Ogive and Frequency Polygon

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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.

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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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