To complete the table, we need to calculate the absolute deviation for each data value from the given center, which is 20. The absolute deviation is found by taking the absolute value of the difference between each data value and the center. Let's go through each data value step by step:
1. Data value: 10
- Deviation from center: [tex]\(10 - 20 = -10\)[/tex]
- Absolute deviation: [tex]\(|-10| = 10\)[/tex]
2. Data value: 19
- Deviation from center: [tex]\(19 - 20 = -1\)[/tex]
- Absolute deviation: [tex]\(|-1| = 1\)[/tex]
3. Data value: 16
- Deviation from center: [tex]\(16 - 20 = -4\)[/tex]
- Absolute deviation: [tex]\(|-4| = 4\)[/tex]
4. Data value: 17
- Deviation from center: [tex]\(17 - 20 = -3\)[/tex]
- Absolute deviation: [tex]\(|-3| = 3\)[/tex]
5. Data value: 15
- Deviation from center: [tex]\(15 - 20 = -5\)[/tex]
- Absolute deviation: [tex]\(|-5| = 5\)[/tex]
Now we can fill these values into the table:
[tex]\[
\begin{tabular}{|l|c|c|c|c|c|}
\hline Data value & 10 & 19 & 16 & 17 & 15 \\
\hline Absolute deviation & 10 & 1 & 4 & 3 & 5 \\
\hline
\end{tabular}
\][/tex]
Here is the completed table:
[tex]\[
\begin{array}{|l|c|c|c|c|c|}
\hline
\text{Data value} & 10 & 19 & 16 & 17 & 15 \\
\hline
\text{Absolute deviation} & 10 & 1 & 4 & 3 & 5 \\
\hline
\end{array}
\][/tex]
