Q.
The approximate value of the mean deviation about the mean for the following data is
Class
0-2
2-4
4-6
6-8
8-10
Frequency
1
2
3
2
1
| Class | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 |
| Frequency | 1 | 2 | 3 | 2 | 1 |
TS EAMCET 2019
Solution:
Classinterval
mid-value $(x_{i})$
frequency $(f_{i})$
$x_{i}f_{i}$
$\left(x_{i}-\bar{x}\right)=d_{i}$
$f_{i}d_{i}$
0-2
1
1
1
4
4
2-4
3
2
6
2
4
4-6
5
3
15
0
0
6-8
7
2
14
2
4
8-10
9
1
9
4
4
$\Sigma f_{i}=9$
$\Sigma f_{i} X_{i}=45$
$\Sigma f_{i}d_{i}=16$
$\bar{x}=\frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}=\frac{45}{9}=5$
Mean deviation = $\frac{\Sigma f_{i} d_{i}}{\Sigma f_{i}}$
$=\frac{16}{9}=1.78$
| Classinterval | mid-value $(x_{i})$ | frequency $(f_{i})$ | $x_{i}f_{i}$ | $\left(x_{i}-\bar{x}\right)=d_{i}$ | $f_{i}d_{i}$ | |
|---|---|---|---|---|---|---|
| 0-2 | 1 | 1 | 1 | 4 | 4 | |
| 2-4 | 3 | 2 | 6 | 2 | 4 | |
| 4-6 | 5 | 3 | 15 | 0 | 0 | |
| 6-8 | 7 | 2 | 14 | 2 | 4 | |
| 8-10 | 9 | 1 | 9 | 4 | 4 | |
| $\Sigma f_{i}=9$ | $\Sigma f_{i} X_{i}=45$ | $\Sigma f_{i}d_{i}=16$ |