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

Frequency Table
\begin{tabular}{|c|c|c|c|}
\hline & C & D & Total \\
\hline A & 15 & 25 & 40 \\
\hline B & 24 & 12 & 36 \\
\hline Total & 39 & 37 & 76 \\
\hline
\end{tabular}

Relative Frequency Table
\begin{tabular}{|l|c|c|c|}
\hline & C & D & Total \\
\hline & & & \\
\hline
\end{tabular}

What is the value of [tex][tex]$g$[/tex][/tex] in the relative frequency table?
Round the answer to the nearest percent.

A. [tex][tex]$25 \%$[/tex][/tex]
B. [tex][tex]$33 \%$[/tex][/tex]
C. [tex][tex]$63 \%$[/tex][/tex]
D. [tex][tex]$68 \%$[/tex][/tex]



Answer :

GinnyAnswer
To find the value of [tex]\( g \)[/tex] in the relative frequency table, we need to follow a step-by-step process to calculate the relative frequency for a specific category from the given frequency table.

1. Identify the relevant data:
- From the frequency table, we have:
- The sum of category A: [tex]\( \text{Total}_A = 40 \)[/tex]
- The overall total across all categories: [tex]\( \text{Total}_{\text{all}} = 76 \)[/tex]

2. Calculate the relative frequency:
- The relative frequency for category A is calculated by dividing the total for A by the overall total.
[tex]\[ \text{Relative frequency}_A = \frac{\text{Total}_A}{\text{Total}_{\text{all}}} = \frac{40}{76} \][/tex]

3. Convert the relative frequency to a percentage:
- Multiply the relative frequency by 100 to convert it to a percentage.
[tex]\[ \text{Percentage}_A = \left( \frac{40}{76} \right) \times 100 \][/tex]

4. Round to the nearest percent:
- After the calculation, the percentage [tex]\( \text{Percentage}_A \)[/tex] is:
[tex]\[ \text{Percentage}_A \approx 52.63\% \][/tex]
- When rounded to the nearest percent, it becomes [tex]\( 53\% \)[/tex].

Therefore, the value of [tex]\( g \)[/tex] in the relative frequency table is [tex]\( 53\% \)[/tex].

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