To find the cumulative frequency ([tex]$Fi$[/tex]) for each class interval given the frequencies ([tex]$fi$[/tex]) in the table, we need to compute the cumulative frequency by successively adding each frequency to the sum of the previous frequencies.
Here's the detailed step-by-step process:
1. First Interval [tex]$[0-2[$[/tex]:
- [tex]$fi$[/tex] (frequency) = 1
- [tex]$Fi$[/tex] (cumulative frequency) = 1 (since there are no previous classes)
2. Second Interval [tex]$[2-4[$[/tex]:
- [tex]$fi$[/tex] (frequency) = 12
- Add the frequency of the current interval to the cumulative frequency of the previous interval: [tex]$1 + 12 = 13$[/tex]
- [tex]$Fi$[/tex] (cumulative frequency) = 13
3. Third Interval [tex]$[4-6[$[/tex]:
- [tex]$fi$[/tex] (frequency) = 13
- Add the frequency of the current interval to the cumulative frequency of the previous interval: [tex]$13 + 13 = 26$[/tex]
- [tex]$Fi$[/tex] (cumulative frequency) = 26
4. Fourth Interval [tex]$[6-8[$[/tex]:
- [tex]$fi$[/tex] (frequency) = 10
- Add the frequency of the current interval to the cumulative frequency of the previous interval: [tex]$26 + 10 = 36$[/tex]
- [tex]$Fi$[/tex] (cumulative frequency) = 36
5. Fifth Interval [tex]$[8-10]$[/tex]:
- [tex]$fi$[/tex] (frequency) = 14
- Add the frequency of the current interval to the cumulative frequency of the previous interval: [tex]$36 + 14 = 50$[/tex]
- [tex]$Fi$[/tex] (cumulative frequency) = 50
Hence, the complete table including the cumulative frequencies ([tex]$Fi$[/tex]) becomes:
[tex]\[
\begin{tabular}{|l|l|l|}
\hline Peso KG & fi & $Fi$ \\
\hline$[0-2[$ & 1 & 1 \\
\hline$[2-4[$ & 12 & 13 \\
\hline$[4-6[$ & 13 & 26 \\
\hline$[6-8[$ & 10 & 36 \\
\hline$[8-10]$ & 14 & 50 \\
\hline Total & 50 & \\
\hline
\end{tabular}
\][/tex]
In summary, the cumulative frequencies ([tex]$Fi$[/tex]) for each interval are as follows: [tex]$[1, 13, 26, 36, 50]$[/tex].
