For the following distribution draw a histogram.
| Weight (in kg) | $44 - 47$ | $48 - 51$ | $52 - 55$ | $56 - 59$ | $60 - 63$ | $64 - 67$ |
|---|---|---|---|---|---|---|
| Frequency | $23$ | $25$ | $37$ | $18$ | $7$ | $2$ |
Estimate the mode from the histogram.
Here, the class intervals given are in inclusive form and need to be converted into exclusive form.
$\begin{aligned}
\text{Adjustment factor} & = \dfrac{1}{2} \left(\text{upper limit of a class} - \text{lower limit of previous class}\right) \\\\
& = \dfrac{1}{2} \left(48 - 47\right) = 0.5
\end{aligned}$
$\therefore \;$ The adjusted class intervals are
| Weight in kg (Inclusive form) | Weight in kg (Exclusive form) | Frequency |
|---|---|---|
| $44 - 47$ | $43.5 - 47.5$ | $23$ |
| $48 - 51$ | $47.5 - 51.5$ | $25$ |
| $52 - 55$ | $51.5 - 55.5$ | $37$ |
| $56 - 59$ | $55.5 - 59.5$ | $18$ |
| $60 - 63$ | $59.5 - 63.5$ | $7$ |
| $64 - 67$ | $63.5 - 67.5$ | $2$ |
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 $= 53.1 \; kg$; $\;$ modal class $= 51.5 - 55.5$