Question
Prove that mean deviation calculated about mean will be greater than that calculate about median.
Solution
In order to prove the statement given in the question we calculate mean deviation about mean and mean deviation from median and compare what is greater :
2, 4, 7, 8 and 9.
Mean deviation about Mean
|
X |
D |
|
2 |
4 |
|
4 |
2 |
|
7 |
1 |
|
8 |
2 |
|
9 |
3 |
|
ΣX = 30 |
ΣD = 12 |
|
X |
D (X–7) |
|
2 |
5 |
|
4 |
3 |
|
7 |
0 |
|
8 |
1 |
|
9 |
2 |
|
N = 5 |
ID = 11 |
Mean deviation about mean is 2.4. and mean deviation about median is 2.2. Hence, proved that mean deviation about mean is greater than mean deivation about median.
