Answer:
Option A - 2.2
Step-by-step explanation:
Given : Data 7, 2, 8, 5, 9, 9, 5, 6, 8, 1.
To find : What is the mean absolute deviation for these data?
Solution :
Step 1 - Calculate the mean of the data,
[tex]M=\frac{\sum x_n}{n}[/tex]
[tex]M=\frac{7+2+8+5+9 +9+5+6+8+1}{10}[/tex]
[tex]M=\frac{60}{10}[/tex]
[tex]M=6[/tex]
The mean is 6.
Step 2 - Calculate the distance between each data point and the mean.
Data points Distance from mean
7 |7-6| = 1
2 |2-6| = 4
8 |8-6| = 2
5 |5-6| = 1
9 |9-6| = 3
9 |9-6| = 3
5 |5-6| = 1
6 |6-6| = 0
8 |8-6| = 2
1 |1-6| = 5
Step 3 - Add all the terms of distance from mean
X=1+4+2+1+3+3+1+0+2+5=22
Step 4 - Apply mean absolute deviation formula,
[tex]MAD=\frac{\sum X}{n}[/tex]
[tex]MAD=\frac{22}{10}[/tex]
[tex]MAD=2.2[/tex]
Therefore, Option A is correct.
The mean absolute deviation is 2.2.
