The list shows the maximum flying speeds of the ten fastest birds worldwide.
88, 72, 77, 95, 65, 80, 70, 106, 65, 68
What is the mean absolute deviation of the set of data?
To calculate the mean absolute deviation, we first need to find the mean of the data set.
Mean = (88 + 72 + 77 + 95 + 65 + 80 + 70 + 106 + 65 + 68) / 10
Mean = 786 / 10
Mean = 78.6
Next, we find the absolute deviations for each data point by subtracting the mean from each data point:
|88 - 78.6| = 9.4
|72 - 78.6| = 6.6
|77 - 78.6| = 1.6
|95 - 78.6| = 16.4
|65 - 78.6| = 13.6
|80 - 78.6| = 1.4
|70 - 78.6| = 8.6
|106 - 78.6| = 27.4
|65 - 78.6| = 13.6
|68 - 78.6| = 10.6
Now, we find the mean of these absolute deviations:
Mean absolute deviation = (9.4 + 6.6 + 1.6 + 16.4 + 13.6 + 1.4 + 8.6 + 27.4 + 13.6 + 10.6) / 10
Mean absolute deviation = 99.2 / 10
Mean absolute deviation = 9.92
Therefore, the mean absolute deviation of the set of data is 9.92.