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
59
59
95.4
95.4
15.9
15.9
401
Correct response: 95.4
Explanation: To find the absolute deviation for each number in the dataset, we subtract the mean (66.8) from each number and take the absolute value of the result.
|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
Then we add up all the absolute deviations:
1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8 = 95.4
Therefore, the sum of the absolute deviations is 95.4.
Well, if you want to find the sum of the absolute deviations, you need to do a little "abs" workout! You take the absolute value of each data point minus the mean, and then you add them all up. So let's get to it!
First, let's calculate the absolute deviations for each data point:
68 - 66.8 = 1.2 (absolute value is 1.2)
51 - 66.8 = 15.8 (absolute value is 15.8)
75 - 66.8 = 8.2 (absolute value is 8.2)
78 - 66.8 = 11.2 (absolute value is 11.2)
94 - 66.8 = 27.2 (absolute value is 27.2)
35 - 66.8 = 31.8 (absolute value is 31.8)
Now, let's add them all up: 1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8 = 95.4
So the sum of the absolute deviations in this dataset is 95.4. Keep up the good work!
To find the sum of the absolute deviations in the dataset, we need to calculate the absolute deviation for each data point, which is the absolute value of the difference between each data point and the mean. Then, we sum up all the absolute deviations.
First, let's calculate the absolute deviation for each data point:
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
Next, let's find the absolute value of each of these deviations:
|1.2| = 1.2
|15.8| = 15.8
|8.2| = 8.2
|11.2| = 11.2
|27.2| = 27.2
|31.8| = 31.8
Finally, let's sum up all these absolute deviations:
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.
To find the sum of the absolute deviations in a dataset, you need to follow these steps:
1. Calculate the absolute deviation for each data point, which is the absolute difference between each data point and the mean. The formula for absolute deviation is:
|x - mean|
For the given dataset, with a mean of 66.8, the absolute deviations are as follows:
|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. Sum up all the absolute deviations calculated in step 1.
1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8 = 95.4
Therefore, the sum of the absolute deviations in the given dataset is 95.4.