Question
The marks obtained by $100$ students in a Mathematics test are given below:
Marks $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$ $80 - 90$ $90 - 100$
No. of Students $3$ $7$ $12$ $17$ $23$ $14$ $9$ $6$ $5$ $4$
Draw an ogive for the given distribution on a graph sheet.
(Use a scale of $2 cm = 10$ units on both axis).
use the ogive to estimate the :
(i) median.
(ii) lower quartile.
(iii) number of students who obtained more than 85% marks in the test.
(iv) number of students who did not pass in the test if the pass percentage was $35.$

Answer

Image

(i) Median $=\left(\frac{ n }{2}\right)^{\text {th }}$ observation
$=\left(\frac{100}{2}\right)^{\text {th }}$ observation
$= 50^{th}$​​​​​​​ observation
$= 45.$
(ii) Lower Quartile $\left( Q _1\right)=\left(\frac{ N }{2}\right)^{ th }$ observation
$=\left(\frac{100}{4}\right)^{\text {th }}$ observation
$= 25^{th}$ observation
$= 32.$
(iii) Number of students who obtained more than $85\%$ marks
$= (100 - 94)$
$= 6.$
(iv) Number of students who did not pass if passing $\%$ of marks is $35$
$= 30.$

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