The table shows the distribution of monthly income (in thousands of naira) of workers in a factory Monthly Income (N'1000) 135-139 140-149 150-154 155-164 1...

(a) Histogram

Since the class intervals have unequal widths, the heights of the rectangles are the frequency densities:

\[\text{Frequency density}=\frac{\text{frequency}}{\text{class width}}.\]

Plot the class boundaries on the horizontal axis and frequency density on the vertical axis. The resulting histogram is:

(b) Estimated mode

The modal class is \(149.5\text{–}154.5\), since it has the greatest frequency density, \(5.6\).

Using the standard intersecting-diagonals construction on the modal rectangle gives

\[\begin{aligned} \text{Mode} &=149.5+\frac{5.6-4.2}{(5.6-4.2)+(5.6-3.8)}\times 5\\ &=149.5+\frac{1.4}{3.2}\times5\\ &=151.6875\approx151.7. \end{aligned}\]

Therefore, the estimated modal monthly income is \(151.7\) thousand naira, that is, approximately ₦151,700.