Mathematics
Construct a combined histogram and frequency polygon for the following data :
| Weekly earnings (in rupees) | No. of workers |
|---|---|
| 150 - 165 | 8 |
| 165 - 180 | 14 |
| 180 - 195 | 22 |
| 195 - 210 | 12 |
| 210 - 225 | 15 |
| 225 - 240 | 6 |
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Answer
Frequency distribution table :
| Weekly earnings | Class marks | No. of workers |
|---|---|---|
| 150 - 165 | 157.5 | 8 |
| 165 - 180 | 172.5 | 14 |
| 180 - 195 | 187.5 | 22 |
| 195 - 210 | 202.5 | 12 |
| 210 - 225 | 217.5 | 15 |
| 225 - 240 | 232.5 | 6 |
Steps of construction of histogram :
Since, the scale on x-axis starts at 135, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 135.
Take 2 cm along x-axis = 15 rupees.
Take 2 cm along y-axis = 5 workers.
Construct rectangles corresponding to the above continuous frequency distribution table.
The required histogram is shown in the adjoining figure.
Steps of construction of frequency polygon :
Mark the mid-points of upper bases of rectangles of the histogram.
Join the consecutive mid-points by line segments.
Join the first end point with the mid-point of class 135 - 150 with zero frequency, and join the other end point with the mid-point of class 240 - 255 with zero frequency.
The required frequency polygon is shown by thick line segments in the diagram.
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