Q.
Find the mean deviation about the mean for the following data :
$x_i$
$1$
$4$
$9$
$12$
$13$
$14$
$21$
$22$
$f_i$
$3$
$4$
$5$
$2$
$4$
$5$
$4$
$3$
| $x_i$ | $1$ | $4$ | $9$ | $12$ | $13$ | $14$ | $21$ | $22$ |
| $f_i$ | $3$ | $4$ | $5$ | $2$ | $4$ | $5$ | $4$ | $3$ |
Statistics
Solution:
$x_i$
$f_i$
$f_ix_i$
$|x_i -\bar{x}|$
$f_i|x_i- \bar{x}|$
1
3
3
11
33
4
4
16
8
32
9
5
45
3
15
12
2
24
0
0
13
4
52
1
4
14
5
70
2
10
21
4
84
9
36
22
3
66
10
30
Total
30
360
160
Mean $\left(\bar{x} \right)= \frac{\Sigma f_{i}x_{i}}{\Sigma f_{i}}$
$= \frac{360}{30}= 12$
$M.D. \left(\bar{x}\right)=\frac{\Sigma f_{i}\left|x_{i}-\bar{x}\right|}{\Sigma f_{i}}$
$= \frac{160}{30}=5.33$.
| $x_i$ | $f_i$ | $f_ix_i$ | $|x_i -\bar{x}|$ | $f_i|x_i- \bar{x}|$ |
|---|---|---|---|---|
| 1 | 3 | 3 | 11 | 33 |
| 4 | 4 | 16 | 8 | 32 |
| 9 | 5 | 45 | 3 | 15 |
| 12 | 2 | 24 | 0 | 0 |
| 13 | 4 | 52 | 1 | 4 |
| 14 | 5 | 70 | 2 | 10 |
| 21 | 4 | 84 | 9 | 36 |
| 22 | 3 | 66 | 10 | 30 |
| Total | 30 | 360 | 160 |