Question

The given table shows the Marks obtained by students in Mathematics.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 0-10& 3\\ 10-20& 7\\ 20-30& 12\\ 30-40& 15\\ 40-50& 20\\ 50-60& 9\\ 60-70& 8\\ 70-80& 16\\ 80-90& 14\\ 90-100& 6\end{array}$

Using the table determine the InterQuartile Range by drawing an ogive curve.

• A. 40
• B. 42
• C. 45
• D. 48

Answer 1

The correct option is B

42

$\begin{array}{cccc}\text{Marks}& \text{No. of Students}& \text{Cumulative Frequency}& \text{Points to be plotted}\\ 0-10& 3& 3& (10,3)\\ 10-20& 7& 10& (20,10)\\ 20-30& 12& 22& (30,22)\\ 30-40& 15& 37& (40,37)\\ 40-50& 20& 57& (50,57)\\ 50-60& 9& 66& (60,66)\\ 60-70& 8& 74& (70,74)\\ 70-80& 16& 90& (80,90)\\ 80-90& 14& 104& (90,104)\\ 90-100& 6& 110& (100,110)\end{array}$

The No. of observations n = 110 (Sum of frequency)

Upper Quartile = $\frac{3n}{4}$ = $\frac{330}{4}$ = 82.5

So the 82.5th Observation will give the Value for Upper quartile when we extend it to meet the ogive and then drop a line from it to the x-axis.

As we can see from the graph, The value obtained is 76

Lower Quartile = $\frac{n}{4}$ = $\frac{110}{4}$ = 27.5

So the 27.5th Observation will give the Value for Upper quartile when we extend it to meet the ogive and then drop a line from it to the x-axis.

As we can see from the graph, The value obtained is 34

$\therefore$ InterQuartile Range = Upper Quartile - Lower Quartile = 76 - 34 = 42