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

Number of ball	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.]

It can be observed from the given data that the class intervals of the given data are not continuous. There is a gap of ‘1’ unit between them. So, to make the class intervals continuous, 0.5 has to be added to every upper-class limit and 0.5 has to be subtracted from the lower-class limit.

Here upper limit is 6 and lower limit is 1 so, we add and subtract 0.5 in both the term

So, 6 + 0.5 = 6.5

and 1 - 0.5 = 0.5

By formula,

Class Mark = $\dfrac{\text{Upper limit + Lower limit}}{2}$

Now, the upper limit is 6.5 and the lower limit is 0.5.

Substitute the values and we get :

So, class mark = $\dfrac{6.5 + 0.5}{2} = \dfrac{7.0}{2}$ = 3.5

Similarly, proceeding in this manner, we get the following table with continuous interval and class mark:

Steps of construction of frequency polygon :

1. Take number of balls on x-axis using class mark values.

2. Take runs scored on y-axis by taking 1 unit = 1 run

3. The lowest run is 1 and the highest is 10.

4. We draw a frequency polygon by plotting the class-marks on x-axis and the frequencies on y-axis, marks the points M(3.5, 2), N(9.5, 1), O(15.5, 8), P(21.5, 9), Q(27.5, 4), R(33.5, 5), S(39.5, 6), T(45.5, 10), U(51.5, 6), V(57.5, 2) and K(63.5, 0) by line segments.

5. For team B, we draw a frequency polygon by plotting the class-marks on x-axis and the frequencies on y-axis, marks the points A(3.5, 5), B(9.5, 6), C(15.5, 2), D(21.5, 10), E(27.5, 5), F(33.5, 6), G(39.5, 3), H(45.5, 4), I(51.5, 8), J(57.5, 10) and K(63.5, 0) by line segments.

6. To complete the polygon, we assume that there is a class interval with frequency zero before the first class i.e. (-5.5) - 0, and one after the last class interval i.e. 60.5 - 66.5, with class marks -2.5 and 63.5 respectively. Mark points L(-2.5, 0) and K(63.5, 0).

7. Join the points LMNOPQRSTUVK and LABCDEFGHIJK with the help of different line segments.

8. Frequency polygon LMNOPQRSTUVK formed for Team A

9. Frequency polygon LABCDEFGHIJK formed for Team B.