The given cumulative frequency should be changed into simple frequency. Thereafter, the median should be calculated.
Example 1.
Find out the median from the following series :
| Rate of Wages (Less Than) |
10 |
20 |
30 |
40 |
50 |
60 |
70 |
80 |
| No. of Workers |
15 |
35 |
60 |
84 |
96 |
127 |
198 |
250 |
Solution:
M No. = value of \(\frac{N}{2}\) th term = \(\frac {250}{2}\) = 125th term
Item 125th is included in the cumulative frequency 127. Therefore the class in front of this is called the median class and the class is (50 – 60)
Example 2.
In the following table, 65 students received marks in some examination. Calculate Median.
| Obtained Marks (More Than) |
70 |
60 |
50 |
40 |
30 |
20 |
| No. of Students |
7 |
18 |
40 |
40 |
63 |
65 |
Solution:
| Rate of wages |
No. of Workers (f) |
Cumulative frequency (cf) |
| 20-30 |
2 (65-63) |
2 |
| 30-40 |
23 (63-40) |
25 |
| 40-50 |
00 (40-40) |
25 c |
| L1 50-60 |
22 f (40-18) |
47 |
| 60-70 |
11(18-7) |
58 |
| 70-80 |
7 |
65 |
M No. = value of \(\frac{N}{2}\) th term = \(\frac {65}{2}\) 32.5th term
Item 32.5th is included in the cumulative frequency 47. Therefore the class in front of this is called the median class and the class is (50-60).
Median = 53.41 Marks
