RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Created by: Abhishek Kapoor

Class 8 : RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

The document RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
All you need of Class 8 at this link: Class 8

Question 1:

Given below is the frequency distribution of the heights of 50 students of a class:

Class interval:140−145145−150150−155155−160160−165
Frequency:81218105

Draw a histogram representing the above data.

Answer 1:

The class limits are represented along the x-axis on a suitable scale and the frequencies are represented along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be constructed to obtain the histogram of the given frequency distribution as shown in the figure below:

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

Question 2:

Draw a histogram of the following data:

Class interval:10−1515−2020−2525−3030−3534−40
Frequency:309880582950

Answer 2:

The class limits are represented along the x-axis and the frequencies are represented along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

 

Question 3:

Number of workshops organized by a school in different areas during the last five years are as follows:

YearsNo. of workshops
1995−199625
1996−199730
1997−199842
1998−199950
1999−200065

Draw a histogram representing the above data.

Answer 3:

The class limits are represented along the x-axis and the frequencies are represented along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be constructed to obtain histogram for the given frequency. The histogram is shown below:

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

Question 4:

In a hypothetical sample of 20 people the amounts of money with them were found to be as follows:
 114, 108, 100, 98, 101, 109, 117, 119, 126, 131, 136, 143, 156, 169, 182, 195, 207, 219, 235, 118.
 Draw the histogram of the frequency distribution (taking one of the class intervals as 50−100).

Answer 4:

We first prepare the frequency table for the class intervals 50−100, 100−150,..., 200−250, as shown below:

MoneyTally AmountFrequency
50−100981
100−150114, 108, 100, 101, 109, 117, 119, 126, 131, 136, 143, 11812
150−200156, 169, 182, 1954
200−250207, 219, 2353

The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking the class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

Question 5:

Construct a histogram for the following data:

Monthly school fee (in Rs):30−6060−9090−120120−150150−180180−210210−240
Number of schools:51214181094

Answer 5:

The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and corresponding frequencies as heights of the rectangles, the histogram of the given data can be obtained as shown in the figure below:

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

Question 6:

Draw a histogram for the daily earnings of 30 drug stores in the following table:

Daily earnings (in Rs):450−500500−550550−600600−650650−700
Numbers of stores:1610731

Answer 6:

The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is given below:
RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

Question 7:

Draw a histogram to represent the following data:

Monthly salary (in Rs)Number of teachers
5600−57008
5700−58004
5800−59003
5900−60005
6000−61002
6100−62003
6200−63001
6300−64002

Answer 7:

Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be constructed to obtain the histogram of the given data. The class intervals are represented along the x-axis and the frequencies along the y-axis on a suitable scale.
The histogram representing the given data is shown below:
RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

Question 8:

The following histogram shows the number of literate females in the age group of 10 to 40 years in a town:

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev
 (i) Write the age group in which the number of literate female is the highest.
 (ii) What is the class width?
 (iii) What is the lowest frequency?
 (iv) What are the class marks of the classes?
 (v) In which age group literate females are the least?

Answer 8:

(i) The highest rectangle corresponds to the highest number of literate females, which is in the interval 15−20 years.
(ii) The class intervals are 10−15, 15−20, 20−25, 30−35, 35−40. Hence, the class width is 5.
(iii) The lowest rectangle corresponds to the lowest frequency, which is 320.
(iv) The class mark is the mid-point of the class interval.
 class mark = RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev
Hence, the class mark of each class is as follows:

IntervalClass Mark
10−1512.5
15−2017.5
20−2522.5
25−3027.5
30−3532.5
35−4037.5


(v) The lowest rectangle corresponds to the least number of literate females, which is in the interval 10−15 years.

Question 9:

The following histogram shows the monthly wages (in Rs) of workers in a factory:

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev
 (i) In which wage-group the largest number of workers are being kept? What is their number?
 (ii)  What wages are the least number of workers getting? What is the number of such workers?
 (iii) What is the total number of workers?
 (iv) What is the factory size?

Answer 9:

(i) In Fig 24.8, the highest rectangle corresponds to the largest number of workers. The required interval is Rs 950−1000. There are 8 workers in this interval.
(ii) The lowest rectangle corresponds to the least number of workers. The required interval is Rs 900−950. There are 2 workers in this interval.
(iii) The total number of workers is the sum of workers in all the intervals. It can be calculated as follows:
      Total workers = 3 + 7 + 5 + 4 + 2 + 8 + 6 + 5 = 40 workers
(iv) The factory intervals are 750−800, 800−850, .. 1050−100. Hence, the factory size is 50.

Question 10:

Below is the histogram depicting marks obtained by 43 students of a class:
 (i) Write the number of students getting the highest marks.
 (ii) What is the class size?
RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

Answer 10:

(i) In the given histogram, the interval with the highest marks is 90−100.
Three students are there in this interval because the height of the rectangle (90−100) is 3 units.
(ii) The class intervals are 10−20, 20−30, ..., 90−100. So, the class size is 10.

Question 11:

The following histogram shows the frequency distribution f the ages of 22 teachers in a school:

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev
 (i) What is the number of eldest and youngest teachers in the school?
 (ii) Which age group teachers are more in the school and which least?
 (iii) What is the size of the classes?
 (iv) What are the class marks of the classes?

Answer 11:

(i) The eldest (50−55 years) = 1 person
  This is because the height of the rectangle with class interval 50−55 as base is 1 unit.
  The youngest (20−25 years) = 2 persons
 This is because the height of the rectangle with class interval 20−25 as base is 2 units.

(ii) The group containing the most number of teachers is 35−40 years. This is because the height of the rectangle with class interval 35−40 as base is the maximum.
     The group containing the least number of teachers is 50−55 years. This is because the height of the rectangle with class interval 50−55 as base is the minimum.

(iii) Class size = The range between the upper and the lower boundaries of the class
     For example, the size of the class 20−25 years is 5.

(iv) Class mark = RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev
For class 20−25:Class mark  =  RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev =  22.5
Similarly, the class marks of the other classes are 27.5; 32.5; 37.5; 42.5; 47.5; 52.5.

Question 12:

The weekly wages (in Rs.) of 30 workers in a factory are given:
 830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840
 Mark a frequency table with intervals as 800-810, 810-820 and so on, using tally marks. Also, draw a histogram and answer the following questions:
 (i) Which group has the maximum number of workers?
 (ii) How many workers earn Rs 850 and more?
 (iii) How many workers earn less than Rs 850?

Answer 12:

The frequency table with intervals 800−820, 810−820,...890−900 is given below:
 

Wage (in Rs)Tally WageFrequencyTally marks
800−810804, 808, 806III
810−820810, 8122II
820−8308201I
830−840830, 835, 835, 836, 832, 833, 835, 835, 8369IIII IIII
840−850845, 845, 840, 840, 8405IIII
850−8608551I
860−870869, 860, 8683III
870−8808781I
880−8908851I
890−900890, 898, 890, 8904IIII


The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev
(i) The group that has the maximum number of workers is represented as the highest rectangle. It is in the interval 830−840.
(ii) The number of workers who earn Rs 850 or more can be calculated from frequency table in the following manner:
1 + 3 + 1 + 1 + 4 = 101 + 3 + 1 + 1 + 4 = 10
(iii) The number of workers who earn less than Rs 850 can be calculated from frequency table in the following manner:
3 + 2 + 1 + 9 + 5 = 203 + 2 + 1 + 9 + 5 = 20

Complete Syllabus of Class 8

Dynamic Test

Content Category

Related Searches

video lectures

,

Exam

,

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

,

Free

,

shortcuts and tricks

,

study material

,

Important questions

,

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

,

Extra Questions

,

pdf

,

Sample Paper

,

Summary

,

mock tests for examination

,

MCQs

,

past year papers

,

RD Sharma Solutions - Chapter 24 - Data Handling-II (Graphical Representation of Data as Histograms) Class 8 Notes | EduRev

,

Viva Questions

,

Objective type Questions

,

Previous Year Questions with Solutions

,

ppt

,

practice quizzes

,

Semester Notes

;