Question

(38 points please help!)

The list shows the heights of 6 students in inches. 63, 70, 68, 73, 58, 67 What is the mean absolute deviation for these numbers?

Answer 1

4

Explanation:

Mean absolute deviation means mean of the absolute deviation around mean

so, first we calculate the mean

Mean= sum of all observations/total number of observations

= (63+70+68+73+58+67)/6

=66.5

Absolute deviations around mean:

|63-66.5|=3.5

|70-66.5|=3.5

|68-66.5|=1.5

|73-66.5|=6.5

|58-66.5|=8.5

|67-66.5|=0.5

Mean of absolute deviation around mean=(3.5+3.5+1.5+6.5+8.5+0.5)/6

= 4

Hence, mean absolute deviation is:

4

Answer 2

`M.A.D=4`

Explanation:

The given data set is :{63, 70, 68, 73, 58, 67}

The mean absolute deviation is the mean of how far all the entries in the data set are from the mean. Follow the procedure below;

• find the mean of the data set
• find the absolute value of the difference between the mean and each entry.
• find the mean of these entries.

The mean is give by:

`\bar X=(\sum x)/(n)`

`\bar X=(63+70+68+73+58+67)/(6)`

`\bar X=(399)/(6)=66.5`

The mean absolute deviation is given by:

`M.A.D=(\sum |x-\bar X|)/(n)`

`M.A.D=(|63-66.5|+|70-66.5|+|68-66.5|+|73-66.5|+|58-66.5|+|67-66.5|)/(6)`

`M.A.D=(3.5+3.5+1.5+6.5+8.5+0.5)/(6)`

`M.A.D=(24)/(6)=4`