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Question
Draw frequency polygons for each of the following frequency distribution:
(a) using histogram
(b) without using histogram
|
C.I |
10 - 30 |
30 - 50 |
50 - 70 | 70 - 90 | 90 - 110 | 110 - 130 | 130 - 150 |
| ƒ | 4 | 7 | 5 | 9 | 5 | 6 | 4 |
Solution
using histogram
| C.I | ƒ |
| 10 - 30 | 4 |
| 30 - 50 | 7 |
| 50 - 70 | 5 |
| 70 - 90 | 9 |
| 90 - 110 | 5 |
| 110 - 130 | 6 |
| 130 - 150 | 4 |
Steps:
-
- Draw a histogram for the given data.
- Mark the mid-point at the top of each rectangle of the histogram drawn.
- Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.
- Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.
Without using Histogram:
Steps:
- Find the class-mark (mid-value) of each given class-interval.
classmark = mid-value = `" Upper limit + Lower limit"/2` - On a graph paper, mark class-marks along X-axis and frequencies along Y-axis.
-
On this graph paper, mark points taking values of class-marks along the X-axis and the values of their corresponding frequencies along Y-axis.
- Draw line segments joining the consecutive points marked in step (3) above.
C.I. Class-mark f -10 - 10 0 0 10 - 30 20 4 30 - 50 40 7 50 - 70 60 5 70 - 90 80 9 90 - 110 100 5 110 - 130 120 6 130 - 150 140 4 150 - 170 160 0 
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