Advertisement Remove all ads

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 - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Graph

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.

Advertisement Remove all ads

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

Concept: Graphical Location of Partition Values
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×