Name: Drawing a Bar Graph
Uploaded: 2019-07-19
Duration: 5 min 41 s
Description: Do you know how to draw a bar graph? Draw the vertical and horizontal axes. Label both the axes. Watch this video for complete information on drawing a bar g...

Question

$100$ students in a school have heights as tabulated below:

Height (in $cm$ )	Number of students
$121 - 130$	$12$
$131 - 140$	$16$
$141 - 150$	$30$
$151 - 160$	$20$
$161 - 170$	$14$
$171 - 180$	$8$

Draw a frequency polygon of the above data.

Accepted Answer

The given frequency distribution is discontinuous. To convert into continuous distribution,

Adjustment factor $= \frac{lower limit of one class - upper limit of previous class}{2}$

$= \frac{131 - 130}{2} = 0.5$

Subtract the adjustment factor $0.5$ from all the lower limits and add the adjustment factor $0.5$ to all the upper limits.

Find class marks and prepare the table as under:

Classes before adjustment (Height in $cm$ ) Classes after adjustment (Height in $cm$ ) Class marks Number of students

$121 - 130$ $120.5 - 130.5$ $125.5$ $12$

$131 - 140$ $130.5 - 140.5$ $135.5$ $16$

$141 - 150$ $140.5 - 150.5$ $100$ $30$

$151 - 160$ $150.5 - 160.5$ $155.5$ $20$

$161 - 170$ $160.5 - 170.5$ $165.5$ $14$

$171 - 180$ $170.5 - 180.5$ $175.5$ $8$

Steps to draw frequency polygon:

(i) Take $1 cm$ on $x$ -axis $= 10 cm$ height and $1 cm$ on $y$ -axis $= 4$ students.

(ii) Plot the points $(125.5, 12), (135.5, 16), (145.5, 30), (155.5, 20), (165.5, 14), (175.5, 8)$ .

(iii) Join the consecutive points by thick line segments.

(iv) Join the first end-point with mid-point of class $110.5 - 120.5$ with zero frequency and join the other end point with the mid-point of class $180.5 - 190.5$ with zero frequency.

The required frequency polygon (thick line segments) is shown below:

Class intervals $(km / h)$	Frequency
$30 - 40$	$3$
$40 - 50$	$6$
$50 - 60$	$25$
$60 - 70$	$65$
$70 - 80$	$50$
$80 - 90$	$28$
$90 - 100$	$14$

Section $A$		Section $B$
Marks	Frequency	Marks	Frequency
$0 - 15$	$5$	$0 - 15$	$3$
$15 - 30$	$12$	$15 - 30$	$16$
$30 - 45$	$28$	$30 - 45$	$25$
$45 - 60$	$30$	$45 - 60$	$27$
$60 - 75$	$35$	$60 - 75$	$40$
$75 - 90$	$13$	$75 - 90$	$10$

$100$ students in a school have heights as tabulated below:

Height (in $cm$ ) Number of students

$121 - 130$ $12$

$131 - 140$ $16$

$141 - 150$ $30$

$151 - 160$ $20$

$161 - 170$ $14$

$171 - 180$ $8$

Draw a frequency polygon of the above data.

Important Questions on Statistics

Learn and Prepare for any exam you want !

100 students in a school have heights as tabulated below: Height (in cm) Number of students 121-130 12 131-140 16 141-150 30 151-160 20 161-170 14 171-180 8 Draw a frequency polygon of the above data.

Important Questions on Statistics

Learn and Prepare for any exam you want !

$100$ students in a school have heights as tabulated below:

Height (in $cm$ ) Number of students

$121 - 130$ $12$

$131 - 140$ $16$

$141 - 150$ $30$

$151 - 160$ $20$

$161 - 170$ $14$

$171 - 180$ $8$

Draw a frequency polygon of the above data.