Sure, let's construct a frequency distribution with the given data:
First, let's list the data:
[tex]\[ 13.6, 12.4, 9.2, 8.7, 7.6, 13.5, 11.7, 9.1, 8.4, 7.2, 13.3, 10.7, 9.1, 8.4, 7.1, 12.7, 9.6, 8.8, 7.9, 7.1 \][/tex]
Now, let's define our class intervals starting with the first class of [tex]\(6.5-7.5\)[/tex]:
1. [tex]\(6.5-7.5\)[/tex]
2. [tex]\(7.5-8.5\)[/tex]
3. [tex]\(8.5-9.5\)[/tex]
4. [tex]\(9.5-10.5\)[/tex]
5. [tex]\(10.5-11.5\)[/tex]
6. [tex]\(11.5-12.5\)[/tex]
7. [tex]\(12.5-13.5\)[/tex]
8. [tex]\(13.5-14.5\)[/tex]
Next, we'll count the number of data points that fall into each class interval:
1. [tex]\(6.5-7.5\)[/tex]:
- Values: [tex]\(7.2, 7.1, 7.1\)[/tex]
- Frequency: 3
2. [tex]\(7.5-8.5\)[/tex]:
- Values: [tex]\(7.6, 8.4, 8.4, 7.9\)[/tex]
- Frequency: 4
3. [tex]\(8.5-9.5\)[/tex]:
- Values: [tex]\(9.2, 8.7, 9.1, 9.1, 8.8\)[/tex]
- Frequency: 5
4. [tex]\(9.5-10.5\)[/tex]:
- Values: [tex]\(9.6\)[/tex]
- Frequency: 1
5. [tex]\(10.5-11.5\)[/tex]:
- Values: [tex]\(10.7\)[/tex]
- Frequency: 1
6. [tex]\(11.5-12.5\)[/tex]:
- Values: [tex]\(11.7, 12.4\)[/tex]
- Frequency: 2
7. [tex]\(12.5-13.5\)[/tex]:
- Values: [tex]\(12.7, 13.3\)[/tex]
- Frequency: 2
8. [tex]\(13.5-14.5\)[/tex]:
- Values: [tex]\(13.6, 13.5\)[/tex]
- Frequency: 2
The completed frequency distribution is as follows:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Class Interval} & \text{Frequency} \\
\hline 6.5-7.5 & 3 \\
\hline 7.5-8.5 & 4 \\
\hline 8.5-9.5 & 5 \\
\hline 9.5-10.5 & 1 \\
\hline 10.5-11.5 & 1 \\
\hline 11.5-12.5 & 2 \\
\hline 12.5-13.5 & 2 \\
\hline 13.5-14.5 & 2 \\
\hline
\end{array}
\][/tex]
This table provides a clear visual representation of the frequency distribution of the population data based on the given class intervals.
