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Davita works at a shoe store. She measured the feet of nine customers and found that their shoe sizes were 4, 5, 5, 6, 7, 8, 8, 10, 10. Find the sum of the absolute deviations from the mean and the mean absolute deviation. Explain how you found the MAD.

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Answer:

Sum of absolute deviation = 16

MAD = 1.78

Step-by-step explanation:

Given the following data:

X = 4, 5, 5, 6, 7, 8, 8, 10, 10

Absolute deviation from the mean means how each value in X deviates from the mean of the data without considering if the difference is positive or negative. Therefore, the absolute value is recorded and all deviations are recorded as positive.

Absolute deviation from the mean :

Mean of data (u) = (sum of data / number of observations)

( 4 + 5 + 5 + 6 + 7 + 8 + 8 + 10 + 10) / 9

= 63/9

= 7

Absolute deviation = ( x - u)

Sum of absolute deviation ;

|4-7| + |5-7| + |5-7| + |6-7| + |7-7| + |8-7| + |8-7| + |10-7| + |10-7|

3 + 2 + 2 + 1 + 0 + 1 + 1 + 3 + 3 = 16

Mean absolute deviation(MAD) ;

SUM OF ABSOLUTE DEVIATION / N

Where N = number of observations

MAD = 16/9 = 1.78

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