In the previous class, we learnt how to draw bar graphs to represent the frequency distribution of ungrouped data. In this chapter, we will learn how to represent a grouped frequency distribution graphically. The most common graphic representation is the histogram. Students can utilise the RD Sharma Solutions for Class 8 for any doubt clearance and can also strengthen their conceptual knowledge. When solutions are practised regularly, students can speed up their problem-solving abilities. The PDF of RD Sharma Solutions Class 8 contains questions from this chapter and can be downloaded easily from the links available below.
Chapter 24 Data Handling – II (Graphical Representation of Data as Histogram) contains one exercise, and the RD Sharma Class 8 Solutions available on this page provide solutions to the questions in this exercise. Now, let us have a look at the concepts discussed in this chapter.
- Graphical method of representing data.
- Histogram.
RD Sharma Solutions for Class 8 Maths Chapter 24 Data Handling – II (Graphical Representation of Data as Histogram)
Access Answers to RD Sharma Class 8 Maths Solutions for Chapter 24 Data Handling – II (Graphical Representation of Data as Histogram)
1. Given below is the frequency distribution of the heights of 50 students in a class:
| Class Interval | 140-145 | 145-150 | 150-155 | 155-160 | 160-165 |
| Frequency | 8 | 12 | 18 | 10 | 5 |
Draw a histogram representing the above data.
Solution:
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:
2. Draw a histogram of the following data:
| Class Interval | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 |
| Frequency | 30 | 98 | 80 | 58 | 29 | 50 |
Solution:
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:
3. Number of workshops organised by a school in different areas during the last five years are as follows:
| Years | No. of Workshops |
| 1995-1996 | 25 |
| 1996-1997 | 30 |
| 1997-1998 | 42 |
| 1998-1999 | 50 |
| 1999-2000 | 65 |
Draw a histogram representing the above data:
Solution:
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 a histogram for the given frequency. The histogram is shown below:
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, 168, 182, 195, 207, 219, 235, 118.
Draw the histogram of the frequency distribution (taking one of the class intervals as 50-100).
Solution:
First, prepare the frequency table for the class intervals 50−100, 100−150,…, 200−250, as shown below:
| Class Interval | Frequency |
| 50-100 | 2 |
| 100-150 | 11 |
| 150-200 | 4 |
| 200-250 | 3 |
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:
5. Construct a histogram for the following data:
| Monthly School Fee (in Rs) | 30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 | 210-240 |
| No. of Schools | 5 | 12 | 14 | 18 | 10 | 9 | 4 |
Solution:
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:
6. Draw a histogram for the daily earnings of 30 drug stores in the following table:
| Daily Earnings(in Rs) | 450 – 500 | 500 – 550 | 550 – 600 | 600 – 650 | 650 – 700 |
| No. of Stores | 16 | 10 | 7 | 3 | 1 |
Solution:
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:
7. Draw a histogram to represent the following data:
| Monthly Salary (in Rs) | No. of Teachers |
| 5600-5700 | 8 |
| 5700-5800 | 4 |
| 5800-5900 | 3 |
| 5900-6000 | 5 |
| 6000-6100 | 2 |
| 6100-6200 | 3 |
| 6200-6300 | 1 |
| 6300-6400 | 2 |
Solution:
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:
8. The following histogram shows the number of literate females in the age group of 10 to 40 years in a town:
(i) Write the age group in which the number of literate females 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 are literate females the least?
Solution:
(i) The highest rectangle corresponds to the highest number of literate females, which is in the interval of 15−20 years.
(ii) The class intervals are 10−15, 15−20, 20−25, 30−35 and 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.
i.e., Class mark = (upper limit + lower limit) / 2
Hence, the class mark of each class is as follows:
| Class Interval | Class Marks |
| 10-15 | 12.5 |
| 15-20 | 17.5 |
| 20-25 | 22.5 |
| 25-30 | 27.5 |
| 30-35 | 32.5 |
| 35-40 | 37.5 |
(v) The lowest rectangle corresponds to the least number of literate females, which is in the interval of 10−15 years.
9. The following histogram shows the monthly wages (in Rs) of workers in a factory:
(i) In which wage-group are the largest numbers of workers 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?
Solution:
(i) From the figure, 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.
10. Below is the histogram depicting marks obtained by 43 students in a class:
(i) Write the number of students getting the highest marks.
(ii) What is the class size?
Solution:
(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.
11. The following histogram shows the frequency distribution of the ages of 22 teachers in a school:
(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?
Solution:
(i) The eldest (50−55 years) = 1 person
This is because the height of the rectangle with class interval 50−55 as the 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 the 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 the 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 the base is the minimum.
(iii) Class size = The range between the upper and the lower boundaries of the class.
For example, the size of class 20−25 years is 5.
(iv) The class mark is the mid-point of the class interval.
i.e., Class mark = (upper limit + lower limit)/2
Hence, the class mark of each class is as follows:
For Class 20-25:
Class mark = (20+25)/2 = 45/2 = 22.5
Similarly, the class marks of the other classes are 27.5, 32.5, 37.5, 42.5, 47.5, and 52.5.
12. The weekly wages (in Rs.) of 30 workers in a factory are given below:
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 then Rs. 850?
Solution:
The frequency table with intervals 800−820, 810−820,…890−900 is shown below:
| Wages (in Rs) | Frequency |
| 800-810 | 4 |
| 810-820 | 2 |
| 820-830 | 1 |
| 830-840 | 11 |
| 840-850 | 2 |
| 850-860 | 2 |
| 860-870 | 2 |
| 870-880 | 1 |
| 880-890 | 4 |
| 890-900 | 1 |
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:
(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 the 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 the frequency table in the following manner:
3 + 2 + 1 + 9 + 5 = 203 + 2 + 1 + 9 + 5 = 20
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