Find the mean absolute deviation for the chilis used in the competition.

Question

Number of Chilis 4 5 5 5 5 6 6 6 7 7 8 8
Distance from 6 2 1 1 1 1 0 0 0 1 1 2 2

The mean absolute deviation is
.

Answer 1

1.18.

To calculate the mean absolute deviation, you first find the average of the distances from 6:

(2 + 1 + 1 + 1 + 1 + 0 + 0 + 0 + 1 + 1 + 2 + 2) / 12 = 12 / 12 = 1

Then, you find the absolute value of the differences between each distance and the mean:

|2-1| = 1
|1-1| = 0
|1-1| = 0
|1-1| = 0
|0-1| = 1
|0-1| = 1
|0-1| = 1
|1-1| = 0
|1-1| = 0
|2-1| = 1
|2-1| = 1
|2-1| = 1

Add up all these absolute differences and divide by the total number of values:

(1 + 0 + 0 + 0 + 1 + 1 + 1 + 0 + 0 + 1 + 1 + 1) / 12 = 6 / 12 = 0.5

Therefore, the mean absolute deviation is 0.5.