Greg teaches an art class. The table below shows how many drawings his students had

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Question:

Greg teaches an art class. The table below shows how many drawings his students hadsubmitted by last Friday. Greg calculates the mean absolute deviation (MAD) of the data.
Then, one student submits 25 additional drawings. Greg cannot remember whether the
drawings are Amy’s or Emily’s, but he thinks the MAD will increase no matter who submitted
the drawings. Is Greg correct? Use the drop-down menus to explain your reasoning.

Answer:

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:

where m(X) is the average value of the data set, n is the number of data values and is the data values in the set.

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m(X) = 31

MAD = 10

Now, one student submits 25 additional drawings. If that 25 drawing is Amy’s then MAD of the updated data is:

m(X) = 36

MAD = 3.2

Now, one student submits 25 additional drawings. If that 25 drawing is Emily’s then MAD of the updated data is:

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.

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They would possibly hopefully assist the student sort out the question by using the questions and answer examples. Then could actually make some sharing in a group discussion and also learning with the classmate that is related to the topic, so another student also have some enlightenment and still keeps up the school learning.

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