Class 09 To draw histograms for classes of equal widths and varying widths.

 Activity 32

   OBJECTIVE                                                                    

To draw histograms for classes of equal widths and varying widths.

MATERIAL REQUIRED

Graph paper, geometry box, sketch pens, scissors, adhesive, cardboard.

 METHOD OF CONSTRUCTION

 1. Collect data from day to day life such as weights of students in a class and make a frequency distribution table.

 Case I : For classes of equal widths 

Class	a-b	b-c	c-d	d-e	e-f
Frequency	f 1	f 2	f3	f4	f5

 Case II : For classes of varying widths

 Here : d – f = 2 (a – b) 

Class	a-b		b-c		c-d		d-f
	(width x)		(width x)		(width x)		(width 2x)
Frequency	f1		f 2		f3		f 4
Modified frequency	f		f		f		F′ =	f4
		1		2		3
							2

 2.   Take a graph paper ( 20 cm × 20 cm) and paste it on a cardboard.

 3.   Draw two perpendicular axes X′OX and YOY′ on the graph paper.

 Mark classes on x-axis and frequencies on y-axis at equal distances as shown in Fig. 1

5.   On intervals (a-b), (b-c), (c-d), (d-e), (e- f), draw rectangles of equal widths and of heights f₁, f₂, f₃, f₄ and f₅, respectively, as shown in Fig. 2.

 6.   On intervals (a-b), (b-c), (c-d), (d-f), draw rectangles of heights f₁, f₂, f₃, and F ' as shown in Fig. 3.

 DEMONSTRATION

 1.   Different numerical values can be taken for a, b, c, d, e and f.

 2.   With these numerical values, histograms of equal widths and varying widths can be drawn.

 OBSERVATION

 Case I

 1. The intervals are 

a-b =

.................,

b-c =

.................,

c-d =

.................,

.................

d-e =	................., e– f	= .................
2. f1 = .................	,  f2 =	.................		,	f3 =	.................	,
f4 = .................	,  f5 =	.................
Case II
1. a-b =	.................,	b-c = .................			,	c-d = .................	,
d-f = .................	,
2. f1 = .................	,	f2 = .................			,	f3 = .................	,
f4 =	,	F′ =	f4	=
			.................
		2

APPLICATION

 Histograms are used in presenting large data in a concise form pictorially.