To calculate the sum of the absolute deviations from the mean, we need to follow these steps:
- Find the absolute deviations for each data point from the mean.
- Sum those absolute deviations.
Given the dataset: 68, 51, 75, 78, 94, 35, and the mean (which you've provided) is 66.8.
Now for each value \( x \) in the dataset, we compute the absolute deviation \( |x - \text{mean}| \):
- For 68: \( |68 - 66.8| = |1.2| = 1.2 \)
- For 51: \( |51 - 66.8| = |-15.8| = 15.8 \)
- For 75: \( |75 - 66.8| = |8.2| = 8.2 \)
- For 78: \( |78 - 66.8| = |11.2| = 11.2 \)
- For 94: \( |94 - 66.8| = |27.2| = 27.2 \)
- For 35: \( |35 - 66.8| = |-31.8| = 31.8 \)
Now, let's add these absolute deviations together:
\[ 1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8 \]
Calculating step-by-step:
- \( 1.2 + 15.8 = 17.0 \)
- \( 17.0 + 8.2 = 25.2 \)
- \( 25.2 + 11.2 = 36.4 \)
- \( 36.4 + 27.2 = 63.6 \)
- \( 63.6 + 31.8 = 95.4 \)
Thus, the sum of the absolute deviations is 95.4.
So the correct answer is:
95.4