Q.
If the median of following frequency distribution is $k,$ then $10\,k=$
C.I.
0 - 10
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
$f_1$
4
6
3
8
5
4
| C.I. | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 |
| $f_1$ | 4 | 6 | 3 | 8 | 5 | 4 |
NTA AbhyasNTA Abhyas 2022
Solution:
We have,
Class Interval Frequency Cumulative frequency $0-10$ $4$ $4$ $10-20$ $6$ $10$ $20-30$ $3$ $13$ $30-40$ $8$ $21$ $40-50$ $5$ $26$ $50-60$ $4$ $30$
Total, $N=30\Rightarrow \frac{N}{2}=15$
This value appears in the class $30-40$ . Therefore,
$L=30$ , $\text{CF}=21$ , $f=8$ , $h=10$
Median $=\ell +\frac{\frac{N}{2} - CF}{f}\times h$
$=30+\frac{15 - 13}{8}\times 10$
$k=30+\frac{20}{8}=32.5$
| Class Interval | Frequency | Cumulative frequency |
| $0-10$ | $4$ | $4$ |
| $10-20$ | $6$ | $10$ |
| $20-30$ | $3$ | $13$ |
| $30-40$ | $8$ | $21$ |
| $40-50$ | $5$ | $26$ |
| $50-60$ | $4$ | $30$ |