Question

Find the Median for the given data by drawing a 'less than ogive' :

$\begin{array}{cccccc}\text{Class Interval}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 5& 10& 14& 16& 8\end{array}$

Answer 1

To draw the Less than Ogive , first we prepare the Cumulative frequency table as given below :

$\begin{array}{cccc}\text{Observations}& \text{Frequency}& \text{Observations}& \text{Cumulative}\\ \left(\text{in classes}\right)& & \left(\text{in 'less than' form}\right)& \text{Frequency}\\ 0-10& 5& \text{Less than 10}& 5\\ 10-20& 10& \text{Less than 20}& 15\\ 20-30& 14& \text{Less than 30}& 29\\ 30-40& 16& \text{Less than 40}& 45\\ 40-50& 8& \text{Less than 50}& 53\end{array}$

Now, we mark the upper class limits along the x-axis on a suitable scale and the corresponding Cumulative Frequencies along the y-axis on a suitable scale.

We plot the points (0,0) , (10,5) , (20,15) , (30,29) , (40,45) and (50,53).

We join the plotted points by a freehand curve to obtain the required ogive as shown in the Graph :

Total number of observations = n = 53

To find the median from this ogive , first we locate the number $\frac{n}{2}$ = $\frac{53}{2}$ = 26.5 on the y - axis

From the point marked 26.5 on the y - axis , we draw a horizontal line parallel to the x - axis intersecting the ogive at point A. From the point A , we draw a vertical line perpendicular to the x - axis meeting it at B. the value of point B on the x - axis is 29.

Hence, the required Median is 29.