Question

find the mean absolute deviation for the set below s equals 65 , 90, 85, 70, 70, 95, 55 a 12.24b 75.7c 85.7d 40

Answer 1

We are given the following data set

65 , 90, 85, 70, 70, 95, 55

The mean absolute deviation is given by

$MAD=\frac{\sum|x_i-m|}{n}$

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

$m=\frac{\sum x_i}{n}=\frac{65+90+85+70+70+95+55}{7}=\frac{530}{7}=75.7$

So, the mean absolute deviation is

$\begin{gathered} MAD=\frac{\sum|x_i-m|}{n}=\frac{|65-75.7|+|90-75.7|+|85-75.7|+|70-75.7|+|70-75.7|+|95-75.7|+|55-75.7|}{7} \\ MAD=\frac{|-10.7|+|14.3|+|9.3|+|-5.7|+|-5.7|+|19.3|+|-20.7|}{7} \\ MAD=\frac{10.7+14.3+9.3+5.7+5.7+19.3+20.7}{7} \\ MAD=\frac{85.7}{7} \\ MAD=12.24 \end{gathered}$

Therefore, the mean absolute deviation for the given data set is 12.24

Option a is the correct answer.