Answer:
The mean absolute deviation (MAD) of this data set is 2.4
Step-by-step explanation:
step 1
Find the mean
To find out the mean sum all values and divide by the number of values in the data set
we have the set of data
[tex][2, 4, 7, 2, 3, 7, 9, 3, 1, 7][/tex]
The number of values is 10
so
The mean is equal to
[tex][2+4+7+2+3+7+9+3+1+7]/10=45/10=4.5[/tex]
step 2
Find out the absolute value of the difference of each value from that mean
[tex]\left|2-4.5\right|=2.5[/tex]
[tex]\left|4-4.5\right|=0.5[/tex]
[tex]\left|7-4.5\right|=2.5[/tex]
[tex]\left|2-4.5\right|=2.5[/tex]
[tex]\left|3-4.5\right|=1.5[/tex]
[tex]\left|7-4.5\right|=2.5[/tex]
[tex]\left|9-4.5\right|=4.5[/tex]
[tex]\left|3-4.5\right|=1.5[/tex]
[tex]\left|1-4.5\right|=3.5[/tex]
[tex]\left|7-4.5\right|=2.5[/tex]
so
we have
[tex][2.5, 0.5, 2.5, 2.5, 1.5, 2.5, 4.5, 1.5, 3.5, 2.5][/tex]
step 3
we know that
The Mean Absolute Deviation (MAD) is the mean of those distances
[tex][2.5+0.5+2.5+2.5+1.5+2.5+4.5+1.5+3.5+2.5]/10=24/10=2.4[/tex]
therefore
The mean absolute deviation (MAD) of this data set is 2.4
