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

95.4
95.4

401
401

15.9
15.9

59

Answer 1

To find the sum of the absolute deviations from the mean, we first calculate the absolute deviation for each data point in the dataset compared to the mean (66.8). The absolute deviation is calculated as the absolute difference between each data point and the mean.

Let's calculate it step by step:

1. Data points: 68, 51, 75, 78, 94, 35
2. Mean: 66.8

Now we compute the absolute deviations:

- 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, we sum the absolute deviations:

Sum = 1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8

Calculating the sum:

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

Therefore, the sum of the absolute deviations is **95.4**.

So, the correct response is:

**95.4**