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.
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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