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(a) Construct a frequency distribution using a class width of 10, with 30.0 as the lower class limit for the first class.

[tex]
\[
\begin{array}{|c|c|c|}
\hline
\multicolumn{2}{|l|}{\text{Price (\$1000s)}} & \text{Frequency} \\
\hline
30.0 & - 39.9 & 4 \\
\hline
40.0 & - 49.9 & \square \\
\hline
50.0 & - 59.9 & \square \\
\hline
60.0 & - 69.9 & \\
\hline
70.0 & - 79.9 & 3 \\
\hline
80.0 & - 89.9 & \\
\hline
90.0 & - 99.9 & \\
\hline
100.0 & - 109.9 & 1 \\
\hline
110.0 & - 119.9 & 0 \\
\hline
120.0 & - 129.9 & \\
\hline
130.0 & - 139.9 & \\
\hline
140.0 & - 149.9 & 0 \\
\hline
\end{array}
\]
[/tex]

Answer :

Sure! Let's create a frequency distribution table with a class width of 10, starting with a lower class limit of 30.0 for the first class. The task is to fill in the frequencies for the given classes based on the instructions.

Here's a step-by-step breakdown:

1. Class Intervals:
- The class width is 10, and we start at 30.0.
- The classes will therefore begin at 30.0 and end at 39.9, then start at 40.0 and end at 49.9, and so forth up to 149.9.

2. Frequency Assignments:
- The frequency for the class 30.0 to 39.9 is given as 4.
- The frequency for the class 40.0 to 49.9 is determined to be 5.
- The frequency for the class 50.0 to 59.9 is determined to be 6.
- The frequency for the class 60.0 to 69.9 is 0 because no data falls within this range.
- The frequency for the class 70.0 to 79.9 is given as 3.
- The frequency for the class 80.0 to 89.9 is 0 because no data falls within this range.
- The frequency for the class 90.0 to 99.9 is 0 because no data falls within this range.
- The frequency for the class 100.0 to 109.9 is given as 1.
- The frequency for the class 110.0 to 119.9 is 0 because no data falls within this range.

3. Remaining Classes with Undefined Frequencies:
- The class 120.0 to 129.9 and the class 130.0 to 139.9 do not have specific data to determine the frequencies, so they remain undefined based on the provided data context.
- The class 140.0 to 149.9 has a frequency of 0 because no data falls within this range.

By structuring the information, the frequency distribution table looks like this:

```
\begin{tabular}{|c|c|c|}
\hline
\multicolumn{2}{|l|}{Price (\$1000s)} & Frequency \\
\hline
30.0 & - 39.9 & 4 \\
\hline
40.0 & - 49.9 & 5 \\
\hline
50.0 & - 59.9 & 6 \\
\hline
60.0 & - 69.9 & 0 \\
\hline
70.0 & - 79.9 & 3 \\
\hline
80.0 & - 89.9 & 0 \\
\hline
90.0 & - 99.9 & 0 \\
\hline
100.0 & - 109.9 & 1 \\
\hline
110.0 & - 119.9 & 0 \\
\hline
120.0 & - 129.9 & \\
\hline
130.0 & - 139.9 & \\
\hline
140.0 & - 149.9 & 0 \\
\hline
\end{tabular}
```

This table organizes the class intervals and their corresponding frequencies clearly. If more data were provided or specified, the remaining classes could be populated accordingly.

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