Question

A die was rolled eight times. The rolls were 2, 2, 3, 4, 4, 5, 6, and 6. What is the mean absolute deviation for this data? A) 1 1/4 B) 1 2/3 C) 4 D) 10 (B is not 12/3)

Answer 1

The correct option is A:

MAD = 1 + 1/4

Explanation:

For a set of N elements {x₁, x₂, ..., xₙ}

The mean is calculated as:

`M = (x_1 + x_2 + ... + x_n)/(N)`

And the mean absolute deviation is calculated as:

`MAD = (Ix_1 - MI + Ix_2 - MI + ...+ IX_n - MI)/(N)`

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 = (I2 - 4I + I2 - 4I + I3 - 4I + I4 - 4I + I4 - 4I + I5 - 4I + I6 - 4I + I6 - 4I)/(8) = 10/8`

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.