. In our frequency table, the number of entries at the intersection of E and G is \(12\), and the total number of entries is \(45\).

  1. Apply the relative frequency formula

The formula to calculate the relative frequency \(y\) as a percentage is:
\[ y = \left( \frac{\text{Frequency of (E, G)}}{\text{Total Frequency}} \right) \times 100\% \]
Substituting the known values from the table:
\[ y = \left( \frac{12}{45} \right) \times 100\% \]

  1. Calculate and round the value of y

We perform the calculation:
\[ \frac{12}{45} \approx 0.2666... \]
Multiplying by \(100\%\) gives:
\[ 0.2666... \times 100\% \approx 26.66...\% \]
Rounding this value to the nearest percent, we get \(27\%\). Therefore, the value of \(y\) in the relative frequency table is \(27\%\).

Examples

Relative frequency tables are essential in statistics for comparing datasets of different sizes. For instance, if you were comparing the preferences of two different classrooms, you might convert raw counts into percentages (relative frequencies) to identify trends, such as "27% of students prefer activity G," regardless of whether one classroom has 45 students and the other has 100. This method provides a standardized way to interpret and present data across diverse contexts.

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