The given table shows the Marks obtained by students in Mathematics.

$\begin{matrix} Marks & No. of Students 0 - 10 & 3 10 - 20 & 7 20 - 30 & 12 30 - 40 & 15 40 - 50 & 20 50 - 60 & 9 60 - 70 & 8 70 - 80 & 16 80 - 90 & 14 90 - 100 & 6 \end{matrix}$

Using the table determine the Lower Quartile by drawing an ogive curve.

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Solution

$\begin{matrix} Marks & No. of Students & Cumulative Frequency & Points to be plotted 0 - 10 & 3 & 3 & (10, 3) 10 - 20 & 7 & 10 & (20, 10) 20 - 30 & 12 & 22 & (30, 22) 30 - 40 & 15 & 37 & (40, 37) 40 - 50 & 20 & 57 & (50, 57) 50 - 60 & 9 & 66 & (60, 66) 60 - 70 & 8 & 74 & (70, 74) 70 - 80 & 16 & 90 & (80, 90) 80 - 90 & 14 & 104 & (90, 104) 90 - 100 & 6 & 110 & (100, 110) \end{matrix}$

The No. of observations n = 110 (Sum of frequency)

Lower Quartile = $\frac{n}{4}$ = $\frac{110}{4}$ = 27.5

So the 27.5th Observation will give the Value for Upper quartile when we extend it to meet the ogive and then drop a line from it to the x-axis.

As we can see from the graph, The value obtained is 34

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Similar questions

The given table shows the Marks obtained by students in Mathematics.

$\begin{matrix} Marks & No. of Students 0 - 10 & 3 10 - 20 & 7 20 - 30 & 12 30 - 40 & 15 40 - 50 & 20 50 - 60 & 9 60 - 70 & 8 70 - 80 & 16 80 - 90 & 14 90 - 100 & 6 \end{matrix}$

Using the table determine the Number of students who got above 74 % by drawing an ogive curve.

The given table shows the Marks obtained by students in Mathematics.

$\begin{matrix} Marks & No. of Students 0 - 10 & 3 10 - 20 & 7 20 - 30 & 12 30 - 40 & 15 40 - 50 & 20 50 - 60 & 9 60 - 70 & 8 70 - 80 & 16 80 - 90 & 14 90 - 100 & 6 \end{matrix}$

Using the table determine the InterQuartile Range by drawing an ogive curve.

Q. The marks obtained by 40 students in a class are presented in the form of a table. Find the mean marks using direct method.

\begin{matrix} Marks obtained & Number of students 0 - 10 & 3 10 - 20 & 4 20 - 30 & 13 30 - 40 & 15 40 - 50 & 5 \end{matrix}

Following table shows the marks of 120 students at an examination. Draw an ogive for the table: estimate Inter-quartile range.

Q. The marks obtained by

100

students in a Mathematics test are given below:

Marks	No. of Students
$0 - 10$	$3$
$10 - 20$	$7$
$20 - 30$	$12$
$30 - 40$	$17$
$40 - 50$	$23$
$50 - 60$	$14$
$60 - 70$	$09$
$70 - 80$	$06$
$80 - 90$	$05$
$90 - 100$	$04$

Draw an ogive for the given distribution on a graph sheet.
(Use a scale of

2 c m = 10

units on both axis).
Use the ogive to estimate the lower quartile.

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The given table shows the Marks obtained by students in Mathematics. MarksNo. of Students0−10310−20720−301230−401540−502050−60960−70870−801680−901490−1006 Using the table determine the Lower Quartile by drawing an ogive curve.