Answer:
The correct option is A:
MAD = 1 + 1/4
Step-by-step explanation:
For a set of N elements {x₁, x₂, ..., xₙ}
The mean is calculated as:
![M = \frac{x_1 + x_2 + ... + x_n}{N}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7Bx_1%20%2B%20x_2%20%2B%20...%20%2B%20x_n%7D%7BN%7D)
And the mean absolute deviation is calculated as:
![MAD = \frac{Ix_1 - MI + Ix_2 - MI + ...+ IX_n - MI}{N}](https://tex.z-dn.net/?f=MAD%20%3D%20%5Cfrac%7BIx_1%20-%20MI%20%2B%20Ix_2%20-%20MI%20%2B%20...%2B%20IX_n%20-%20MI%7D%7BN%7D)
Here we have the set of 8 elements:
{ 2, 2, 3, 4, 4, 5, 6, 6}
The mean of this set is:
M = (2 + 2 + 3 + 4 + 4 + 5 + 6 + 6)/8 = 4
Then the mean standard deviation is:
![MAD = \frac{I2 - 4I + I2 - 4I + I3 - 4I + I4 - 4I + I4 - 4I + I5 - 4I + I6 - 4I + I6 - 4I}{8} = 10/8](https://tex.z-dn.net/?f=MAD%20%3D%20%5Cfrac%7BI2%20-%204I%20%2B%20I2%20-%204I%20%2B%20I3%20-%204I%20%2B%20I4%20-%204I%20%2B%20I4%20-%204I%20%2B%20I5%20-%204I%20%2B%20I6%20-%204I%20%2B%20I6%20-%204I%7D%7B8%7D%20%3D%2010%2F8)
If we simplify this, we get:
MAD = 10/8 = 5/4 = (4 + 1)/4 = 4/4 + 1/4 = 1 + 1/4
MAD = 1 + 1/4
The correct option is A.