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Question
The following table gives the distribution of females in an Indian village. Determine the median age of graphically.
| Age group | No. of females (in ‘000) |
| 0 – 10 | 175 |
| 10 – 20 | 100 |
| 20 – 30 | 68 |
| 30 – 40 | 48 |
| 40 – 50 | 25 |
| 50 – 60 | 50 |
| 60 – 70 | 23 |
| 70 – 80 | 8 |
| 80 – 90 | 2 |
| 90 – 100 | 1 |
Solution
To draw a ogive curve, we construct the less than cumulative frequency table as given below:
| Age group | No. of females (in ‘000) (f) |
Les than cumulative frequency (c.f.) |
| 0 – 10 | 175 | 175 |
| 10 – 20 | 100 | 275 |
| 20 – 30 | 68 | 343 |
| 30 – 40 | 48 | 391 |
| 40 – 50 | 25 | 416 |
| 50 – 60 | 50 | 466 |
| 60 – 70 | 23 | 489 |
| 70 – 80 | 8 | 497 |
| 80 – 90 | 2 | 499 |
| 90 – 100 | 1 | 500 |
| Total | 500 |
Points to be plotted are (10, 175), (20, 275), (30, 343), (40, 391), (50, 416), (60, 466), (70, 489), (80, 497), (90, 499), (100, 500)
N = 500
For median we have to consider `"N"/(2) = (500)/(2)` = 250
∴ We consider the value 250 on Y-axis. From this point, we draw a line parallel to X-axis. From the point it intersects the less than ogive, we draw a perpendicular to X-axis. The foot of the perpendicular represents the value of the median.
∴ Median ≈ 17.5
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