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Sagot :
We are given the following data set
65 , 90, 85, 70, 70, 95, 55
The mean absolute deviation is given by
[tex]MAD=\frac{\sum|x_i-m|}{n}[/tex]Where xi is the individual values in the data set, m is the average value of the data set, and n is the number values in the data set.
The average value of the data set is given by
[tex]m=\frac{\sum x_i}{n}=\frac{65+90+85+70+70+95+55}{7}=\frac{530}{7}=75.7[/tex]So, the mean absolute deviation is
[tex]\begin{gathered} MAD=\frac{\sum|x_i-m|}{n}=\frac{|65-75.7|+|90-75.7|+|85-75.7|+|70-75.7|+|70-75.7|+|95-75.7|+|55-75.7|}{7} \\ MAD=\frac{|-10.7|+|14.3|+|9.3|+|-5.7|+|-5.7|+|19.3|+|-20.7|}{7} \\ MAD=\frac{10.7+14.3+9.3+5.7+5.7+19.3+20.7}{7} \\ MAD=\frac{85.7}{7} \\ MAD=12.24 \end{gathered}[/tex]Therefore, the mean absolute deviation for the given data set is 12.24
Option a is the correct answer.
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