Question

Draw a Ogive for the following distribution which shows the marks of 100 students,then find the median

$$\begin{array}{ccccccccc}\text{Marks}& \text{0-10}& \text{10-20}& \text{20-30}& \text{30-40}& \text{40-50}& \text{50-60}& \text{60-70}& \text{70-80}\\ \text{Number of students}& \text{5}& \text{10}& \text{20}& \text{25}& \text{15}& \text{12}& \text{9}& \text{4}\end{array}$$

• A. 34
• B. 36
• C. 50
• D. 45

Answer 1

The correct option is B

36

Constructing the cumulative frequency table we have

$$\begin{array}{ccccccccc}\text{Marks}& \text{0-10}& \text{10-20}& \text{20-30}& \text{30-40}& \text{40-50}& \text{50-60}& \text{60-70}& \text{70-80}\\ \text{Number of students}& \text{5}& \text{10}& \text{20}& \text{25}& \text{15}& \text{12}& \text{9}& \text{4}\\ \text{Cumulative Frequency}& \text{5}& \text{15}& \text{35}& \text{60}& \text{75}& \text{87}& \text{96}& \text{100}\end{array}$$

On a graph paper , Marks on the x - axis and mark the cumulative frequency on the y axis and plot the graph for different interval.

Since n = 100 , Median = ${\frac{n}{2}}^{\text{th}}$ term = 50th term .

Through mark 50 on y-axis , draw a horizontal line which meets the graph at point A. Then through point A , draw a vertical line which meets x axis at the mark 36

Hence Median = 36