The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth

Question

The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 13,14,15,6,17,16,3

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Thu Giang 3 years 2021-07-15T23:35:29+00:00 1 Answers 22 views 0

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  1. vankhanh
    0
    2021-07-15T23:36:37+00:00
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    Given:

    The data set is 13, 14, 15, 6, 17, 16, 3.

    To find:

    The mean absolute deviation for the data set.

    Solution:

    We have,

    13, 14, 15, 6, 17, 16, 3

    Mean of the data set is:

    \text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}

    \overline{x}=\dfrac{13+14+15+6+17+16+3}{7}

    \overline{x}=\dfrac{84}{7}

    \overline{x}=12

    The formula for mean absolute deviation is:

    MAD=\dfrac{\sum_{i=1}^n|x_i-\overline{x}|}{n}

    Using this formula, the mean absolute deviation for the data set is:

    MAD=\dfrac{|13-12|+|14-12|+|15-12|+|6-12|+|17-12|+|16-12|+|3-12|}{7}

    MAD=\dfrac{1+2+3+6+5+4+9}{7}

    MAD=\dfrac{30}{7}

    MAD\approx 4.29

    Therefore, the mean absolute deviation for the data set is about 4.29.

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