Remember that the mean absolute deviation is the average of the absolute values of the differences between the mean and each value in the data set. Let's start by calculating the mean of the given set of numbers.
Mean
First, we can find the sum of the given values.
40 + 48 + 58 + 60 +
66 + 72 + 80 + 88 =
512
Because there are 8 values in our set, we need to divide the sum by 8.
Mean: 512/8 = 64
Mean Absolute Deviation
Now, the MAD of a set of data is the average of the absolute values of the differences between the mean and each value in the data set. Let's use a table to find the sum of the absolute values of the differences.
Data Value
Data Value - Mean
|Data Value - Mean|
40
40-64=-24
|-24|=24
48
48-64=-16
|-16|=16
58
58-64=-6
|-6|=6
60
60-64=-4
|-4|=4
66
66-64=2
|2|=2
72
72-64=8
|8|=8
80
80-64=16
|16|=16
88
88-64=24
|24|=24
Sum of Values
100
Finally, we need to divide this sum by 8.
Mean Absolute Deviation (MAD)
100/8=12.5
A MAD of 12.5 indicates that the data, on average, are 3.5 units away from the mean. In the context of the problem, this means that the maximum speeds of boats, on average, are 12.5 mph away from the mean of 64 mph.
