Question

The following table shows the number of deaths due to fatal accidents in different age groups in a town.

Age (in years)	$5-15$	$15-25$	$25-35$	$35-45$	$45-55$	$55-65$	$65-75$
No. of deaths	$6$	$10$	$10$	$16$	$24$	$8$	$7$

Draw a less than ogive for the above data and estimate the median from it.

Answer 1

Step 1: Making a less than cumulative frequency distribution

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

We prepare the less than cumulative frequency distribution as follows:

Age (in years)	Less than $15$	Less than $25$	Less than $35$	Less than $45$	Less than $55$	Less than $65$	Less than $75$
No. of deaths	$6$	$16$	$26$	$42$	$66$	$74$	$81$

Now, we plot the points $\left(15,6\right),\left(25,16\right),\left(35,26\right),\left(45,42\right),\left(55,66\right),\left(65,74\right),\left(75,81\right)$ on the graph to get the required ogive.

Here,

$$\begin{gathered} n=81 \\ \Rightarrow \frac{n}{2}=40.5 \end{gathered}$$

Therefore from the graph, the median is the ${41}^{th}$ observation.

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

Let, N be the point on the $y$-axis representing $41$. From N, draw a line parallel to the $x$-axis meeting the ogive at I. From I, draw IM perpendicular to $x$-axis, meeting $x$-axis at M, M represents $42$.

From the ogive, the ${41}^{th}$ observation is at $42$.

Hence, the estimated median is $42$ years.