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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 & G & H & Total \\
\hline E & 12 & 11 & 23 \\
\hline F & 14 & 8 & 22 \\
\hline Total & 26 & 19 & 45 \\
\hline
\end{tabular}

Relative Frequency Table
\begin{tabular}{|c|c|c|c|}
\hline & G & H & Total \\
\hline E & & & \\
\hline F & & & \\
\hline Total & & & \\
\hline
\end{tabular}

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

A. [tex]$12 \%$[/tex]
B. [tex]$27 \%$[/tex]
C. [tex]$46 \%$[/tex]
D. [tex]$52 \%$[/tex]

Sagot :

GinnyAnswer
To determine the value of [tex]\( y \)[/tex] in the relative frequency table, we need to calculate the relative frequency of a specific value from the frequency table.

Given the frequency table:

[tex]\[ \begin{array}{|c|c|c|c|} \hline & G & H & \text{Total} \\ \hline E & 12 & 11 & 23 \\ \hline F & 14 & 8 & 22 \\ \hline \text{Total} & 26 & 19 & 45 \\ \hline \end{array} \][/tex]

The total number of values (sum of all frequencies) is [tex]\( 45 \)[/tex].

We are focusing on the value 12 in cell E-G. To find its relative frequency, we use the formula:

[tex]\[ \text{Relative Frequency} = \left( \frac{\text{Frequency of the value}}{\text{Total number of values}} \right) \times 100 \][/tex]

For cell E-G:

[tex]\[ \text{Relative Frequency} = \left( \frac{12}{45} \right) \times 100 \][/tex]

This gives us:

[tex]\[ \left( \frac{12}{45} \right) \times 100 \approx 26.6667 \][/tex]

Rounding this to the nearest percent, we get:

[tex]\[ 27\% \][/tex]

Thus, the value of [tex]\( y \)[/tex] in the relative frequency table is:

[tex]\[ \boxed{27\%} \][/tex]
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