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?

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lidaralbany lidaralbany · Answer 1 · 2019-10-15T10:41:15+02:00

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

abidemiokin abidemiokin · Answer 2 · 2022-01-21T15:18:56+01:00

The mean absolute deviation of the numbers is 0.516

Given the list of the heights of 6 students as 63, 70, 68, 73, 58, 67

The formula for calculating the mean deviation is expressed as;

[tex]m=\frac{\sum |x_i-\overline x|}{n} [/tex]

Get the mean value:

[tex]\overline x =\frac{63+70+68+73+58+67}{6} \\ \overline x = 399/6\\ \overline x =66.5[/tex]

The sample size "n" = 6

Substitute the given parameters into the formula

[tex]m=\frac{ |-3.5+3.5+1.5+6.5-5.5+0.6|}{6}\\ m=\frac{3.1}{6}\\ m=0.516[/tex]

Hence the mean absolute deviation of the numbers is 0.516

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