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Question
The following table gives frequency distribution of marks of 100 students in an examination.
| Marks | 15 –20 | 20 – 25 | 25 – 30 | 30 –35 | 35 – 40 | 40 – 45 | 45 – 50 |
| No. of students | 9 | 12 | 23 | 31 | 10 | 8 | 7 |
Determine D6, Q1, and P85 graphically.
Solution
To draw an ogive curve, we construct the less than cumulative frequency table as given below:
| Marks | No. of students (f) |
Less than cumulative Frequency (c.f.) |
| 15 – 20 | 9 | 9 |
| 20 – 25 | 12 | 21 |
| 25 – 30 | 23 | 44 |
| 30 – 35 | 31 | 75 |
| 35 – 40 | 10 | 85 |
| 40 – 45 | 8 | 93 |
| 45 – 50 | 7 | 100 |
| Total | 100 |
The points to be plotted for less than ogive are (20, 9), (25, 21), (30 , 44), (35, 75), (40, 85), (45, 93), (50, 100).
Here, N = 100
For D6, `(6"N")/(10) = (6(100))/(10)` = 60
For Q1, `"N"/4=100/4` = 25
For P85, `(85"N")/100=(85xx100)/100` = 85
∴ We take the points having Y coordinates 60, 25, and 85 on Y-axis. From these points, we draw lines parallel to X-axis. From the points where these lines intersect the curve, we draw perpendiculars on X-axis.
X coordinates of these points give the values of D6, Q1, and P85.
∴ D6 = 32.5, Q1 = 26, P85 = 40
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