Question

What is the sum of the absolute deviations in the following dataset: 68, 51, 75, 78, 94, 35? The mean is 66.8.(1 point)
Responses

401
401

59
59

15.9
15.9

95.4

Answer 1

To calculate the sum of the absolute deviations from the mean, we need to follow these steps:

1. **Find the absolute deviations** for each data point from the mean.
2. **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 \( |x - \text{mean}| \):

1. For 68: \( |68 - 66.8| = |1.2| = 1.2 \)
2. For 51: \( |51 - 66.8| = |-15.8| = 15.8 \)
3. For 75: \( |75 - 66.8| = |8.2| = 8.2 \)
4. For 78: \( |78 - 66.8| = |11.2| = 11.2 \)
5. For 94: \( |94 - 66.8| = |27.2| = 27.2 \)
6. 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**