# Ogive and Frequency Polygon

In this section, we will learn about the construction of ogive or cumulative frequency curve and cumulative frequency polygon. There are two methods of constructing frequency polygon and cumulative frequency curve but the techniques of drawing it is same.

1) Less than method
2) More than method

Less than method :
First prepare a less than type cumulative frequency table.
1) On the x – axis use the upper limits of the class.
2) Mark the less than type cumulative frequency on y – axis.
3) Plot the points using upper limits and corresponding cumulative frequencies.
4) Join the points by a free hand curve to get ogive and to get the cumulative frequency polygon join the points by line segments.

More than method :
First prepare a more than type cumulative frequency table.
5) On the x – axis use the lower limits of the class.
6) Mark the more than type cumulative frequency on y – axis.
7) Plot the points using upper limits and corresponding cumulative frequencies.
8) Join the points by a free hand curve to get ogive and to get the cumulative frequency polygon join the points by line segments.

Some solved examples :
1) Draw cumulative frequency curve and cumulative frequency polygon for the frequency distribution by less than type method.
 Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Number of students 7 10 23 51 6 3

Solution :
 Marks No. of students Upper limit Less than cumulative frequency 0 - 10 7 10 17 10 - 20 10 20 17 20 - 30 23 30 40 30 - 40 51 40 91 40 - 50 6 50 97 50 - 60 2 60 100 From the above the red free hand curve is ogive and green line segment is frequency polygon.
2) The frequency distribution of scores obtained by 230 candidates in an engineering entrance test is as follows :
 Scores 400 – 450 450 – 500 500 – 550 550 – 600 600 – 650 650 – 700 700 – 750 750 - 800 No. of candidates 20 35 40 32 24 27 18 34
Draw cumulative frequency curves by more than method on the same axes. Also, draw the cumulative frequency polygons.
Solution :
More than method :
 Scores Number of Candidates Scores more than(Lower limits) Cumulative Frequency 400 –450 20 400 230 450 – 500 35 450 210 500 – 550 40 500 175 550 – 600 32 550 135 600 – 650 24 600 103 650 – 700 27 650 79 700 – 750 18 700 61 750 - 800 34 750 27 Brown line represents Frequency polygon and Green curve represents frequency curve.

Statistics

Statistics
Pictograph
Pie chart
Bar Graph
Double Bar Graph
Histogram
Frequency polygon
Frequency distribution (Discrete )
Frequency distribution continuous (or grouped)
Measures of central tendency ( Mean, Mode and Median)
Ogive or Frequency curve.

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