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 Interquartile range
$\left[4Marks\right]$

Answer 1

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

Scores \( \longrightarrow \)

$\left[1Mark\right]$For finding the Interquartile range, first we have to find upper quartile and lower quartile.

Upper Quartile -

It is Given by $\frac{3n}{4}$

Here n = 155

$\therefore$ $\frac{3n}{4}$ = $\frac{3\times 155}{4}$ = $\frac{465}{4}$ = 116.25

So, we take the ${116}^{th}$ term which comes out to be 84
$\left[1Mark\right]$

Lower Quartile -

It is Given by $\frac{n}{4}$

Here n = 155

$\therefore$ $\frac{n}{4}$ = $\frac{155}{4}$ = 38.75

So, we take the ${39}^{th}$ term which comes out to be 32
$\left[1Mark\right]$

Interquartile range = Upper Quartile - Lower Quartile = 84 - 32 = 52
$\left[1Mark\right]$