Mathematics
For the following distribution, draw a histogram :
| Weight (in kg) | Frequency |
|---|---|
| 44 - 47 | 23 |
| 48 - 51 | 25 |
| 52 - 55 | 37 |
| 56 - 59 | 18 |
| 60 - 63 | 7 |
| 64 - 67 | 2 |
From the histogram, estimate the mode.
Measures of Central Tendency
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Answer
Steps :
- The given frequency distribution is discontinuous, to convert it into continuous distribution,
Adjustment factor = = 0.5
We construct the continuous frequency table for the given data :
| Classes before adjustment | Classes after adjustment | No. of students |
|---|---|---|
| 44 - 47 | 43.5 - 47.5 | 23 |
| 48 - 51 | 47.5 - 51.5 | 25 |
| 52 - 55 | 51.5 - 55.5 | 37 |
| 56 - 59 | 55.5 - 59.5 | 18 |
| 60 - 63 | 59.5 - 63.5 | 7 |
| 64 - 67 | 63.5 - 67.5 | 2 |
Take 2 cm along x-axis = 4 kg and 1 cm along y-axis = 4 (frequency).
Since, the scale on x-axis starts at 43.5, a break (zig-zag curve) is shown near the origin along x-axis to indicate that the graph is drawn to scale beginning at 43.5 and not at origin itself.
Construct rectangles corresponding to the given data.
In highest rectangle, draw two straight 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 53 kg.
Hence, the required mode = 53.
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