To solve this problem, we need to analyze the given table and compute certain values that can help us identify the pattern or find the missing value marked as [tex]$*$[/tex]. We will start by calculating the means of individual columns and rows.
Given the table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline 14 & 8 & $*$ & 1 \\
\hline 7 & 5 & 3 & 6 \\
\hline 10 & 11 & 22 & 5 \\
\hline 1 & 9 & 2 & 8 \\
\hline
\end{tabular}
\][/tex]
1. Calculate the mean of the first column:
- Values: 14, 7, 10, 1
- Mean: [tex]\(\frac{14 + 7 + 10 + 1}{4} = \frac{32}{4} = 8.0\)[/tex]
2. Calculate the mean of the second column:
- Values: 8, 5, 11, 9
- Mean: [tex]\(\frac{8 + 5 + 11 + 9}{4} = \frac{33}{4} = 8.25\)[/tex]
3. Calculate the mean of the fourth column:
- Values: 1, 6, 5, 8
- Mean: [tex]\(\frac{1 + 6 + 5 + 8}{4} = \frac{20}{4} = 5.0\)[/tex]
4. Calculate the mean of the first row:
- Values: 14, 8, 1 (excluding the missing value [tex]$$[/tex])
- Mean: [tex]\(\frac{14 + 8 + 1}{3} = \frac{23}{3} \approx 7.6667\)[/tex]
5. Calculate the mean of the fourth row:
- Values: 1, 9, 2, 8
- Mean: [tex]\(\frac{1 + 9 + 2 + 8}{4} = \frac{20}{4} = 5.0\)[/tex]
### Summary of Calculated Means:
- Mean of the first column: 8.0
- Mean of the second column: 8.25
- Mean of the fourth column: 5.0
- Mean of the first row (without [tex]$$[/tex]): 7.6667
- Mean of the fourth row: 5.0
With these calculated means, we have a clearer understanding of the table. These values suggest a consistency in the way the data is structured, and they help us understand the properties of the missing value [tex]$*$[/tex].
