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My score: [tex][tex]$12.94 / 26$[/tex][/tex] pts (49.76%)

The data below represent the per capita (average) disposable income (income after taxes) for 25 randomly selected cities in a recent year. Complete parts (a) and (b).

\begin{tabular}{llll}
30,200 & 34,274 & 36,932 & 40,200 \\
30,443 & 34,773 & 37,252 & 41,034 \\
30,724 & 34,983 & 37,875 & 41,326 \\
32,125 & 35,286 & 38,472 & 52,425 \\
32,936 & 35,524 & 38,776 & \\
33,787 & 35,830 & 38,880 & \\
34,036 & 35,941 & 39,702 &
\end{tabular}

\begin{tabular}{cc}
Class & Frequency \\
\hline
[tex]$30,000-35,999$[/tex] & 14 \\
[tex]$36,000-41,999$[/tex] & 10 \\
[tex]$42,000-47,999$[/tex] & 0 \\
[tex]$48,000-53,999$[/tex] & 1
\end{tabular}

(b) Construct a relative frequency distribution with the first class having a lower class limit of 30,000 and a class width of 6,000.
(Type integers or decimals.)



Answer :

GinnyAnswer
To solve this problem, we need to construct a relative frequency distribution table for the given data on per capita disposable income in 25 cities.

### Step-by-Step Solution:

#### Step 1: Identify the Classes
The first class limit is given as [tex]$30,000 and the class width is $[/tex]6,000. So, we break down the income ranges as follows:
- Class 1: [tex]$30,000 - $[/tex]35,999
- Class 2: [tex]$36,000 - $[/tex]41,999
- Class 3: [tex]$42,000 - $[/tex]47,999
- Class 4: [tex]$48,000 - $[/tex]53,999

#### Step 2: Count the Frequencies
We count how many data points fall into each class:
- Class 1 ([tex]$30,000 - $[/tex]35,999): 14 data points
- Class 2 ([tex]$36,000 - $[/tex]41,999): 10 data points
- Class 3 ([tex]$42,000 - $[/tex]47,999): 0 data points
- Class 4 ([tex]$48,000 - $[/tex]53,999): 1 data point

This directly matches the information provided in the question:
[tex]\[ \begin{tabular}{|c|c|} \hline Class & Frequency \\ \hline $30,000-35,999$ & 14 \\ $36,000-41,999$ & 10 \\ $42,000-47,999$ & 0 \\ $48,000-53,999$ & 1 \\ \hline \end{tabular} \][/tex]

#### Step 3: Calculate Relative Frequencies
The relative frequency for each class is calculated by dividing the frequency of each class by the total number of data points, which is 25.

[tex]\[ \text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Data Points}} \][/tex]

So, for each class:
- Class 1: [tex]\( \frac{14}{25} = 0.56 \)[/tex]
- Class 2: [tex]\( \frac{10}{25} = 0.40 \)[/tex]
- Class 3: [tex]\( \frac{0}{25} = 0.00 \)[/tex]
- Class 4: [tex]\( \frac{1}{25} = 0.04 \)[/tex]

#### Step 4: Construct the Relative Frequency Distribution Table
The relative frequency distribution table will be:
[tex]\[ \begin{tabular}{|c|c|} \hline Class & Relative Frequency \\ \hline $30,000-35,999$ & 0.56 \\ $36,000-41,999$ & 0.40 \\ $42,000-47,999$ & 0.00 \\ $48,000-53,999$ & 0.04 \\ \hline \end{tabular} \][/tex]

### Conclusion:
The final relative frequency distribution table is:

[tex]\[ \begin{tabular}{|c|c|} \hline Class & Relative Frequency \\ \hline $30,000-35,999$ & 0.56 \\ $36,000-41,999$ & 0.40 \\ $42,000-47,999$ & 0.00 \\ $48,000-53,999$ & 0.04 \\ \hline \end{tabular} \][/tex]

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