Q.
The mean deviation about the mean for the following frequency distribution is
Class interval
0-4
4-8
8-12
12-16
16-20
Frequency
4
6
8
5
2
| Class interval | 0-4 | 4-8 | 8-12 | 12-16 | 16-20 |
| Frequency | 4 | 6 | 8 | 5 | 2 |
Statistics
Solution:
Class interval
$f_i$
$x_i$
$f_ix_i$
$|d_i| = |x_i - \bar{x}| = |x_i - 9.2|$
$f_i |d_i|$
0 - 4
4
2
8
7.2
28.8
4-8
6
6
36
3.2
19.2
8-12
8
10
80
0.8
6.4
12-16
5
14
70
4.8
24.0
16-20
2
18
36
8.8
17.6
$\Sigma f_i = 25$
$\Sigma f_i x_i = 230$
96.0
Mean $(\bar{x})=\frac{\Sigma f_i x_i}{\Sigma f_i}=\frac{230}{25}=9.2$
Mean deviation$=\frac{\Sigma f_i\left|d_{i j}\right|}{\Sigma f_i}=\frac{96}{25}=3.84$
Hence, the mean deviation about the mean is $3.84$.
| Class interval | $f_i$ | $x_i$ | $f_ix_i$ | $|d_i| = |x_i - \bar{x}| = |x_i - 9.2|$ | $f_i |d_i|$ |
|---|---|---|---|---|---|
| 0 - 4 | 4 | 2 | 8 | 7.2 | 28.8 |
| 4-8 | 6 | 6 | 36 | 3.2 | 19.2 |
| 8-12 | 8 | 10 | 80 | 0.8 | 6.4 |
| 12-16 | 5 | 14 | 70 | 4.8 | 24.0 |
| 16-20 | 2 | 18 | 36 | 8.8 | 17.6 |
| $\Sigma f_i = 25$ | $\Sigma f_i x_i = 230$ | 96.0 |