Alright, let's go through this step-by-step to complete the table and find the deviation of each data point from the mean.
1. Identify the Mean:
The mean given is [tex]\( 9.25 \)[/tex].
2. List the Data Points:
The data points are [tex]\( 7 \)[/tex], [tex]\( 9 \)[/tex], and [tex]\( 12 \)[/tex].
3. Calculate the Deviations:
The deviation is calculated as the difference between each data point and the mean.
- For the data point [tex]\( 7 \)[/tex]:
[tex]\[
\text{Deviation} = 7 - 9.25 = -2.25
\][/tex]
- For the data point [tex]\( 9 \)[/tex]:
[tex]\[
\text{Deviation} = 9 - 9.25 = -0.25
\][/tex]
- For the data point [tex]\( 12 \)[/tex]:
[tex]\[
\text{Deviation} = 12 - 9.25 = 2.75
\][/tex]
4. Complete the Table:
Now we can fill in the deviations for each data point in the table.
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
Mean & 9.25 & & \\
\hline
Data Point & 7 & 9 & 12 \\
\hline
Deviation & -2.25 & -0.25 & 2.75 \\
\hline
\end{tabular}
\][/tex]
So, the deviations for each data point from the mean are as follows:
- [tex]\( 7 \)[/tex] has a deviation of [tex]\( -2.25 \)[/tex]
- [tex]\( 9 \)[/tex] has a deviation of [tex]\( -0.25 \)[/tex]
- [tex]\( 12 \)[/tex] has a deviation of [tex]\( 2.75 \)[/tex]
