Mathematics
Find the mode of the following distribution by drawing a histogram :
| Mid-value | Frequency |
|---|---|
| 28 | 10 |
| 34 | 8 |
| 40 | 24 |
| 46 | 16 |
| 52 | 8 |
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Answer
Size of each class = difference between two consecutive mid-values = 34 - 28 = 6.
Constructing the table as under :
| Mid-value | Class | Frequency |
|---|---|---|
| 28 | 25-31 | 10 |
| 34 | 31-37 | 8 |
| 40 | 37-43 | 24 |
| 46 | 43-49 | 16 |
| 52 | 49-55 | 8 |
Steps :
Take 2 cm along x-axis = 6 units and 1 cm along y-axis = 10 units.
Since, the scale on x-axis starts at 25, a break (zig-zag curve) is shown near the origin along x-axis to indicate that the graph is drawn to scale beginning at 25 and not at origin itself.
Construct rectangles corresponding to the given data.
In highest rectangle, draw two st. lines AC and BD from corners of the rectangles on either side of the highest rectangle to the opposite corners of the highest rectangle. Let P be the point of intersection of AC and BD.
Through P, draw a vertical line to meet the x-axis at M. The abscissa of the point M represents 40.5.
Hence, mode = 40.5
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