Question

Find the median for the given data by drawing a 'less than ogive': [6 MARKS]
$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 4& 9& 15& 14& 8\end{array}$

Answer 1

Formula: 2 Marks
Table: 2 Marks
Graph: 2 Marks

To draw the 'less than ogive', first we prepare the cumulative frequency table as given below:
$\begin{array}{cccc}Observations& Frequency& Observations& Cumulativefrequency\\ \left(inclasses\right)& & \left(in{}^{\prime }lesstha{n}^{\prime }form\right)& \\ 0-10& 4& Lessthan10& 4\\ 10-20& 9& Lessthan20& 13\\ 20-30& 15& Lessthan30& 28\\ 30-40& 14& Lessthan40& 42\\ 40-50& 8& Lessthan50& 50\end{array}$
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, 4), (20, 13), (30, 28), (40, 42) and (50, 50). We join the plotted points by a freehand curve to obtain the required ogive as shown below.
Total no. of observations = n = 50.
To find the median from this ogive, first we locate the number $\frac{n}{2}=\frac{50}{2}=25$ on the y-axis.

From the point marked 25 on they-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 x-axis is 28. Hence, the required median is 28.