The MAD of the new data set does depend on whether it was Amy or Emily who turned in the additional drawings. So, Greg is incorrect and this can be determined by finding the mean absolute deviation in each condition.
Given :
The table given shows how many drawings his students had submitted by last Friday.
Mean absolute deviation can determine by using the following formula:
[tex]\rm MAD = \dfrac{1}{n}\sum^{n}_{i=1}|x_i-m(X)|[/tex]
where m(X) is the average value of the data set, n is the number of data values and [tex]\rm x_i[/tex] is the data values in the set.
[tex]\rm m(X) = \dfrac{6+34+35+37+43}{5}[/tex]
m(X) = 31
[tex]\rm MAD = \dfrac{|6-31|+|34-31|+|35-31|+|37-31|+|43-31|}{5}[/tex]
[tex]\rm MAD =\dfrac{25+3+4+6+12}{5}[/tex]
MAD = 10
Now, one student submits 25 additional drawings. If that 25 drawing is Amy's then MAD of the updated data is:
[tex]\rm m(X) = \dfrac{31+34+35+37+43}{5}[/tex]
m(X) = 36
[tex]\rm MAD = \dfrac{|31-36|+|34-36|+|35-36|+|37-36|+|43-36|}{5}[/tex]
[tex]\rm MAD =\dfrac{5+2+1+1+7}{5}[/tex]
MAD = 3.2
Now, one student submits 25 additional drawings. If that 25 drawing is Emily's then MAD of the updated data is:
[tex]\rm m(X) = \dfrac{6+34+35+37+68}{5}[/tex]
m(X) = 36
[tex]\rm MAD = \dfrac{|6-36|+|34-36|+|35-36|+|37-36|+|68-36|}{5}[/tex]
[tex]\rm MAD =\dfrac{11+2+1+1+32}{5}[/tex]
MAD = 9.4
The MAD of the new data set does depend on whether it was Amy or Emily who turned in the additional drawings. So, Greg is incorrect.
For more information, refer to the link given below;
https://brainly.com/question/20638608
