Question

The following table shows the distribution of the daily wages earned by workers in a building site.

Wages (in Rs/day)	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$	$100-110$	$110-120$	$120-130$
No. of workers	$12$	$20$	$30$	$38$	$24$	$16$	$12$	$8$

Change the distribution to a more than type distribution and draw its ogive. Hence, obtain the median wage per day from the graph.

Answer 1

Step 1: Making a more than cumulative frequency distribution

A more than cumulative frequency distribution can be calculated by adding all the frequencies more than the considered class interval.

We prepare the more than cumulative frequency distribution as follows:

Wages (in Rs/day)	More than $50$	More than $60$	More than $70$	More than $80$	More than $90$	More than $100$	More than $110$	More than $120$
No. of workers	$160$	$148$	$128$	$98$	$60$	$36$	$20$	$8$

Now, we plot the points $\left(50,160\right),\left(60,148\right),\left(70,128\right),\left(80,98\right),\left(90,60\right),\left(100,36\right),\left(110,20\right),\left(120,8\right)$ on the graph to get the required ogive.

Here,

$$\begin{gathered} n=160 \\ \Rightarrow \frac{n}{2}=80 \end{gathered}$$

Therefore from the graph, the median is the ${80}^{th}$ observation.

Step 2: Drawing a more than ogive to find the median

Let, J be the point on the $y$-axis representing $80$. From J, draw a line parallel to the $x$-axis meeting the ogive at I. From I, draw IK perpendicular to $x$-axis, meeting $x$-axis at K, K represents $95$.

From the ogive, the ${80}^{th}$ observation is at $95$.

Hence, the estimated median is $Rs95$.