Question

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

	g	h	total
f	14	8	22
total	26	19	45

relative frequency table

	g	h	total

what is the value of y in the relative frequency table? round the answer to the nearest percent.
○ 12%
○ 27%
○ 46%
○ 52%

Explanation:

Step1: Identify the relevant frequency

In the frequency table, for the row or column related to \( y \), we need to find the frequency. Looking at the relative frequency table context, likely \( y \) is related to the frequency of a cell. Let's assume \( y \) is the relative frequency of a cell, say the cell for F and G or F and H? Wait, no, let's check the total. The total number of observations is 45 (from the frequency table's total). Let's see, maybe \( y \) is the relative frequency of the cell for F and G? Wait, the frequency for F and G is 14. Wait, no, maybe the row F? Wait, the relative frequency table has a total for E as 54%? Wait, no, the frequency table: E has total 23, F has total 22. Wait, the relative frequency is frequency divided by total (45). Let's check the options. The options are 12%, 27%, 46%, 52%. Wait, maybe \( y \) is the relative frequency of the cell for F and G? Wait, frequency of F and G is 14. So relative frequency is \( \frac{14}{45} \approx 0.311 \), no. Wait, maybe the row F? The total for F is 22. So \( \frac{22}{45} \approx 0.488 \), no. Wait, maybe the column G? Total for G is 26. \( \frac{26}{45} \approx 0.577 \), no. Wait, maybe the cell for E and G? Frequency 12. \( \frac{12}{45} \approx 0.266 \), which is 27% when rounded. Ah, that's one of the options. Let's verify: \( \frac{12}{45} = \frac{4}{15} \approx 0.2667 \), which is approximately 27%.

Step2: Calculate the relative frequency

To find the relative frequency, we use the formula: \( \text{Relative Frequency} = \frac{\text{Frequency of the cell}}{\text{Total number of observations}} \). Let's take the cell with frequency 12 (E and G). Total observations is 45. So \( \frac{12}{45} \approx 0.2667 \), which is 27% when rounded to the nearest percent.

Answer:

27% (Option: 27%)