Data Handling-II (Graphical Representation of Data as Histograms) - Exercise 24 | Mathematics (Maths) Class 8 PDF Download

 Page 1


 
 
 
 
  
   
 
 
                                                     
 
1. Given below is the frequency distribution of the heights of 50 students of 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: 
Page 2


 
 
 
 
  
   
 
 
                                                     
 
1. Given below is the frequency distribution of the heights of 50 students of 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 organized 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 histogram for the given 
frequency. The histogram is shown below: 
Page 3


 
 
 
 
  
   
 
 
                                                     
 
1. Given below is the frequency distribution of the heights of 50 students of 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 organized 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 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:
We 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 
Page 4


 
 
 
 
  
   
 
 
                                                     
 
1. Given below is the frequency distribution of the heights of 50 students of 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 organized 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 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:
We 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: 
Page 5


 
 
 
 
  
   
 
 
                                                     
 
1. Given below is the frequency distribution of the heights of 50 students of 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 organized 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 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:
We 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: