To construct a grouped frequency distribution, we'll organize the given ages into defined class ranges and count how many ages fall into each range. Let's use class widths of 5, starting from 41, as directed.
The class ranges will be:
- 41 - 45
- 46 - 50
- 51 - 55
- 56 - 60
- 61 - 65
- 66 - 70
We will count the number of ages that fall within each range.
1. 41 - 45:
- The ages within this class: 43, 44, 44, 44, 44, 44, 45, 44, 45, 44, 44
- The frequency is [tex]\(11\)[/tex].
2. 46 - 50:
- The ages within this class: 47, 47, 50, 47, 47
- The frequency is [tex]\(4\)[/tex].
3. 51 - 55:
- The ages within this class: 55, 53, 55, 53, 54, 51, 53, 51, 55, 52
- The frequency is [tex]\(10\)[/tex].
4. 56 - 60:
- The ages within this class: 59, 59, 56, 60, 60
- The frequency is [tex]\(5\)[/tex].
5. 61 - 65:
- The ages within this class: 62, 62, 63, 63, 65, 62, 63, 61, 61, 62
- The frequency is [tex]\(10\)[/tex].
6. 66 - 70:
- The ages within this class: 67, 67, 67, 68
- The frequency is [tex]\(4\)[/tex].
Now, we can complete the grouped frequency distribution table:
[tex]\[
\begin{array}{|c|c|}
\hline Age & Frequency \\
\hline 41-45 & 11 \\
\hline 46-50 & 4 \\
\hline 51-55 & 10 \\
\hline 56-60 & 5 \\
\hline 61-65 & 10 \\
\hline 66-70 & 4 \\
\hline
\end{array}
\][/tex]
These are the frequency values for each class range in our grouped frequency distribution table.
