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].
