Statistics — Question 6

Frequency polygons can be drawn independently without drawing histograms. This requires the midpoints of the class intervals used in the data. The mid-points are called class-marks.

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

Substituting the values we get,

Class mark = $\dfrac{10 + 0}{2} = \dfrac{10}{2}$ = 5

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

Section A

Section B

Steps of construction of frequency polygon :

1. Take class marks on the x-axis.

2. Take frequency on the y-axis with an appropriate scale of 1 unit = 2 students.

3. We draw frequency polygon for section A by plotting the class-marks on x-axis and the frequencies on y-axis, mark the points A(5, 3), B(15, 9), C(25, 17), D(35, 12) and E(45, 9).

4. We draw a frequency polygon for section B by plotting the class-marks on x-axis and the frequencies on y-axis, marks the points U(5, 5), V(15, 19), W(25, 15), X(35,10) and Y(45, 1).

5. To complete the polygon, we assume that there is a class interval with frequency zero before the first interval i.e., -10 - 0, and one after the last interval i.e. (50, 60), with class marks -5 and 55 respectively. Mark points G(-5, 0) and Z(55, 0).

6. Join the points GABCDEZ and GUVWXYZ with the help of different line segments.

7. Frequency polygon GABCDEZ is formed for Section A.

8. Frequency polygon GUVWXYZ is formed for Section B.

From graph,

We observe that,

The performance of students of Section A is better than the performance of students of Section B, as section A shows more students securing marks between class intervals 30 – 40 and 40 – 50.