Question

Find the median of the following data by making a 'less than ogive'.

$\begin{array}{ccccccccccc}Marks& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80& 80-90& 90-100\\ Numberofstudents& 5& 3& 4& 3& 3& 4& 7& 9& 7& 8\end{array}$

Answer 1

The frequency distribution table of less than type is given as follows:

Maks (upper class limits)	Cumulative frequency (cf)
Less than 10	5
Less than 20	5+3=8
Less than 30	8+4=12
Less than 40	12+3=15
Less than 50	15+3 = 18
Less than 60	18+4 = 22
Less than 70	22+7 =29
Less than 80	29+9 =38
Less than 90	38+7 =45
Less than 100	45+8 =53

Taking upper class limits of class intervals on x-axis and their respective frequencies on y-axis, its ogive can be drawn as follows:

Here, N=53,

⇒ $\frac{N}{2}$=26.5

Mark the point A whose ordinate is 26.5 and its x-coordinate is 66.4 .

The median of the data is 66.4 .