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?
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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 deviation for each number by subtracting the mean from each number and taking the absolute value:
|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 calculate the mean absolute deviation by finding the average 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 = 98.2 / 10
Mean absolute deviation = 9.82
Therefore, the mean absolute deviation of the data set is 9.82.