Question

Question 8
Refer to Question 7, draw the frequency polygon representing the above data without drawing the histogram.

Answer 1

We have to draw a frequency polygon without a histogram.
Firstly, we find the class marks of the classes given; that is 30-40, 40-50, 50-60, 60-70…..
$\therefore$ The class mark $=\frac{30+40}{2}$
$=\frac{70}{2}=35$
Similarly, we can determine the class marks of the other classes.
So, table for class marks is shown below

$\begin{array}{ccc}\text{Class interval(km/h)}& \text{Class marks}& \text{Frequency}\\ 30-40& 35& 3\\ 40-50& 45& 6\\ 50-60& 55& 25\\ 60-70& 65& 65\\ 70-80& 75& 50\\ 80-90& 85& 28\\ 90-100& 95& 14\end{array}$

We can draw a frequency polygon by plotting the class marks along with horizontal axis and the frequency along the vertical axis.
Now, plotting all the points B(35, 3), C(45, 6), D(55, 25), E(65, 65), F(75, 50), G(85, 28), H(95, 14).
Also, plot the point corresponding to the considering classes 20 - 30 and 100 - 110 each with frequency 0. Join all these points to get the required frequency polygon.