Frequency polygon and Frequency Curve Frequency polygon and Frequency Curve a closed geometric figure which presents the frequency gra...
Frequency polygon and Frequency Curve
Frequency polygon and Frequency Curve a closed geometric figure which presents the frequency graphically
is known as frequency polygon It can be obtained by the mid points of
rectangles Of a histogram and extending the ends to X-axis To construct
frequency polygon directly from the frequency distribution following steps are
Take two classes one in the beginning and one at the end With zero.
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| Diagrams or Charts |
frequencies and calculate points of a" classes
(ii) Mark the mid points along X-axis at equal distance.
(iii) Plot the frequencies along Y-axis by taking the scale as.
Plotted points are joined by strings line segments to get frequency polygon If
plotted points are joined smoothly then a smooth curve is obtained which is
called frequency curve.
Frequency polygon
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Cumulative frequency polygon
It is a graph of cumulative frequency distribution in which the cumulative
frequencies are plotted along Y-axis against upper or lower class bounties
and plotted points are joined by straight-line segments. It can be used to
calculate median. quartiles: deciles and percentiles etc. It is an increasing
function. The curve rises upward towards right starting from X-axis with zero
distance, if it is constructed from less than type cumulative frequency
distribution. If it is constructed from more than type cumulative frequency
distribution then the curve rises to the left starting from X-axis With zero distance
Cumulative frequency Curve or Ogive
In the cumulative frequency polygon if the plotted points are joined smoothly, an
increasing curve is obtained known as cumulative frequency curve or Ogive (read as Ojive).
Ogive IS another name of cumulative frequency curve not of cumulative frequency polygon.
Cumulative frequency polygon of Discrete Data
Cumulative frequency polygon constructed from discrete data assumes a shape
like steps of stairs because discrete variable does not assume any value
between two selected points, It is Increasing function between smallest and
largest value of given data, Its procedure of construction is as follows:
(i) Mark the values of discrete variable along X-axis at equal distance.
(ii) Plot the cumulative frequencies along Y-axis taking the suitable scale.
Join the plotted points like jumps of stairs as:
DIAGRAMS OR CHARTS
Diagrams and Charts are visual display of data in the form of lines, separated
bars. subdivided bars, circles or two or three dimensional geometrical forms.
Graphs provide the facility of comparisons to a layman at a look. Diagrams are
constructed using suitable scale and paper. available. It is usually colored or
shaded to show different parts.
Diagrams or Charts
1 Simple bar chart
2 Multiple bar chart
3 Component bar chart
4 Pie chart
1Simple Bar Chart
A simple bar chart is a one dimensional set of separate vertical bars of equal
widths whose heights are proportional to the values they represent. These
charts are suitable for categorical data. Following steps are involved in its construction.
(i)Plot the values or categories along X-axis.
(ii) Choose the scale and draw bars along Y-axis whose heights are
proportional to the values they represent.
(iii) To make the chart attractive take a suitable difference usually equal to
the width of bars between them,
Multiple Bar Charts
A multiple bar chart is a one dimensional set of grouped vertical bars of equal Widths in which one
group is separated from the other by suitable distance whose heights are proportional to the
values they represent, Following steps are involved in its construction.
(i)Plot the values or categories along X-axis in the form of groups
(ii)Choose the scale and draw grouped bars along Y-axis whose heights
are proportional to the values they represent.
Component Bar Charts
It is a one dimensional set of separate vertical bars of equal widths. The heights
of bars are proportional to the total of group wise values. Each bar is divided
into sections proportional to the size of component part. Following steps are
involved in its construction:
(i) Plot the values or categories along X-axis.
(ii) Choose the scale and draw grouped bars along Y-axis whose heights
are proportional to the total of component part.
(iii) Divide the bars into sections whose heights are proportional to the component parts.
Pie Charts or Sector Diagram
This diagram is constructed in a circle that is divided into sectors whose areas
are proportional to the component parts in which whole quantity is divided.
Following steps are involved in the construction of pie chart.
(i) Draw a circle of suitable radius.
(ii) Divide the angle of a circle of 3600 into sectors. The angle and area of sector
are proportional to the value it represents and are calculated by the formulae:
Value of component part
Angle of sector
x 3600
Total value
Stem and Leaf Display
Stem and leaf display technique was introduced by John Tukey. In this
technique each number of data is divided into two parts, first part of leading
digit(s) is called stem and second part of tailing digit(s) of remaining number is
known as leaf. All possible stems are arranged in ascending order of
magnitude and written on left hand side and leaves on right hand side leaving a
suitable distance between them. Stems and leaves may separated by drawing a
vertical line between them. Stems are associated with their respective leaves to know
the numbers.
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