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# R S Aggarwal and V Aggarwal Solution for Class 9 Mathematics Chapter 17 - Bar Graph, Histogram and Frequency Polygon

Our RS Aggarwal & V Agarwal Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 9 board exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 17 - Bar Graph, Histogram and Frequency Polygon.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RS Aggarwal & V Agarwal Textbook Solutions for CBSE Class 9 Mathematics will strengthen your fundamentals in this chapter and will help you in your attempts to score more marks in the final examination. CBSE Class 9 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

Exercise/Page

## R S Aggarwal and V Aggarwal Solution for Class 9 Mathematics Chapter 17 - Bar Graph, Histogram and Frequency Polygon Page/Excercise 17B

Solution 1

Given frequency distribution is as below :

 Daily wages (in Rs) 340-380 380-420 420-460 460-500 500-540 540-580 No. of workers 16 9 12 2 7 4

In the class intervals, if the upper limit of one class is the lower limit of the next class, it is known as the exclusive method of classification.

Clearly, the given frequency distribution is in the exclusive form.

To draw the required histogram , take class intervals , i.e. daily wages (in Rs. ) along x-axis and frequencies i.e.no.of workers alongy-axisand draw rectangles . So , we get the requiredhistogram .

Since the scale on X-axis starts at 340, a kink(break) is indicated near the origin to show that the graph is drawn to scale beginning at 340. Solution 2

Given frequency distribution is as below :

 Daily earnings (in Rs) 700-750 750-800 800-850 850-900 900-950 950-1000 No of stores 6 9 2 7 11 5

In the class intervals, if the upper limit of one class is the lower limit of the next class, it is known as the exclusive method of classification.

Clearly, the given frequency distribution is in the exclusive form.

We take class intervals, i.e. daily earnings (in Rs .) along x-axis and frequencies i.e. number of stores along y-axis. So , we get the required histogram .

Since the scale on X-axis starts at 700, a kink(break) is indicated near the origin to show that the graph is drawn to scale beginning at 700. Solution 3

 Height (in cm) 130-136 136-142 142-148 148-154 154-160 160-166 No. of students 9 12 18 23 10 3

In the class intervals, if the upper limit of one class is the lower limit of the next class, it is known as the exclusive method of classification.

Clearly, the given frequency distribution is in the exclusive form.

We take class intervals, i.e. height (in cm ) along x-axis and frequencies i.e. number of student s along y-axis . So we get the required histogram.

Since the scale on X-axis starts at 130, a kink(break) is indicated near the origin to show that the graph is drawn to scale beginning at 130. Solution 4

(i) Histogram is as follows: (ii) Number of lamps having lifetime more than 700 hours = 74 + 62 + 48 = 184

Solution 5

Give frequency distribution is as below :

 Class interval 8-13 13-18 18-23 23-28 28-33 33-38 38-43 Frequency 320 780 160 540 260 100 80

In the class intervals, if the upper limit of one class is the lower limit of the next class, it is known as the exclusive method of classification.

Clearly, the given frequency distribution is in the exclusive form.

We take class intervals along x-axis and frequency along y-axis . So , we get the required histogram.

Since the scale on X-axis starts at 8, a kink(break) is indicated near the origin to show that the graph is drawn to scale beginning at 8. Solution 6

Histogram is the graphical representation of a frequency distribution in the form of rectangles, such that there is no gap between any two successive rectangles.

Clearly the given frequency distribution is in inclusive form, that is there is a gap between the upper limit of a class and the lower limit of the next class.

Therefore, we need to convert the given frequency distribution into exclusive form, as shown below:

 Class interval 4.5-12.5 12.5-20.5 20.5-28.5 28.5-36.5 36.5-44.5 44.5-52.5 Frequency 6 15 24 18 4 9

To draw the required histogram , take class intervals, along x-axis and frequencies along y-axis and draw rectangles . So, we get the required histogram .

Since the scale on X-axis starts at 4.5, a kink(break) is indicated near the origin to show that the graph is drawn to scale beginning at 4.5. Solution 7

Given frequency distribution is as below :

 Age group (in years ) 10-16 17-23 24-30 31-37 38-44 45-51 52-58 No. of illiterate persons 175 325 100 150 250 400 525

Histogram is the graphical representation of a frequency distribution in the form of rectangles, such that there is no gap between any two successive rectangles.

Clearly the given frequency distribution is in inclusive form, that is there is a gap between the upper limit of a class and the lower limit of the next class.

Therefore, we need to convert the frequency distribution in exclusive form, as shown below:

 Age group(in years) 9.5-16.5 16.5-23.5 23.5-30.5 30.5-37.5 37.5-44.4 44.5-51.5 51.5-58.5 No of illiterate persons 175 325 100 150 250 400 525

To draw the required histogram , take class intervals, that is age group, along x-axis and frequencies, that is number of illiterate persons along y-axis and draw rectangles . So , we get the required histogram.

Since the scale on X-axis starts at 9.5, a kink(break) is indicated near the origin to show that the graph is drawn to scale beginning at 9.5. Solution 8

given frequency distribution is as below :

 Class interval 10-14 14-20 20-32 32-52 52-80 Frequency 5 6 9 25 21

In the above table , class intervals are of unequal size, so we calculate the adjusted frequency by using the following formula : Thus , the adjusted frequency table is

 Class intervals frequency Adjusted Frequency 10-14   14-20   20-32   32-52   52-80 5   6   9   25   21 Now take class intervals along x-axis and adjusted frequency along y-axis and constant rectangles having their bases as class size and heights as the corresponding adjusted frequencies.

Thus, we obtain the histogram as shown below: Solution 9

(i) Minimum class size = 6 - 4 = 2  (ii) Maximum number of surnames lies in the class interval 6 - 8.

Solution 10

Minimum class size = 10 - 5 = 5  Solution 11

Minimum class size = 50 - 45 = 5  Solution 12

The given frequency distribution is as below:

 Age in years 10-20 20-30 30-40 40-50 50-60 60-70 No of patients 2 5 12 19 9 4

In order to draw, frequency polygon, we require class marks.

The class mark of a class interval is: The frequency distribution table with class marks is given below:

 Class- intervals Class marks Frequency 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 5 15 25 35 45 55 65 75 0 2 5 12 19 9 4 0

In the above table, we have taken imaginary class intervals 0-10 at beginning and 70-80 at the end, each with frequency zero . Now take class marks along x-axis and the corresponding frequencies along y-axis.

Plot points (5,0), (15,2), (25, 5), (35, 12), (45, 19), (55, 9), (65, 4) and (75, 0) and draw line segments. Solution 13

The given frequency distribution table is as below:

 Class intervals 1-10 11-20 21-30 31-40 41-50 51-60 Frequency 8 3 6 12 2 7

This table has inclusive class intervals and so these are to be converted into exclusive class intervals (i.e true class limits).

These are (0.5-10.5), (10.5-20.5), (20.5-30.5), (30.5-40.5),
(40.5-50.5), and (50.5-60.5)

In order to draw a frequency polygon, we need to determine the class marks. Class marks of a class interval = Take imaginary class interval ( -9.5-0.5) at the beginning and (60.5-70.5) at the end , each with frequency zero. So we have the following table

 Class intervals True class intervals Class marks Frequency (-9)-0 1-10 11-20 21-30 31-40 41-50 51-60 61-70 (-9.5)-0.5 0.5-10.5 10.5-20.5 20.5-30.5 30.5-40.5 40.5-50.5 50.5-60.5 60.5-70.5 -4.5 5.5 15.5 25.5 35.5 45.5 55.5 65.5 0 8 3 6 12 2 7 0

Now, take class marks along x-axis and their corresponding frequencies along y-axis.

Mark the points and join them.

Thus, we obtain a complete frequency polygon as shown below: Solution 14

The given frequency distribution is as under

 Age in years 10-20 20-30 30-40 40-50 50-60 60-70 Numbers of patients 90 40 60 20 120 30

Take class intervals i.e age in years along x-axis and number of patients of width equal to the size of the class intervals and height equal to the corresponding frequencies.

Thus we get the required histogram.

In order to draw frequency polygon,we take imaginary intervals 0-10 at the beginning and 70-80 at the end each with frequency zero and join the mid-points of top of the rectangles.

Thus, we obtain a complete frequency polygon, shown below: Solution 15

The given frequency distribution is as below :

 Class intervals 20-25 25-30 30-35 35-40 40-45 45-50 Frequency 30 24 52 28 46 10

Take class intervals along x-axis and frequencies along y-axis and draw rectangle s of width equal to the size of the class intervals and heights equal to the corresponding frequencies.

Thus we get required histogram.

Now take imaginary class intervals 15-20 at the beginning and 50-55 at the end , each with frequency zero and join the mid points of top of the rectangles to get the required frequency polygon. Solution 16

The given frequency distribution table is given below :

 Class interval 600-640 640-680 680-720 720-760 760-800 800-840 Frequency 18 45 153 288 171 63

Take class intervals along x-axis and frequencies along y-axis and draw rectangles of width equal to to size of class intervals and height equal to their corresponding frequencies.

Thus we get the requiredhistogram.

Take imaginary class intervals 560-600 at the beginning and 840-880 at the end, each with frequency zero.

Now join the mid points of the top of the rectangles to get the required frequency polygon. ## R S Aggarwal and V Aggarwal Solution for Class 9 Mathematics Chapter 17 - Bar Graph, Histogram and Frequency Polygon Page/Excercise 17A

Solution 1

Take the various types of games along the x-axis and the number of students along the y-axis.

Along the y-axis, take 1 small square=3 units.

All the bars should be of same width and same space should be left between the consecutive bars.

Now we shall draw the bar chart, as shown below: Solution 2

Take the timings along the x-axis and the temperatures along the y-axis.

Along the y-axis, take 1 small square=5 units.

All the bars should be of same width and same space should be left between the consecutive bars.

Now we shall draw the bar chart, as shown below: Solution 3 Solution 4

Take the various types of sports along the x-axis and the number of students along the y-axis.

Along the y-axis, take 1 small square=10 units.

All the bars should be of same width and same space should be left between the consecutive bars.

Now we shall draw the bar chart, as shown below: Solution 5

Take the academic year along the x-axis and the number of students along the y-axis.

Along the y-axis, take 1 big division =200 units.

All the bars should be of same width and same space should be left between the consecutive bars.

Now we shall draw the bar chart, as shown below: Solution 6 Solution 7

Take city along the x-axis and distance from Delhi (in Km) along the y-axis.

Along the y-axis, take 1 big division =200 units.

All the bars should be of same width and same space should be left between the consecutive bars.

Now we shall draw the bar chart, as shown below: Solution 8

Take the countries along the x-axis and the birth rate (per thousand) along the y-axis.

Along the y-axis, take 1 big division = 5 units.

All the bars should be of same width and same space should be left between the consecutive bars.

Now we shall draw the bar chart, as shown below: Solution 9 Solution 10 Solution 11

Take themode of transport along the x-axis and the number of students along the y-axis.

Along the y-axis, take 1 big division = 100 units.

All the bars should be of same width and same space should be left between the consecutive bars.

Now we shall draw the bar chart, as shown below: Solution 12

(i) The bar graph shows the marks obtained by a student in various subject in an examination.

(ii) The student is very good in mathematics.

(iii) He is poor in Hindi

(iv)  Average marks = ## Browse Study Material

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CBSE IX - Mathematics

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