To find the sum of the absolute deviations for the given table, follow these steps:
1. Identify the pairs of values:
- The first pair is (3, 4).
- The second pair is (4, 7).
- The third pair is (8, 12).
- The fourth pair is (10, 16).
- The fifth pair is (16, 22).
- The sixth pair is (20, 28).
- The seventh pair is (24, 30).
2. Calculate the absolute deviations for each pair:
- For the first pair (3, 4), the absolute deviation is |3 - 4| = 1.
- For the second pair (4, 7), the absolute deviation is |4 - 7| = 3.
- For the third pair (8, 12), the absolute deviation is |8 - 12| = 4.
- For the fourth pair (10, 16), the absolute deviation is |10 - 16| = 6.
- For the fifth pair (16, 22), the absolute deviation is |16 - 22| = 6.
- For the sixth pair (20, 28), the absolute deviation is |20 - 28| = 8.
- For the seventh pair (24, 30), the absolute deviation is |24 - 30| = 6.
3. Sum the absolute deviations:
- The absolute deviations are: 1, 3, 4, 6, 6, 8, and 6.
- Adding these values together gives: 1 + 3 + 4 + 6 + 6 + 8 + 6 = 34.
The sum of the absolute deviations is therefore [tex]\(34\)[/tex], which does not match any of the given multiple-choice options. So there might be a mistake in the provided choices. The correct answer should be [tex]\(34\)[/tex].
