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Question
Draw frequency polygons for each of the following frequency distribution:
(a) using histogram
(b) without using histogram
|
C.I |
5 -15 | 15 -25 | 25 -35 | 35 - 45 | 45-55 | 55-65 |
| ƒ | 8 | 16 | 18 | 14 | 8 | 2 |
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Solution
Using Histogram:
| C.I. | f |
| 5 - 15 | 8 |
| 15 - 25 | 16 |
| 25 - 35 | 18 |
| 35 - 45 | 14 |
| 45 - 55 | 8 |
| 55 - 65 | 2 |
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.
- 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 the Y-axis.
- Draw line segments joining the consecutive points marked in step (3) above.
C.I.
Class-mark
f
-5 - 5
0
0
5 - 15
10
8
15 - 25
20
16
25 - 35
30
18
35 - 45
40
14
45 - 55
50
8
55 - 65
60
2
65 - 75
70
0
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