Data Handling – I (Presentation of Data Exercise 21.1) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

 Page 1


 
 
 
 
 
  
                                                                              
1. Define the following terms: 
(i) Observations 
(ii) data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
Solution: 
 
(i) The active acquisition of information which is obtained from a primary source is called observation. 
 
(ii) Data is a collection of facts such as values measurements. 
 
(iii) The number of times an observation occurs in the given data, is called the frequency of the observation. 
 
(iv) Frequency table or frequency distribution is a method to present raw data in the form from which one can 
easily understand the information contained in the raw data. 
 
2. The final marks in mathematics of 30 students are as follows: 
53, 61, 48, 60, 78, 68, 55, 100, 67, 90 
75, 88, 77, 37, 84, 58, 60, 48, 62, 56 
44, 58, 52, 64, 98, 59, 70, 39, 50, 60 
(i) Arrange these marks in the ascending order. 30 to 39 one group, 40 to 49 second group, etc. 
(ii) What is the highest score? 
(iii) What is the lowest score? 
(iv) What is the range? 
(v) If 40 is the pass mark how many have failed? 
(vi) How many have scored 75 or more? 
(vii) Which observations between 50 and 60 have not actually appeared? 
(viii) How many have scored less than 50? 
Solution: 
 
(i) Frequency distribution table of the marks obtained in Mathematics by students: 
 
 
 
(ii) The highest score is 100 from the given data. 
 
(iii) The lowest score is 37 from the above data. 
 
(iv) We know that 
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1. Define the following terms: 
(i) Observations 
(ii) data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
Solution: 
 
(i) The active acquisition of information which is obtained from a primary source is called observation. 
 
(ii) Data is a collection of facts such as values measurements. 
 
(iii) The number of times an observation occurs in the given data, is called the frequency of the observation. 
 
(iv) Frequency table or frequency distribution is a method to present raw data in the form from which one can 
easily understand the information contained in the raw data. 
 
2. The final marks in mathematics of 30 students are as follows: 
53, 61, 48, 60, 78, 68, 55, 100, 67, 90 
75, 88, 77, 37, 84, 58, 60, 48, 62, 56 
44, 58, 52, 64, 98, 59, 70, 39, 50, 60 
(i) Arrange these marks in the ascending order. 30 to 39 one group, 40 to 49 second group, etc. 
(ii) What is the highest score? 
(iii) What is the lowest score? 
(iv) What is the range? 
(v) If 40 is the pass mark how many have failed? 
(vi) How many have scored 75 or more? 
(vii) Which observations between 50 and 60 have not actually appeared? 
(viii) How many have scored less than 50? 
Solution: 
 
(i) Frequency distribution table of the marks obtained in Mathematics by students: 
 
 
 
(ii) The highest score is 100 from the given data. 
 
(iii) The lowest score is 37 from the above data. 
 
(iv) We know that 
 
 
 
 
 
  
Range = Highest score – Lowest score 
By substituting the values 
Range = 100 – 37 = 63 
 
(v) If 40 is the pass mark, the number of students who scored less than 40 have failed.  
Students who scored 37 and 39 have failed. 
Hence, 2 students have failed in the exam. 
 
(vi) The number of students who have scored 75 or more are 8 from the data given above. 
So the marks obtained by them are 75, 77, 78, 84, 88, 90, 98 and 100. 
 
(vii) Observations 51, 54 and 57 have not actually appeared in the range 50 – 60. 
 
(viii) From the above data we know that 5 students have scored less than 50 i.e. 37, 39, 44, 48 and 48. 
 
3. The weights of new born babies (in kg) in a hospital on a particular day are as follows: 
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4 
(i) Rearrange the weights in descending order. 
(ii) Determine the highest weight. 
(iii) Determine the lowest weight. 
(iv) Determine the range. 
(v) How many babies were born on that day? 
(vi) How many babies weigh below 2.5 kg? 
(vii) How many babies weight more than 2.8 kg? 
(viii) How many babies weight 2.8 kg? 
Solution: 
 
(i) Rearranging the weights in descending order 
3.1, 3.0, 2.9, 2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.5, 2.4, 2.3, 2.2, 2.1 
 
(ii) The highest weight is 3.1 kg from the given data. 
 
(iii) The lowest weight is 2.1 kg from the given data. 
 
(iv) We know that 
Range = Highest weight – Lowest weight 
By substituting the values 
Range = 3.1 – 2.1 = 1.0 kg 
 
(v) The number of babies born on that day can be found by counting the number of observations. 
Hence, 15 babies were born on that day. 
 
(vi) The babies which weigh below 2.5 kg are 2.1, 2.2, 2.3 and 2.4 kg. 
Hence, 4 babies weigh below 2.5 kg. 
 
(vii) The babies which weigh more than 2.8 kg are 2.9, 2.9, 3.0 and 3.1 kg. 
Hence, 4 babies weigh more than 2.8 kg. 
 
(viii) From the given data we know that 2 babies weigh 2.8 kg. 
 
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1. Define the following terms: 
(i) Observations 
(ii) data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
Solution: 
 
(i) The active acquisition of information which is obtained from a primary source is called observation. 
 
(ii) Data is a collection of facts such as values measurements. 
 
(iii) The number of times an observation occurs in the given data, is called the frequency of the observation. 
 
(iv) Frequency table or frequency distribution is a method to present raw data in the form from which one can 
easily understand the information contained in the raw data. 
 
2. The final marks in mathematics of 30 students are as follows: 
53, 61, 48, 60, 78, 68, 55, 100, 67, 90 
75, 88, 77, 37, 84, 58, 60, 48, 62, 56 
44, 58, 52, 64, 98, 59, 70, 39, 50, 60 
(i) Arrange these marks in the ascending order. 30 to 39 one group, 40 to 49 second group, etc. 
(ii) What is the highest score? 
(iii) What is the lowest score? 
(iv) What is the range? 
(v) If 40 is the pass mark how many have failed? 
(vi) How many have scored 75 or more? 
(vii) Which observations between 50 and 60 have not actually appeared? 
(viii) How many have scored less than 50? 
Solution: 
 
(i) Frequency distribution table of the marks obtained in Mathematics by students: 
 
 
 
(ii) The highest score is 100 from the given data. 
 
(iii) The lowest score is 37 from the above data. 
 
(iv) We know that 
 
 
 
 
 
  
Range = Highest score – Lowest score 
By substituting the values 
Range = 100 – 37 = 63 
 
(v) If 40 is the pass mark, the number of students who scored less than 40 have failed.  
Students who scored 37 and 39 have failed. 
Hence, 2 students have failed in the exam. 
 
(vi) The number of students who have scored 75 or more are 8 from the data given above. 
So the marks obtained by them are 75, 77, 78, 84, 88, 90, 98 and 100. 
 
(vii) Observations 51, 54 and 57 have not actually appeared in the range 50 – 60. 
 
(viii) From the above data we know that 5 students have scored less than 50 i.e. 37, 39, 44, 48 and 48. 
 
3. The weights of new born babies (in kg) in a hospital on a particular day are as follows: 
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4 
(i) Rearrange the weights in descending order. 
(ii) Determine the highest weight. 
(iii) Determine the lowest weight. 
(iv) Determine the range. 
(v) How many babies were born on that day? 
(vi) How many babies weigh below 2.5 kg? 
(vii) How many babies weight more than 2.8 kg? 
(viii) How many babies weight 2.8 kg? 
Solution: 
 
(i) Rearranging the weights in descending order 
3.1, 3.0, 2.9, 2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.5, 2.4, 2.3, 2.2, 2.1 
 
(ii) The highest weight is 3.1 kg from the given data. 
 
(iii) The lowest weight is 2.1 kg from the given data. 
 
(iv) We know that 
Range = Highest weight – Lowest weight 
By substituting the values 
Range = 3.1 – 2.1 = 1.0 kg 
 
(v) The number of babies born on that day can be found by counting the number of observations. 
Hence, 15 babies were born on that day. 
 
(vi) The babies which weigh below 2.5 kg are 2.1, 2.2, 2.3 and 2.4 kg. 
Hence, 4 babies weigh below 2.5 kg. 
 
(vii) The babies which weigh more than 2.8 kg are 2.9, 2.9, 3.0 and 3.1 kg. 
Hence, 4 babies weigh more than 2.8 kg. 
 
(viii) From the given data we know that 2 babies weigh 2.8 kg. 
 
 
 
 
 
 
  
4. Following data gives the number of children in 40 families: 
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2 
2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2 
Represent it in the form of a frequency distribution. 
Solution: 
 
Frequency distribution table for the given data: 
 
 
 
5. Prepare a frequency table of the following scores obtained by 50 students in a test: 
42 51 21 42 37 37 42 49 38 52 
7 33 17 44 39 7 14 27 39 42 
42 62 37 39 67 51 53 53 59 41 
29 38 27 31 54 19 53 51 22 61 
42 39 59 47 33 34 16 37 57 43 
Solution: 
 
Frequency distribution of the scores obtained by 50 students in a test is given below: 
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1. Define the following terms: 
(i) Observations 
(ii) data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
Solution: 
 
(i) The active acquisition of information which is obtained from a primary source is called observation. 
 
(ii) Data is a collection of facts such as values measurements. 
 
(iii) The number of times an observation occurs in the given data, is called the frequency of the observation. 
 
(iv) Frequency table or frequency distribution is a method to present raw data in the form from which one can 
easily understand the information contained in the raw data. 
 
2. The final marks in mathematics of 30 students are as follows: 
53, 61, 48, 60, 78, 68, 55, 100, 67, 90 
75, 88, 77, 37, 84, 58, 60, 48, 62, 56 
44, 58, 52, 64, 98, 59, 70, 39, 50, 60 
(i) Arrange these marks in the ascending order. 30 to 39 one group, 40 to 49 second group, etc. 
(ii) What is the highest score? 
(iii) What is the lowest score? 
(iv) What is the range? 
(v) If 40 is the pass mark how many have failed? 
(vi) How many have scored 75 or more? 
(vii) Which observations between 50 and 60 have not actually appeared? 
(viii) How many have scored less than 50? 
Solution: 
 
(i) Frequency distribution table of the marks obtained in Mathematics by students: 
 
 
 
(ii) The highest score is 100 from the given data. 
 
(iii) The lowest score is 37 from the above data. 
 
(iv) We know that 
 
 
 
 
 
  
Range = Highest score – Lowest score 
By substituting the values 
Range = 100 – 37 = 63 
 
(v) If 40 is the pass mark, the number of students who scored less than 40 have failed.  
Students who scored 37 and 39 have failed. 
Hence, 2 students have failed in the exam. 
 
(vi) The number of students who have scored 75 or more are 8 from the data given above. 
So the marks obtained by them are 75, 77, 78, 84, 88, 90, 98 and 100. 
 
(vii) Observations 51, 54 and 57 have not actually appeared in the range 50 – 60. 
 
(viii) From the above data we know that 5 students have scored less than 50 i.e. 37, 39, 44, 48 and 48. 
 
3. The weights of new born babies (in kg) in a hospital on a particular day are as follows: 
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4 
(i) Rearrange the weights in descending order. 
(ii) Determine the highest weight. 
(iii) Determine the lowest weight. 
(iv) Determine the range. 
(v) How many babies were born on that day? 
(vi) How many babies weigh below 2.5 kg? 
(vii) How many babies weight more than 2.8 kg? 
(viii) How many babies weight 2.8 kg? 
Solution: 
 
(i) Rearranging the weights in descending order 
3.1, 3.0, 2.9, 2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.5, 2.4, 2.3, 2.2, 2.1 
 
(ii) The highest weight is 3.1 kg from the given data. 
 
(iii) The lowest weight is 2.1 kg from the given data. 
 
(iv) We know that 
Range = Highest weight – Lowest weight 
By substituting the values 
Range = 3.1 – 2.1 = 1.0 kg 
 
(v) The number of babies born on that day can be found by counting the number of observations. 
Hence, 15 babies were born on that day. 
 
(vi) The babies which weigh below 2.5 kg are 2.1, 2.2, 2.3 and 2.4 kg. 
Hence, 4 babies weigh below 2.5 kg. 
 
(vii) The babies which weigh more than 2.8 kg are 2.9, 2.9, 3.0 and 3.1 kg. 
Hence, 4 babies weigh more than 2.8 kg. 
 
(viii) From the given data we know that 2 babies weigh 2.8 kg. 
 
 
 
 
 
 
  
4. Following data gives the number of children in 40 families: 
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2 
2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2 
Represent it in the form of a frequency distribution. 
Solution: 
 
Frequency distribution table for the given data: 
 
 
 
5. Prepare a frequency table of the following scores obtained by 50 students in a test: 
42 51 21 42 37 37 42 49 38 52 
7 33 17 44 39 7 14 27 39 42 
42 62 37 39 67 51 53 53 59 41 
29 38 27 31 54 19 53 51 22 61 
42 39 59 47 33 34 16 37 57 43 
Solution: 
 
Frequency distribution of the scores obtained by 50 students in a test is given below: 
 
 
 
 
 
  
 
 
6. A die was thrown 25 times and following scores were obtained: 
1 5 2 4 3 
6 1 4 2 5 
1 6 2 6 3  
5 4 1 3 2  
3 6 1 5 2 
Prepare a frequency table of the scores. 
Solution: 
 
Frequency table of the given scores: 
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1. Define the following terms: 
(i) Observations 
(ii) data 
(iii) Frequency of an observation 
(iv) Frequency distribution 
Solution: 
 
(i) The active acquisition of information which is obtained from a primary source is called observation. 
 
(ii) Data is a collection of facts such as values measurements. 
 
(iii) The number of times an observation occurs in the given data, is called the frequency of the observation. 
 
(iv) Frequency table or frequency distribution is a method to present raw data in the form from which one can 
easily understand the information contained in the raw data. 
 
2. The final marks in mathematics of 30 students are as follows: 
53, 61, 48, 60, 78, 68, 55, 100, 67, 90 
75, 88, 77, 37, 84, 58, 60, 48, 62, 56 
44, 58, 52, 64, 98, 59, 70, 39, 50, 60 
(i) Arrange these marks in the ascending order. 30 to 39 one group, 40 to 49 second group, etc. 
(ii) What is the highest score? 
(iii) What is the lowest score? 
(iv) What is the range? 
(v) If 40 is the pass mark how many have failed? 
(vi) How many have scored 75 or more? 
(vii) Which observations between 50 and 60 have not actually appeared? 
(viii) How many have scored less than 50? 
Solution: 
 
(i) Frequency distribution table of the marks obtained in Mathematics by students: 
 
 
 
(ii) The highest score is 100 from the given data. 
 
(iii) The lowest score is 37 from the above data. 
 
(iv) We know that 
 
 
 
 
 
  
Range = Highest score – Lowest score 
By substituting the values 
Range = 100 – 37 = 63 
 
(v) If 40 is the pass mark, the number of students who scored less than 40 have failed.  
Students who scored 37 and 39 have failed. 
Hence, 2 students have failed in the exam. 
 
(vi) The number of students who have scored 75 or more are 8 from the data given above. 
So the marks obtained by them are 75, 77, 78, 84, 88, 90, 98 and 100. 
 
(vii) Observations 51, 54 and 57 have not actually appeared in the range 50 – 60. 
 
(viii) From the above data we know that 5 students have scored less than 50 i.e. 37, 39, 44, 48 and 48. 
 
3. The weights of new born babies (in kg) in a hospital on a particular day are as follows: 
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4 
(i) Rearrange the weights in descending order. 
(ii) Determine the highest weight. 
(iii) Determine the lowest weight. 
(iv) Determine the range. 
(v) How many babies were born on that day? 
(vi) How many babies weigh below 2.5 kg? 
(vii) How many babies weight more than 2.8 kg? 
(viii) How many babies weight 2.8 kg? 
Solution: 
 
(i) Rearranging the weights in descending order 
3.1, 3.0, 2.9, 2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.5, 2.4, 2.3, 2.2, 2.1 
 
(ii) The highest weight is 3.1 kg from the given data. 
 
(iii) The lowest weight is 2.1 kg from the given data. 
 
(iv) We know that 
Range = Highest weight – Lowest weight 
By substituting the values 
Range = 3.1 – 2.1 = 1.0 kg 
 
(v) The number of babies born on that day can be found by counting the number of observations. 
Hence, 15 babies were born on that day. 
 
(vi) The babies which weigh below 2.5 kg are 2.1, 2.2, 2.3 and 2.4 kg. 
Hence, 4 babies weigh below 2.5 kg. 
 
(vii) The babies which weigh more than 2.8 kg are 2.9, 2.9, 3.0 and 3.1 kg. 
Hence, 4 babies weigh more than 2.8 kg. 
 
(viii) From the given data we know that 2 babies weigh 2.8 kg. 
 
 
 
 
 
 
  
4. Following data gives the number of children in 40 families: 
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2 
2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2 
Represent it in the form of a frequency distribution. 
Solution: 
 
Frequency distribution table for the given data: 
 
 
 
5. Prepare a frequency table of the following scores obtained by 50 students in a test: 
42 51 21 42 37 37 42 49 38 52 
7 33 17 44 39 7 14 27 39 42 
42 62 37 39 67 51 53 53 59 41 
29 38 27 31 54 19 53 51 22 61 
42 39 59 47 33 34 16 37 57 43 
Solution: 
 
Frequency distribution of the scores obtained by 50 students in a test is given below: 
 
 
 
 
 
  
 
 
6. A die was thrown 25 times and following scores were obtained: 
1 5 2 4 3 
6 1 4 2 5 
1 6 2 6 3  
5 4 1 3 2  
3 6 1 5 2 
Prepare a frequency table of the scores. 
Solution: 
 
Frequency table of the given scores: 
 
 
 
 
 
  
 
 
7. In a study of number of accidents per day, the observations for 30 days were obtained as follows: 
6 3 5 6 4 3 2 5 4 2 
4 2 1 2 2 0 5 4 6 1 
6 0 5 3 6 1 5 5 2 6 
Prepare a frequency distribution table. 
Solution: 
 
Frequency distribution table of the number of accidents per day is given: 
 
 
 
8. Prepare a frequency table of the following ages (in years) of 30 students of class VIII in your school: 
13, 14, 13, 12, 14, 13, 14, 15, 13, 14, 13, 14, 16, 12, 14 
13, 14, 15, 16, 13, 14, 13, 12, 17, 13, 12, 13, 13, 13, 14. 
Solution: 
 
Frequency table of the following ages of 30 students is given below: 
 
 
 
9. Following figures relate the weekly wages (in Rs.) of 15 workers in a factory: 
300, 250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250