Mathematics
Find the mode of the following distribution by drawing a histogram.
| Mid value | Frequency |
|---|---|
| 12 | 20 |
| 18 | 12 |
| 24 | 8 |
| 30 | 24 |
| 36 | 16 |
| 42 | 8 |
| 48 | 12 |
Also state the modal class.
Measures of Central Tendency
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Answer
Size of each class = difference between two consecutive mid-values = 18 - 12 = 6.
Constructing the table as under :
| Mid value | Class | Frequency |
|---|---|---|
| 12 | 9 - 15 | 20 |
| 18 | 15 - 21 | 12 |
| 24 | 21 - 27 | 8 |
| 30 | 27 - 33 | 24 |
| 36 | 33 - 39 | 16 |
| 42 | 39 - 45 | 8 |
| 48 | 45 - 51 | 12 |
Steps :
Take 1 cm along x-axis = 6 units and 1 cm along y-axis = 4 units.
Since, the scale on x-axis starts at 9, a break (zig-zag curve) is shown near the origin along x-axis to indicate that the graph is drawn to scale beginning at 9 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 30.5.
∴ Mode = 30.5
As the class 27 - 33 has the highest frequency, hence modal class = 27 - 33.
Hence, the required mode = 30.5 and modal class = 27 - 33.
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