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Math  /  Data & Statistics

QuestionTo 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}{l} Number of ChildrenNumber of \\ under 5\mathbf{5} \end{tabular} & \begin{tabular}{c} Households \end{tabular} \\ \hline 0 & 17 \\ \hline 1 & 14 \\ \hline 2 & 14 \\ \hline 3 & 4 \\ \hline 4 & 1 \\ \hline \end{tabular} \begin{tabular}{cc} \hline Number of & Relative \\ Children under & Frequency \\ \hline 0 & □\square \\ \hline 1 & □\square \\ \hline 2 & □\square \\ \hline 3 & □\square \\ \hline 4 & □\square \end{tabular} (Type integers or decimals. Do not round.) (b) What percentage of households has two children under the age of 5 ? □\square %\% (Type an integer or a decimal. Do not round.) (c) What percentage of households has one or two children under the age of 5 ? □\square %\% (Type an integer or a decimal. Do not round.)

Studdy Solution

STEP 1

1. The total number of households surveyed is 50.
2. The data for the number of households with children under the age of 5 is given in a table.
3. The relative frequency is calculated as the ratio of the number of households with a specific number of children to the total number of households surveyed.
4. Percentages are calculated by multiplying the relative frequency by 100.

STEP 2

1. Calculate the relative frequency for each category of children under the age of 5.
2. Determine the percentage of households with two children under the age of 5.
3. Determine the percentage of households with one or two children under the age of 5.

STEP 3

Calculate the relative frequency for households with 0 children under the age of 5.
Relative Frequency for 0 children=1750=0.34 \text{Relative Frequency for 0 children} = \frac{17}{50} = 0.34

STEP 4

Calculate the relative frequency for households with 1 child under the age of 5.
Relative Frequency for 1 child=1450=0.28 \text{Relative Frequency for 1 child} = \frac{14}{50} = 0.28

STEP 5

Calculate the relative frequency for households with 2 children under the age of 5.
Relative Frequency for 2 children=1450=0.28 \text{Relative Frequency for 2 children} = \frac{14}{50} = 0.28

STEP 6

Calculate the relative frequency for households with 3 children under the age of 5.
Relative Frequency for 3 children=450=0.08 \text{Relative Frequency for 3 children} = \frac{4}{50} = 0.08

STEP 7

Calculate the relative frequency for households with 4 children under the age of 5.
Relative Frequency for 4 children=150=0.02 \text{Relative Frequency for 4 children} = \frac{1}{50} = 0.02

STEP 8

To find the percentage of households with two children under the age of 5, multiply the relative frequency by 100.
Percentage for 2 children=0.28×100=28% \text{Percentage for 2 children} = 0.28 \times 100 = 28\%

STEP 9

To find the percentage of households with one or two children under the age of 5, add the relative frequencies for 1 child and 2 children, then multiply by 100.
Relative Frequency for 1 or 2 children=0.28+0.28=0.56 \text{Relative Frequency for 1 or 2 children} = 0.28 + 0.28 = 0.56 Percentage for 1 or 2 children=0.56×100=56% \text{Percentage for 1 or 2 children} = 0.56 \times 100 = 56\%
Solution: (a) The relative frequencies are: \begin{itemize} \item 0 children: 0.340.34 \item 1 child: 0.280.28 \item 2 children: 0.280.28 \item 3 children: 0.080.08 \item 4 children: 0.020.02 \end{itemize}
(b) The percentage of households with two children under the age of 5 is 28%28\%.
(c) The percentage of households with one or two children under the age of 5 is 56%56\%.

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