18.
What is the mean absolute deviation of the following data set: {4, 6, 8, 10, 12}?
First, we find the mean of the data set:
mean = (4 + 6 + 8 + 10 + 12) ÷ 5 = 8
Next, we find the absolute deviations from the mean for each data point:
|4 - 8| = 4
|6 - 8| = 2
|8 - 8| = 0
|10 - 8| = 2
|12 - 8| = 4
Then, we find the mean of these absolute deviations:
mean absolute deviation = (4 + 2 + 0 + 2 + 4) ÷ 5 = 2.4
Therefore, the mean absolute deviation of the data set {4, 6, 8, 10, 12} is 2.4.
To find the mean absolute deviation (MAD), you need to follow these steps:
Step 1: Find the mean of the data set.
To find the mean, you need to add up all the values in the data set and then divide the sum by the number of values.
Mean = (4 + 6 + 8 + 10 + 12) / 5 = 40 / 5 = 8
Step 2: Calculate the deviation for each data point.
The deviation of each data point is the absolute difference between the data point and the mean.
Deviation for 4 = |4 - 8| = 4
Deviation for 6 = |6 - 8| = 2
Deviation for 8 = |8 - 8| = 0
Deviation for 10 = |10 - 8| = 2
Deviation for 12 = |12 - 8| = 4
Step 3: Find the average of the deviations.
Add up the deviations from Step 2 and divide the sum by the number of values.
Average deviation = (4 + 2 + 0 + 2 + 4) / 5 = 12 / 5 = 2.4
Therefore, the mean absolute deviation of the data set {4, 6, 8, 10, 12} is 2.4.