# Draw an ogive for the following distribution. Determine the median graphically and verify your result by mathematical formula. Height (in cms.) No. of students 145 − 150 2 150 − 155 5 155 - Mathematics and Statistics

Graph

Draw an ogive for the following distribution. Determine the median graphically and verify your result by mathematical formula.

 Height (in cms.) No. of students 145 − 150 2 150 − 155 5 155 − 160 9 160 − 165 15 165 − 170 16 170 − 175 7 175 − 180 5 180 − 185 1

#### Solution

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

 Height (in cms) No. of students (f) Less than cumulative frequency (c.f.) 145 – 150 2 2 150 – 155 5 7 155 – 160 9 16 160 – 165 15 31 165 – 170 16 47 170 – 175 7 54 175 – 180 5 59 180 – 185 1 60 Total 60

The points to be plotted for less than ogive are (150, 2), (155, 7), (160, 16), (165, 31), (170, 47), (175, 54), (180, 59) and (185, 60).

N = 60

∴ "N"/2=60/2 = 30

∴ We take the value 30 on the Y-axis and from this point, we draw a line parallel to X-axis. From the point where this line intersects the less than ogive, we draw a perpendicular on X-axis. Foot of the perpendicular gives the value of median.
∴ Median ≈ 164.67
Now, let us calculate the median from the mathematical formula.
∵ "N"/2 = 30
The median lies in the class interval of 160 – 165.
∴ L = 160, h = 5, f = 15, c.f. = 16

Median = "L"+"h"/"f"("N"/2-"c.f.")

= 160 + 5/15 (30 - 16)

= 160 + 1/3 xx 14

= 160 + 4.67
= 164.67

Concept: Graphical Location of Partition Values
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 1 Partition Values
Miscellaneous Exercise 1 | Q 10 | Page 21