# Ex.14.3 Q6 Statistics Solution - NCERT Maths Class 9

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## Question

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

 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.

## Text Solution

What is known?

The distribution of students of two sections according to the marks obtained by them.

What is Unknown?

(i) A frequency polygon to represent the marks of the students of both the sections.

(ii) Comparisons of performance of those two sections.

Reasoning:

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

\begin{align} \text{Class Marks}=\frac{\text { Upper Limit }+\text { Lower Limit }}{2}\end{align}

Steps:

Now, the data table with inclusion of class marks:

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

The frequency polygon for the above data can be constructed by:

• Taking class marks on $$x$$-axis.
• Taking ‘frequency’ on $$y$$-axis with an appropriate scale of $$1\,\rm unit = 2$$ students as the lowest frequency value observed is $$1$$ and the highest frequency value is $$19.$$ It can be observed that the performance of students of Section ‘$$A$$’ is better than the students of Section '$$B$$' as section ‘$$A$$’ shows more students securing marks between ‘$$40 – 50$$’ class and ‘$$30 – 40$$’ class.

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