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
15.9
15.9
401
401
95.4
The sum of the absolute deviations in the dataset can be calculated by finding the absolute value of the difference between each data point and the mean, and then summing these absolute values.
The absolute deviations for each data point are:
|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
Summing these absolute deviations, we get:
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 calculate the absolute value of the differences between each data point and the mean, and then sum those absolute values. Here are the steps to find the sum of the absolute deviations in the given dataset:
1. Calculate the absolute difference between each data point and the mean (66.8):
|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 the absolute differences:
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.