What is the sum of the absolute deviations in the following dataset: 68, 51, 75, 78, 94, 35? The mean is 66.8.
To find the sum of the absolute deviations, we need to find the absolute value of the difference between each data point and the mean, and then add them all together.
The absolute deviations from the mean 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
Adding these absolute deviations together, we get:
1.2 + 15.8 + 8.2 + 11.2 + 27.2 + 31.8 = 95.4
Therefore, the sum of the absolute deviations in this dataset is 95.4.
To find the sum of the absolute deviations, we need to calculate the absolute difference between each data point and the mean, and then add up all these differences.
Step 1: Calculate the absolute difference between each data point and the mean:
|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
Step 2: Add up all 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.