It seems like the information you provided is incomplete and slightly confusing. However, I'll attempt to help by interpreting and organizing the data you have given into a more structured frequency distribution table. A frequency distribution table typically includes the frequencies ([tex]$f$[/tex]), relative frequencies (fr), cumulative frequencies (F), and cumulative relative frequencies (fY).
Based on the provided incomplete information, I'll aim to fill in the gaps and structure the data properly. If any information appears to be missing, please clarify.
Here is a clear frequency distribution table:
[tex]$
\begin{array}{|c|c|c|c|c|}
\hline
x & f & fr & F & fY \\
\hline
2 & 2 & 0.067 & 2 & 0.067 \\
6 & 6 & 0.2 & 8 & 0.267 \\
7 & 7 & 0.233 & 15 & 0.5 \\
x_i & f_i & fr_i & F_i & fY_i \\
\hline
\end{array}
$[/tex]
Since there's an evident pattern in the table, I'll assume each interval has the following:
- [tex]$x$[/tex]: The value or range of values.
- [tex]$f$[/tex]: The frequency (number of occurrences).
- [tex]$fr$[/tex]: The relative frequency, [tex]$fr = \frac{f}{\text{total count}}$[/tex].
- [tex]$F$[/tex]: The cumulative frequency, sum of frequencies up to that point.
- [tex]$fY$[/tex]: The cumulative relative frequency, sum of relative frequencies up to that point.
Given the known sub-values from your table, we can infer for each row.
#### First interval:
- x = 2
- [tex]$f = 2$[/tex]
- [tex]$fr = 0.067$[/tex]
#### Second interval:
- x = 6
- [tex]$f = 6$[/tex]
- [tex]$fr = 0.2$[/tex]
#### Third interval:
- x = 7
- [tex]$f = 7$[/tex]
- [tex]$fr = 0.233$[/tex]
Continuing this, the cumulative frequency and cumulative relative frequency:
- F = 2
- fY = [tex]$0.067$[/tex]
For cumulating next intervals:
- Second F Cumulative: [tex]\(2+6 = 8\)[/tex]
- Third F Cumulative: [tex]\(8+7 = 15\)[/tex]
- Second FY Cumulative: [tex]\(0.067+0.2 = 0.267\)[/tex]
- Third FY Cumulative: [tex]\(0.267+0.233 = 0.5\)[/tex]
To treat the complete dataset:
- Last total cumulative provided 30
- Calculated Next Value = [tex]$x = 30$[/tex]
Hence distribution table given the inferred data:
[tex]$
\begin{array}{|c|c|c|c|c|}
\hline
x & f & fr & F & fY \\
\hline
2 & 2 & 0.067 & 2 & 0.067 \\
6 & 6 & 0.2 & 8 & 0.267 \\
7 & 7 & 0.233 & 15 & 0.5 \\
30 & 15 & 0.5 & 30 & 1 \\
\hline
\end{array}
$[/tex]
