Question

The following table shows the literacy rate (in percentage) of cities.

Literacy rate in $\%$	more than $30$	more than $35$	more than $40$	more than $45$	more than $50$	more than $55$	more than $60$	more than $65$	more than $70$
No. of cities	$40$	$32$	$21$	$16$	$12$	$8$	$6$	$4$	$3$

Draw a more than type ogive for the given data. Hence, obtain the median Literacy rate.

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.

From the given table,

Literacy rate in $\%$	more than $30$	more than $35$	more than $40$	more than $45$	more than $50$	more than $55$	more than $60$	more than $65$	more than $70$
No. of cities	$40$	$32$	$21$	$16$	$12$	$8$	$6$	$4$	$3$

we plot the points $\left(30,40\right),\left(35,32\right),\left(40,21\right),\left(45,16\right),\left(50,12\right),\left(55,8\right),\left(60,6\right),\left(65,4\right),\left(70,3\right)$ on the graph to get the required ogive.

Here,

$$\begin{gathered} n=40 \\ \Rightarrow \frac{n}{2}=20 \end{gathered}$$

Therefore from the graph, the median is the ${20}^{th}$ observation.

Step 2: Drawing a more than ogive to find median

Let, K be the point on the $y$-axis representing $20$. From K, draw a line parallel to the $x$-axis meeting the ogive at J. From J, draw JL perpendicular to $x$-axis, meeting the $x$-axis at L, L represents $41$.

From the ogive, the ${20}^{th}$ observation is at $41$.

Hence, the median Literacy rate is $41\%$.