To complete the frequency distribution for the given ages of lottery winners, we need to count how many ages fall into each of the provided age ranges: [tex]\(20-29\)[/tex], [tex]\(30-39\)[/tex], [tex]\(40-49\)[/tex], [tex]\(50-59\)[/tex], [tex]\(60-69\)[/tex], [tex]\(70-79\)[/tex], and [tex]\(80-89\)[/tex].
Here is a detailed count for each age range:
1. Ages 20-29:
- The ages in this range are: 21, 28, 29.
- Count: 3
2. Ages 30-39:
- The ages in this range are: 31, 33, 33, 34, 34, 35.
- Count: 6
3. Ages 40-49:
- The ages in this range are: 41, 46, 46.
- Count: 3
4. Ages 50-59:
- The ages in this range are: 51, 51, 53, 53, 55, 57, 58, 58.
- Count: 8
5. Ages 60-69:
- The ages in this range are: 60, 62, 62, 65, 69.
- Count: 5
6. Ages 70-79:
- The ages in this range are: 70, 70, 74, 75.
- Count: 4
7. Ages 80-89:
- The age in this range is: 83.
- Count: 1
Using those counts, we can fill in the frequency distribution table as follows:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Age} & \text{Frequency} \\
\hline
$20-29$ & 3 \\
\hline
$30-39$ & 6 \\
\hline
$40-49$ & 3 \\
\hline
$50-59$ & 8 \\
\hline
$60-69$ & 5 \\
\hline
$70-79$ & 4 \\
\hline
$80-89$ & 1 \\
\hline
\end{tabular}
\][/tex]
So, the frequency distribution for the given data of ages is as above.
