The following table gives the distribution of students of two sections according to the marks obtained by them:
Marks (Section $A$) Frequency (Section $A$) Marks (Section $B$) Frequency (Section $B$)
$0-10$ $3$ $0-10$ $5$
$10-20$ $9$ $10-20$ $19$
$20-30$ $17$ $20-30$ $15$
$30-40$ $12$ $30-40$ $10$
$40-50$ $9$ $40-50$ $1$

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.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) We can find the class marks of the given class intervals by using the following formula:
$\text{Class mark} = \frac{\text{Upper class limit} + \text{Lower class limit}}{2}$
Marks Class mark Frequency (Section $A$) Frequency (Section $B$)
$0-10$ $5$ $3$ $5$
$10-20$ $15$ $9$ $19$
$20-30$ $25$ $17$ $15$
$30-40$ $35$ $12$ $10$
$40-50$ $45$ $9$ $1$

By plotting the class marks on the $x$-axis and frequency on the $y$-axis,we draw the frequency polygons for both sections.
From the graph,it can be observed that the frequency polygon for section $A$ is shifted more towards the right compared to section $B$. This indicates that the students of section $A$ have performed better than the students of section $B$ in terms of obtaining higher marks.

Explore More

Similar Questions

Give one example of a situation in which $(i)$ the mean is an appropriate measure of central tendency.

$A$ teacher wanted to analyze the performance of two sections of students in a mathematics test of $100$ marks. Looking at their performances,she found that a few students got under $20$ marks and a few got $70$ marks or above. So she decided to group them into intervals of varying sizes as follows: $0-20, 20-30, ..., 60-70, 70-100$. Then she formed the following table:
MarksNumber of students
$0-20$$7$
$20-30$$10$
$30-40$$10$
$40-50$$20$
$50-60$$20$
$60-70$$15$
$70-100$$8$
Total$90$

$A$ histogram for this table was prepared by a student as shown in Fig. Carefully examine this graphical representation. Do you think that it correctly represents the data?

In a particular section of Class $IX,$ $40$ students were asked about the months of their birth and the following graph was prepared for the data so obtained:
Observe the bar graph given above and answer the following questions:
$(i)$ How many students were born in the month of November?
$(ii)$ In which month were the maximum number of students born?

The runs scored by two teams $A$ and $B$ on the first $60$ balls in a cricket match are given below:
Number of balls Teams $A$ Teams $B$
$1-6$ $2$ $5$
$7-12$ $1$ $6$
$13-18$ $8$ $2$
$19-24$ $9$ $10$
$25-30$ $4$ $5$
$31-36$ $5$ $6$
$37-42$ $6$ $3$
$43-48$ $10$ $4$
$49-54$ $6$ $8$
$55-60$ $2$ $10$

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

The relative humidity (in $\%$) of a certain city for a month of $30$ days was as follows:
$98.1$ $98.6$ $99.2$ $90.3$ $86.5$ $95.3$ $92.9$ $96.3$ $94.2$ $95.1$
$89.2$ $92.3$ $97.1$ $93.5$ $92.7$ $95.1$ $97.2$ $93.3$ $95.2$ $97.3$
$96.2$ $92.1$ $84.9$ $90.2$ $95.7$ $98.3$ $97.3$ $96.1$ $92.1$ $89$

$(i)$ Construct a grouped frequency distribution table with classes $84-86, 86-88$,etc.
$(ii)$ Which month or season do you think this data is about?
$(iii)$ What is the range of this data?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo