The marks obtained by 100 students in a Mathematics test are give… - Vidyadip

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

$(i)$ 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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