Question

Determine graphically the value of median, D_3, and P₃₅ for the data given below:

Class	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35	35 – 40	40 – 45
Frequency	8	14	8	25	15	14	6

Answer 1

To draw a ogive curve, we construct the less than cumulative frequency table as given below:

Class	Frequency (f)	Less than cumulative frequency (c.f.)
10 – 15	8	8
15 – 20	14	22
20 – 25	8	30
25 – 30	25	55
30 – 35	15	70
35 – 40	14	84
40 – 45	6	90
Total	90

The points to be plotted for less than ogive are (15, 8), (20, 22), (25, 30), (30, 55), (35, 70), (40, 84), (45, 90).

N = 90

For median, consider `"N"/2=90/2` = 45

For D₃, consider `(3"N")/10=(3xx90)/10` = 27

For P₃₅, consider `(35"N")/100=(35xx90)/100` = 31.5

∴ We take the values 45, 27, and 31.5 on the Y-axis and draw lines from these points parallel to X-axis. From the points where they intersect the less than ogive, we draw perpendicular on the X-axis. Foot of the perpendicular represents the values of median, D_3, and P₃₅ respectively.

∴ Median ≈ 29, D₃ ≈ 23.5, P₃₅ ≈ 26.