To draw histograms for classes of equal widths and varying widths.
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Answers
To draw histograms for classes of equal widths and varying widths.
Materials Required
Graph paper
Geometry box
Adhesive
Sketch pens
Scissors
A piece of cardboard
Prerequisite Knowledge
Knowledge about collection of data.
Concept of histogram.
Theory
Collection of Data
The facts or figures which are numerical or otherwise; collected with a definite purpose (i.e. observation/information collected), are called data. Data is the plural form of the Latin word datum. Some basic terms related to data are given below:
The data collected by the investigator himself for a definite plan or purpose is known as
primary data.
The data collected by someone and used by any other person is known as secondary data.
The data obtained in original form is called raw data or ungrouped data.
We may condense data into classes or groups such a presentation is known as grouped data.
Histogram
A histogram is the graphical representation of a grouped frequency distribution with continuous classes in the form of rectangles with class intervals as bases and the corresponding frequencies as heights. There being no gap between any two consecutive rectangles.
Histogram is commonly used to show frequency distribution.
Procedure
1. Firstly, collect the data from daily life such as weights/heights of children in a class, then make a frequency distribution table.
Case I For classes of equal widths,
Class a-b b-c c -d d -e e-f
Frequency f1 f2 f3 f4 f5
Case II For classes of varying widths,
Here, d – f = 2(a-b)
Class a-b
(width x) b-c
(width x) c-d
(width x)
d-f
(width 2x)
Frequency f1 f2 f3 f4
Modified frequency f1 f2 f3 F’ = \frac { { f }_{ 4 } }{ 2 }
2. Take a graph paper having dimensions (20cm x 20cm) and paste it on a piece of cardboard sheet.
3. Now, draw two perpendicular axes X’OX and Y’OY on the graph paper, (see Fig. 32.1)
4. At equal distances, mark classes on X-axis and frequency Y-axis, (see Fig. 32.1)
NCERT Class 9 Maths Lab Manual - Draw Histograms for Classes of Equal Widths and Varying Widths 1
5. Draw rectangles of equal widths and heights f1, f2, f3, f4 and f5 on intervals (a-b), (b-c), (c-d), (d-e) and (e-f), respectively, (see Fig. 32.2)
NCERT Class 9 Maths Lab Manual - Draw Histograms for Classes of Equal Widths and Varying Widths 2
6. Draw rectangles of heights f1, f2, f3 and F’ on intervals (a-b), (b-c), (c-d) and (d-f) respectively, (see Fig. 32.3)
NCERT Class 9 Maths Lab Manual - Draw Histograms for Classes of Equal Widths and Varying Widths 3
Demonstration
On taking different numerical values of a, b, c, d, e and f, histogram of equal widths and varying widths can be drawn.
Observations
Case I For the classes of equal widths,
The intervals are
a-b = ………..
b-c = …………
c-d = …………..
d-e = ……….
e-f = ………..
f1 = …………
f2 = ………..
f3 = ………….
f4 = ………….
f5 = …………..
Case II For the classes of varying widths,
The intervals are
a-b = ………..
b-c = …………
c-d = …………..
d-f = ……….
f1 = …………
f2 = ………..
f3 = ………….
f4 = ………….
F’ = \frac { { f }_{ 4 } }{ 2 } = …………..
Result
We have drawn histogram of equal widths and varying widths by using the collected data.
Application
Histograms can be used pictorially in representing large data in a concise form.