Question

The Gardener counted the numbers blooms on 10 flower bushes and then arrange the numbers from smallest to largest the numbers of moons on each bush 4,4,6,6,7,8,8,8,9 and 10. The mean pf these measurements is 7

What is the mean absolute deviation?
A) 1.2
B)1.6
C)2.0
D) 12.0

Answer 1

your answer should be B

i just took the test this is correct

Answer 2

The formula of Mean Absolute Deviation is:

MAD = ∑|x- x̄|
----------
n

Where:
x = data value
x̄ = mean
n = number of observations

You already have 2 values given which is the mean (7) and the number of observations (10). First you need to solve for the sum of x - x̄. Let's put that in a table to get a better picture:

x |x-x̄|
4 |4-7| = 3
4 |4-7| = 3
6 |6-7| = 1
6 |6-7| = 1
7 |7-7| = 0
8 |8-7| = 1
8 |8-7| = 1
8 |8-7| = 1
9 |9-7| = 2
10 |10-7| = 3

Now get the sum of the values in the column |x-x̄|.
3+3+1+1+0+1+1+1+2+3 = 16

Now that you have the sum you can input it into the first formula:
MAD = ∑|x- x̄|
----------
n
MAD = 16
----------
10

MAD = 1.6

The answer is then B.