Plot a histogram to represent the following data, using the class marks given in cm. Estimate the mode and list the modal class.
| Height | $125$ | $135$ | $145$ | $155$ | $165$ | $175$ | $185$ |
|---|---|---|---|---|---|---|---|
| Pupils | $8$ | $14$ | $24$ | $30$ | $20$ | $10$ | $6$ |
| Height (Class Marks) | Class Interval | Pupils (Frequency) |
|---|---|---|
| $125$ | $120 - 130$ | $8$ |
| $135$ | $130 - 140$ | $14$ |
| $145$ | $140 - 150$ | $24$ |
| $155$ | $150 - 160$ | $30$ |
| $165$ | $160 - 170$ | $20$ |
| $175$ | $170 - 180$ | $10$ |
| $185$ | $180 - 190$ | $6$ |
In the histogram, the highest rectangle represents the maximum frequency (or modal class).
Inside this rectangle, draw lines $AC$ and $BD$ diagonally from the upper corners $A$ and $D$ of adjacent rectangles.
Let the point of intersection of $AC$ and $BD$ be $K$.
Draw $KL$ perpendicular to the horizontal axis.
The value of point $L$ on the horizontal axis represents the mode and the class interval in which point $L$ lies is the modal class.
From the figure, mode $= 154$; $\;$ modal class $= 150 - 160$