Question

The runs scored by the two teams A and B in the first 60 balls in a cricket match are given below:

Number of balls	Team A	Team B
1 − 6	2	5
7 − 12	1	6
13 − 18	8	2
19 − 24	9	10
25 − 30	4	5
31 − 36	5	6
37 − 42	6	3
43 − 48	10	4
49 − 54	6	8
55 − 60	2	10

Represent the data of both the teams on the same graph by frequency polygons.
[Hint: First make the class intervals continuous.]   

Answer 1

It can be observed that the class intervals of the given data are not continuous.    
There is a gap of 1 in between them. 
Therefore, \(\frac{1}{2}\) = 0.5 has to be added to the upper-class limits and 0.5 has to be subtracted from the lower-class limits.  
 Also, class mark of each interval can be found by using the following formula.    

\(\text{Class mark} =\frac{\text{ 𝑈𝑝𝑝𝑒𝑟 𝑐𝑙𝑎𝑠𝑠 𝑙𝑖𝑚𝑖𝑡+𝐿𝑜𝑤𝑒𝑟 𝑐𝑙𝑎𝑠𝑠 𝑙𝑖𝑚𝑖𝑡}}{ 2}   \) 
Continuous data with class mark of each class interval can be represented as follows.   

Number of balls	Class mark	Team A	Team B
0.5 − 6.5	3.5	2	5
6.5 − 12.5	9.5	1	6
12.5 − 18.5	15.5	8	2
18.5 − 24.5	21.5	9	10
24.5 − 30.5	27.5	4	5
30.5 − 36.5	33.5	5	6
36.5 − 42.5	39.5	6	3
42.5 − 48.5	45.5	10	4
48.5 − 54.5	51.5	6	8
54.5 − 60.5	57.5	2	10

By taking class marks on x-axis and runs scored on y-axis, a frequency polygon can be constructed as follows.