Question

The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition.

$\begin{array}{cc}\text{Scores}& \text{No. of shooters}\\ 0-10& 10\\ 10-20& 12\\ 20-30& 15\\ 30-40& 8\\ 40-50& 20\\ 50-60& 24\\ 60-70& 7\\ 70-80& 11\\ 80-90& 30\\ 90-100& 18\end{array}$

Use a graph sheet to draw an ogive for the distribution.

Using the graph estimate the Median.

Answer 1

First , we prepare the Cumulative frequency table as follows :

$\begin{array}{ccc}\text{C.I}& \text{f}& \text{cf}\\ 0-10& 10& 10\\ 10-20& 12& 22\\ 20-30& 15& 37\\ 30-40& 8& 45\\ 40-50& 20& 65\\ 50-60& 24& 89\\ 60-70& 7& 96\\ 70-80& 11& 107\\ 80-90& 30& 137\\ 90-100& 18& 155\end{array}$

Then draw the Graph of the 'less than ogive' and plot the points :

(0,0) , (10,10) , (20,22) , (30,37) , (40,45) , (50,65) , (60,89) , (70,96) , (80,107) , (90,137) , (100,155)\

n = 155 which is odd

Median will be given by - $(\frac{n+1}{2}{)}^{th}$ term.

$\therefore$ $\frac{n+1}{2}$ = $\frac{156}{2}$ = 78th term

Take a point A on 78 on y - axis and from there draw a line parallel to the X - axis touching the ogive at point B.

From the point B, draw a vertical point which touches the x - axis at point C. The point C represents the required median which is 54.

Median = 78th term = 55.