MEAN ABSOLUTE DEVIATION WORKSHEET

Question 1 : 

What is the mean absolute deviation for the following numbers?

5, 8, 10, 10, 12, 9

Question 2 : 

The data represent the height, in feet, of various buildings. Find the mean absolute deviation.

60, 58, 54, 56, 63, 65, 62, 59, 56, 57

Question 3 :

What is the difference between a measure of center and a measure of variability ?

Detailed Answer Key

Question 1 : 

What is the mean absolute deviation for the following numbers?

5, 8, 10, 10, 12, 9

Answer :

The mean is given by

=  (5 + 8 + 10 + 10 + 12 + 9) / 6

=   54 / 6

=   9

Absolute deviations of observations from mean : 

|5 - 9|  =  |-4|  =  4

|8 - 9|  =  |-1|  =  1

|10 - 9|  =  |1|  =  1

|10 - 9|  =  |1|  =  1

|12 - 9|  =  |3|  =  3

|9 - 9|  =  |0|  =  0

Calculate the mean absolute deviation by finding the mean of the above absolute deviations of observations from mean.  Round to the nearest whole number.

Mean absolute deviation is 

=  (4 + 1 + 1 + 1 + 3 + 0) / 6

=  10 / 6

≈  1.67

So, mean absolute deviation for the given data is about 1.67.

Question 2 : 

The data represent the height, in feet, of various buildings. Find the mean absolute deviation.

60, 58, 54, 56, 63, 65, 62, 59, 56, 57

Answer :

The mean is given by

=  (60 + 58 + 54 + 56 + 63 + 65 + 62 + 59 + 56 + 57) / 10

=   590 / 10

=   59

Absolute deviations of observations from mean : 

|60 - 59|  =  |1|  =  1

|58 - 59|  =  |-1|  =  1

|54 - 59|  =  |-5|  =  5

|56 - 59|  =  |-3|  =  3

|63 - 59|  =  |4|  =  4

|65 - 59|  =  |6|  =  6

|62 - 59|  =  |3|  =  3

|59 - 59|  =  |0|  =  0

|56 - 59|  =  |-3|  =  3

|57 - 59|  =  |-2|  =  2

Calculate the mean absolute deviation by finding the mean of the above absolute deviations of observations from mean.  Round to the nearest whole number.

Mean absolute deviation is 

 =  (1 + 1 + 5 + 3 + 4 + 6 + 3 + 0 + 3 + 2) / 10

=  28 / 10

=  2.8 

≈  3

Question 3 :

What is the difference between a measure of center and a measure of variability ?

Answer :

A measure of center is a number that indicates where the “middle” or center of a data set is, while a measure of variability is a number that indicates how much the data are spread out from the center of the data.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.