Question

How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2?
If necessary, round any values for the MAD to the nearest tenth to help answer the question.
Set 1: 30, 25, 5, 32
Set 2: 25, 30, 32

a.The MAD of set 1 is 29 more than the MAD of set 2.
b.The MAD of set 1 is 6.3 more than the MAD of set 2.
c.The MAD of set 1 is 23 less than the MAD of set 2.
d.The MAD of set 1 is 6.3 less than the MAD of set 2.

Answer 1

c.The MAD of set 1 is 23 less than the MAD of set 2

Answer 2

Option (B) the MAD of set 1 is 6.3 more than the MAD of set 2 is the correct answer.

What is a mean absolute deviation?

Mean absolute deviation (MAD) is a way to describe variation in a data set. It is the average distance between each data value and the mean.

For the given situation,

Data set 1: 30, 25, 5, 32

The formula of mean is

$Mean = \frac{Sum of all data values}{Total number of values}$

⇒ $Mean = \frac{30+25+5+32}{4}$

⇒ $Mean = \frac{92}{4}$

⇒ $Mean = 23$

Mean absolute deviation can be calculated as

Now, subtract the mean from each data value,

$|30-23|=7$

$|25-23|=2$

$|5-23|=18$

$|32-23|=9$

$MAD=\frac{7+2+18+9}{4}$

⇒ $MAD=\frac{36}{4}$

⇒ $MAD=9$

Data set 2: 25, 30, 32

$Mean = \frac{25+30+32}{3}$

⇒ $Mean = \frac{87}{3}$

⇒ $Mean = 29$

Mean absolute deviation can be calculated as

Now, subtract the mean from each data value,

$|25-29|=4$

$|30-29|=1$

$|32-29|=3$

$MAD=\frac{4+1+3}{3}$

⇒ $MAD=\frac{8}{3}$

⇒ $MAD=2.66$ ≈ $2.7$

MAD of set 1 - MAD of set 2 = $9-2.7$

⇒ $6.3$

Hence we can conclude that option (B) the MAD of set 1 is 6.3 more than the MAD of set 2 is the correct answer.

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