To predict future enrollment in a school district, fifty households within the district were sampled and asked to disclose the number of children under the age of five living in the household. The results of the survey are presented in the table. Complete parts (a) through (c) below.

\begin{tabular}{cc}
\hline
\begin{tabular}{c}
Number of Children \\ under 5
\end{tabular} & \begin{tabular}{c}
Households
\end{tabular} \\
\hline
0 & 17 \\
\hline
1 & 13 \\
\hline
2 & 16 \\
\hline
3 & 2 \\
\hline
4 & 2 \\
\hline
\end{tabular}

(a) Construct a relative frequency distribution of the data.

\begin{tabular}{cc}
\hline
\begin{tabular}{c}
Number of \\ Children under 5
\end{tabular} & \begin{tabular}{c}
Relative Frequency
\end{tabular} \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
3 & \\
\hline
4 & \\
\hline
\end{tabular}
(Type integers or decimals. Do not round.)



Answer :

To construct a relative frequency distribution of the data, follow these steps:

1. Determine the Total Number of Households Surveyed:
Add up all the households surveyed:
[tex]\[ 17 + 13 + 16 + 2 + 2 = 50 \][/tex]
Thus, the total number of households surveyed is 50.

2. Calculate the Relative Frequencies:
The relative frequency for each number of children under 5 is obtained by dividing the number of households with that number of children by the total number of households.

Here's the calculation for each category:

- For 0 children:
[tex]\[ \text{Relative Frequency} = \frac{17}{50} = 0.34 \][/tex]

- For 1 child:
[tex]\[ \text{Relative Frequency} = \frac{13}{50} = 0.26 \][/tex]

- For 2 children:
[tex]\[ \text{Relative Frequency} = \frac{16}{50} = 0.32 \][/tex]

- For 3 children:
[tex]\[ \text{Relative Frequency} = \frac{2}{50} = 0.04 \][/tex]

- For 4 children:
[tex]\[ \text{Relative Frequency} = \frac{2}{50} = 0.04 \][/tex]

3. Fill in the Relative Frequency Table:

\begin{tabular}{l|l}
\hline
\begin{tabular}{l}
Number of \\
Children under 5
\end{tabular} & \begin{tabular}{l}
Relative \\
Frequency
\end{tabular} \\
\hline 0 & 0.34 \\
\hline 1 & 0.26 \\
\hline 2 & 0.32 \\
\hline 3 & 0.04 \\
\hline 4 & 0.04 \\
\hline
\end{tabular}

These relative frequencies provide a clearer picture of the distribution of the number of children under 5 across the surveyed households.