Calculate mean deviation from the following data, using mean and median respectively.
SIZE 4, 6, 8, 10, 12, 14, 16
FREQUENCY 2, 4, 5, 3, 2, 1, 4
Mean deviation from median
Size (X) | Frequency (f) | Cumulative frequency | Deviation from median dm = | fdm |
4 | 2 | 2 | 4 | 8 |
6 | 4 | 6 | 2 | 8 |
8 | 5 | 11 | 0 | 0 |
10 | 3 | 14 | 2 | 6 |
12 | 2 | 16 | 4 | 8 |
14 | 1 | 17 | 6 | 6 |
16 | 4 | 21 | 8 | 32 |
| N = = 21 |
|
| = 68 |
Median = value of item
= value of 11th item
= 8
Mean deviation =
= = 3.23
Mean deviation from mean
Size(X) | Frequency (f) | fX | Deviation from mean d = | f d |
4 | 2 | 8 | 5.71 | 11.42 |
6 | 4 | 24 | 3.71 | 14.84 |
8 | 5 | 40 | 1.71 | 6.71 |
10 | 3 | 30 | .29 | .87 |
12 | 2 | 24 | 2.29 | 4.58 |
14 | 1 | 14 | 4.29 | 4.29 |
16 | 4 | 64 | 6.29 | 25.16 |
| ∑F = 21 |
|
| ∑f d = 67.87 |
= = 9.71
Mean deviation for mean =
=
= 3.23