Use a graph paper for this question. (Take 2 cm = 10 Marks along one axis and 2 cm = 10 students along another axis). Draw a Histogram for the following distribution which gives the marks obtained by 164 students in a particular class and hence find the Mode.
| Marks | Number of students |
|---|---|
| 30 - 40 | 10 |
| 40 - 50 | 26 |
| 50 - 60 | 40 |
| 60 - 70 | 54 |
| 70 - 80 | 34 |
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Steps of Construction:
Draw a histogram of the given distribution.
Inside the highest rectangle, which represents the maximum frequency (the modal class 60–70), draw two lines AC and BD diagonally from the upper corners C and D of the adjacent rectangles to the top corners of the modal rectangle.
Through the point K (the point of intersection of diagonals AC and BD), draw KL perpendicular to the horizontal axis (Marks axis).
The value of point L on the horizontal axis represents the value of the mode.
From graph,
The Mode = L = 64 marks (approx.)
Hence, mode = 64.