Question

The following table gives the distribution of students of two sections according to the marks obtained by him: 

Section A		Section B
Marks	Frequency	Marks	Frequency
0 − 10	3	0 − 10	5
10 − 20	9	10 − 20	19
20 − 30	17	20 − 30	15
30 − 40	12	30 − 40	10
40 − 50	9	40 − 50	1

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

Answer 1

We can find the class marks of the given class intervals by using the following formula.    

\(\text{ Class mark} =\frac{\text{ 𝑈𝑝𝑝𝑒𝑟 𝑐𝑙𝑎𝑠𝑠 𝑙𝑖𝑚𝑖𝑡+𝐿𝑜𝑤𝑒𝑟 𝑐𝑙𝑎𝑠𝑠 𝑙𝑖𝑚𝑖𝑡 }}{2}  \)

Section A			Section B
Marks	Class marks	Frequency	Marks	Class marks	Frequency
0 − 10	5	3	0 − 10	5	5
10 − 20	15	9	10 − 20	15	19
20 − 30	25	17	20 − 30	25	15
30 − 40	35	12	30 − 40	35	10
40 − 50	45	9	40 − 50	45	1

We plot the class-mark on x-axis and number of students on y-axis. 

From the above graph, we observed that students of section A performed better because as we move right on x-axis the number of students are spread widely over greater marks as compared to the students of section A.