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
15.9
15.9
95.4
95.4
401
401
59
The sum of the absolute deviations is 59.
To find the sum of the absolute deviations, follow these steps:
1. Subtract the mean (66.8) from each value in the dataset:
68 - 66.8 = 1.2
51 - 66.8 = -15.8
75 - 66.8 = 8.2
78 - 66.8 = 11.2
94 - 66.8 = 27.2
35 - 66.8 = -31.8
2. Take the absolute value of each result:
|1.2| = 1.2
|-15.8| = 15.8
|8.2| = 8.2
|11.2| = 11.2
|27.2| = 27.2
|-31.8| = 31.8
3. Add up all the absolute values:
1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8 = 95.4
Therefore, the sum of the absolute deviations in the dataset is 95.4.