Maharashtra State BoardHSC Commerce 11th
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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
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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
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