Question

Find graphically the values of D₃ and P₆₅ for the data given below:

I.Q of students	60 – 69	70 – 79	80 – 89	90 – 99	100 – 109	110 – 119	120 – 129
No. of students	20	40	50	50	20	10	10

Answer 1

Since the given data is not continuous, we have to convert it in the continuous form by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of every class interval. To draw a ogive curve, we construct the less than cumulative frequency table as given below:

I.Q. of students	No. of students (f)	Less than cumulative frequency (c.f.)
59.5 – 69.5	20	20
69.5 – 79.5	40	60
79.5 – 89.5	50	110
89.5 – 99.5	50	160
99.5 – 109.5	20	180
109.5 – 119.5	10	190
119.5 – 129.5	10	200
Total	200

Points to be plotted are (69.5, 20), (79.5, 60), (89.5, 110), (99.5, 160), (109.5, 180), (119.5, 190), (129.5, 200).

N = 200

For D₃, `(3"N")/10=(3xx200)/10` = 60

For P₆₅, `(65"N")/100=(65xx200)/100` = 130

∴ We take the values 60 and 130 on the Y-axis. From these points we draw lines parallel to X-axis and from the points where these lines intersect less than ogive, we draw perpendiculars on X-axis. The foot of perpendiculars represents the median of the values, D_3, and P₆₅.

∴ D₃ = 79.5, P₆₅ = 93.5