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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

1 Answer

1 vote

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}=\frac{\text{Sum of all observations}}{\text{Number of observations}}


\overline{x}=(13+14+15+6+17+16+3)/(7)


\overline{x}=(84)/(7)


\overline{x}=12

The formula for mean absolute deviation is:


MAD=\frac{\sum_(i=1)^n|x_i-\overline{x}|}{n}

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


MAD=(|13-12|+|14-12|+|15-12|+|6-12|+|17-12|+|16-12|+|3-12|)/(7)


MAD=(1+2+3+6+5+4+9)/(7)


MAD=(30)/(7)


MAD\approx 4.29

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

User Sirmdawg
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