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ICSE Class X Math 2014 Paper

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The marks obtained by 100 students in a Mathematics test are given below :
 Marks  No. of Students
 0-10  3
 10-20  7
 20-30  12
 30-40  17
 40-50  23
 50-60  14
 60-70  9
 70-80  6
 80-90  5
 90-100  4
Draw an ogive for the given distribution on a graph sheet.
(Use a scale of 2 cm=102\,\mathrm{cm}=10 units on both axis).
Use the ogive to estimate the :
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Question : 46 of 52
Marks: +1, -0
lower quartile.
Solution:  
Lower quartile (Q1)=(n4)th (Q_1) = \left(\frac{n}{4}\right)^{\text{th }} term
=(1004)th  term = \left(\frac{100}{4}\right)^{\text{th }} \text{ term }
=25th  term. = 25^{\text{th }} \text{ term. }
From the graph 25th 25^{\text{th }} term =31=31
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