Construct the ‘less than’ cumulative frequency curve.

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Attempt this question on graph paper.

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 21 Measures of Central Tendency Ex 21.6 Q4.1
(i) Construct the ‘less than’ cumulative frequency curve for the above data, using 2 cm = 10 years, on one axis and 2 cm = 10 casualties on the other.
(ii) From your graph determine (1) the median and (2) the upper quartile

Solution:

Representing the given data in less than cumulative frequency.

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 21 Measures of Central Tendency Ex 21.6 Q4.2

Now plot the points (15, 6), (25, 16), (35, 31), (45, 44), (55, 68), (65,76)
and (75, 83) on the graph and join these points in free hand
to form a cumulative frequency curve (ogive) as shown.
Here n = 83, which is odd.

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 21 Measures of Central Tendency Ex 21.6 Q4.3

(i) Median = \frac { n+1 }{ 2 } =\frac { 83+1 }{ 2 } +\frac { 84 }{ 2 } =42
Now we take point A (42) on y-axis and from A,
draw a line parallel to x-axis meeting the curve at P
and from P, draw a perpendicular to x-axis meeting it at Q.
Q is the median which is = 43
(ii) Upper quartile = \frac { 3(n+1) }{ 4 } =\frac { 3\times (83+1) }{ 4 } =\frac { 252 }{ 4 } =63
Take a point B 63 on y-axis and from B,
draw a parallel line to x-axis meeting the curve at L.
From L, draw a perpendicular to x-axis meeting it at M which is 52.
∴ Upper quartile = 52 years

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