The mean absolute deviation (MAD) of their ages is 19.
What is the mean absolute deviation (MAD)?
"The mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set".
For the given situation,
The ages of all family members = 9, 13, 43, 55, 38, 76.
Let n be the number of data, n= 6
The formula for the mean absolute deviation (MAD),
Mean absolute deviation = ( Absolute mean ) / n
Absolute mean = Σ | (mean - data value) |
Mean = (Sum of individual data) / number of data
⇒ Mean = [tex]\frac{9+13+43+55+38+76}{6}[/tex]
⇒ Mean = [tex]\frac{234}{6}[/tex]
⇒ Mean = [tex]39[/tex]
Absolute mean =
Σ [tex][ |(39-9)|+|(39-13)|+|(39-43)|+|(39-55)|+|(39-38)|+|(39-76)|][/tex]
⇒ [tex][|30|+|26|+|-4|+|-16|+|1|+|-37|][/tex]
⇒ [tex][30+26+4+16+1+37][/tex]
⇒ [tex]114[/tex]
Thus MAD = [tex]\frac{114}{6}[/tex]
⇒ MAD = [tex]19[/tex]
Hence we can conclude that the mean absolute deviation (MAD) of their ages is 19.
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