Page 1 DATA HANDLING 69 5.1 Looking for Information In your day-to-day life, you might have come across information, such as: (a) Runs made by a batsman in the last 10 test matches. (b) Number of wickets taken by a bowler in the last 10 ODIs. (c) Marks scored by the students of your class in the Mathematics unit test. (d) Number of story books read by each of your friends etc. The information collected in all such cases is called data. Data is usually collected in the context of a situation that we want to study . For example, a teacher may like to know the average height of students in her class. T o find this, she will write the heights of all the students in her class, organise the data in a systematic manner and then interpret it accordingly. Sometimes, data is represented graphically to give a clear idea of what it represents. Do you remember the different types of graphs which we have learnt in earlier classes? 1. A Pictograph: Pictorial representation of data using symbols. Data Handling CHAPTER 5 = 100 cars ? One symbol stands for 100 cars July = 250 denotes 1 2 of 100 August = 300 September = ? (i) How many cars were produced in the month of July? (ii) In which month were maximum number of cars produced? Page 2 DATA HANDLING 69 5.1 Looking for Information In your day-to-day life, you might have come across information, such as: (a) Runs made by a batsman in the last 10 test matches. (b) Number of wickets taken by a bowler in the last 10 ODIs. (c) Marks scored by the students of your class in the Mathematics unit test. (d) Number of story books read by each of your friends etc. The information collected in all such cases is called data. Data is usually collected in the context of a situation that we want to study . For example, a teacher may like to know the average height of students in her class. T o find this, she will write the heights of all the students in her class, organise the data in a systematic manner and then interpret it accordingly. Sometimes, data is represented graphically to give a clear idea of what it represents. Do you remember the different types of graphs which we have learnt in earlier classes? 1. A Pictograph: Pictorial representation of data using symbols. Data Handling CHAPTER 5 = 100 cars ? One symbol stands for 100 cars July = 250 denotes 1 2 of 100 August = 300 September = ? (i) How many cars were produced in the month of July? (ii) In which month were maximum number of cars produced? 70 MATHEMATICS 2. A bar graph: A display of information using bars of uniform width, their heights being proportional to the respective values. Bar heights give the quantity for each category. Bars are of equal width with equal gaps in between. (i) What is the information given by the bar graph? (ii) In which year is the increase in the number of students maximum? (iii) In which year is the number of students maximum? (iv) State whether true or false: â€˜The number of students during 2005-06 is twice that of 2003-04.â€™ 3. Double Bar Graph: A bar graph showing two sets of data simultaneously. It is useful for the comparison of the data. (i) What is the information given by the double bar graph? (ii) In which subject has the performance improved the most? (iii) In which subject has the performance deteriorated? (iv) In which subject is the performance at par? Page 3 DATA HANDLING 69 5.1 Looking for Information In your day-to-day life, you might have come across information, such as: (a) Runs made by a batsman in the last 10 test matches. (b) Number of wickets taken by a bowler in the last 10 ODIs. (c) Marks scored by the students of your class in the Mathematics unit test. (d) Number of story books read by each of your friends etc. The information collected in all such cases is called data. Data is usually collected in the context of a situation that we want to study . For example, a teacher may like to know the average height of students in her class. T o find this, she will write the heights of all the students in her class, organise the data in a systematic manner and then interpret it accordingly. Sometimes, data is represented graphically to give a clear idea of what it represents. Do you remember the different types of graphs which we have learnt in earlier classes? 1. A Pictograph: Pictorial representation of data using symbols. Data Handling CHAPTER 5 = 100 cars ? One symbol stands for 100 cars July = 250 denotes 1 2 of 100 August = 300 September = ? (i) How many cars were produced in the month of July? (ii) In which month were maximum number of cars produced? 70 MATHEMATICS 2. A bar graph: A display of information using bars of uniform width, their heights being proportional to the respective values. Bar heights give the quantity for each category. Bars are of equal width with equal gaps in between. (i) What is the information given by the bar graph? (ii) In which year is the increase in the number of students maximum? (iii) In which year is the number of students maximum? (iv) State whether true or false: â€˜The number of students during 2005-06 is twice that of 2003-04.â€™ 3. Double Bar Graph: A bar graph showing two sets of data simultaneously. It is useful for the comparison of the data. (i) What is the information given by the double bar graph? (ii) In which subject has the performance improved the most? (iii) In which subject has the performance deteriorated? (iv) In which subject is the performance at par? DATA HANDLING 71 THINK, DISCUSS AND WRITE If we change the position of any of the bars of a bar graph, would it change the information being conveyed? Why? 1. Month July August September October November December Number of 1000 1500 1500 2000 2500 1500 watches sold 2. Children who prefer School A School B School C W alking 40 55 15 Cycling 45 25 35 3. Percentage wins in ODI by 8 top cricket teams. Teams From Champions Last 10 Trophy to World Cup-06 ODI in 07 SouthAfrica 75% 78% Australia 61% 40% Sri Lanka 54% 38% New Zealand 47% 50% England 46% 50% Pakistan 45% 44% W est Indies 44% 30% India 43% 56% TRY THESE Draw an appropriate graph to represent the given information. 5.2 Organising Data Usually , data available to us is in an unorganised form called raw data. T o draw meaningful inferences, we need to organise the data systematically . For example, a group of students was asked for their favourite subject. The results were as listed below: Art, Mathematics, Science, English, Mathematics, Art, English, Mathematics, English, Art, Science, Art, Science, Science, Mathematics, Art, English, Art, Science, Mathematics, Science,Art. Which is the most liked subject and the one least liked? Page 4 DATA HANDLING 69 5.1 Looking for Information In your day-to-day life, you might have come across information, such as: (a) Runs made by a batsman in the last 10 test matches. (b) Number of wickets taken by a bowler in the last 10 ODIs. (c) Marks scored by the students of your class in the Mathematics unit test. (d) Number of story books read by each of your friends etc. The information collected in all such cases is called data. Data is usually collected in the context of a situation that we want to study . For example, a teacher may like to know the average height of students in her class. T o find this, she will write the heights of all the students in her class, organise the data in a systematic manner and then interpret it accordingly. Sometimes, data is represented graphically to give a clear idea of what it represents. Do you remember the different types of graphs which we have learnt in earlier classes? 1. A Pictograph: Pictorial representation of data using symbols. Data Handling CHAPTER 5 = 100 cars ? One symbol stands for 100 cars July = 250 denotes 1 2 of 100 August = 300 September = ? (i) How many cars were produced in the month of July? (ii) In which month were maximum number of cars produced? 70 MATHEMATICS 2. A bar graph: A display of information using bars of uniform width, their heights being proportional to the respective values. Bar heights give the quantity for each category. Bars are of equal width with equal gaps in between. (i) What is the information given by the bar graph? (ii) In which year is the increase in the number of students maximum? (iii) In which year is the number of students maximum? (iv) State whether true or false: â€˜The number of students during 2005-06 is twice that of 2003-04.â€™ 3. Double Bar Graph: A bar graph showing two sets of data simultaneously. It is useful for the comparison of the data. (i) What is the information given by the double bar graph? (ii) In which subject has the performance improved the most? (iii) In which subject has the performance deteriorated? (iv) In which subject is the performance at par? DATA HANDLING 71 THINK, DISCUSS AND WRITE If we change the position of any of the bars of a bar graph, would it change the information being conveyed? Why? 1. Month July August September October November December Number of 1000 1500 1500 2000 2500 1500 watches sold 2. Children who prefer School A School B School C W alking 40 55 15 Cycling 45 25 35 3. Percentage wins in ODI by 8 top cricket teams. Teams From Champions Last 10 Trophy to World Cup-06 ODI in 07 SouthAfrica 75% 78% Australia 61% 40% Sri Lanka 54% 38% New Zealand 47% 50% England 46% 50% Pakistan 45% 44% W est Indies 44% 30% India 43% 56% TRY THESE Draw an appropriate graph to represent the given information. 5.2 Organising Data Usually , data available to us is in an unorganised form called raw data. T o draw meaningful inferences, we need to organise the data systematically . For example, a group of students was asked for their favourite subject. The results were as listed below: Art, Mathematics, Science, English, Mathematics, Art, English, Mathematics, English, Art, Science, Art, Science, Science, Mathematics, Art, English, Art, Science, Mathematics, Science,Art. Which is the most liked subject and the one least liked? 72 MATHEMATICS TRY THESE It is not easy to answer the question looking at the choices written haphazardly . W e arrange the data in T able 5.1 using tally marks. Table 5.1 Subject Tally Marks Number of Students Art | | | | | | 7 Mathematics | | | | 5 Science | | | | | 6 English | | | | 4 The number of tallies before each subject gives the number of students who like that particular subject. This is known as the frequency of that subject. Frequency gives the number of times that a particular entry occurs. From Table 5.1, Frequency of students who like English is 4 Frequency of students who like Mathematics is 5 The table made is known as frequency distribution table as it gives the number of times an entry occurs. 1. A group of students were asked to say which animal they would like most to have as a pet. The results are given below: dog, cat, cat, fish, cat, rabbit, dog, cat, rabbit, dog, cat, dog, dog, dog, cat, cow, fish, rabbit, dog, cat, dog, cat, cat, dog, rabbit, cat, fish, dog. Make a frequency distribution table for the same. 5.3 Grouping Data The data regarding choice of subjects showed the occurrence of each of the entries several times. For example, Art is liked by 7 students, Mathematics is liked by 5 students and so on (Table 5.1). This information can be displayed graphically using a pictograph or a bargraph. Sometimes, however, we have to deal with a large data. For example, consider the following marks (out of 50) obtained in Mathematics by 60 students of Class VIII: 21, 10, 30, 22, 33, 5, 37, 12, 25, 42, 15, 39, 26, 32, 18, 27, 28, 19, 29, 35, 31, 24, 36, 18, 20, 38, 22, 44, 16, 24, 10, 27, 39, 28, 49, 29, 32, 23, 31, 21, 34, 22, 23, 36, 24, 36, 33, 47, 48, 50, 39, 20, 7, 16, 36, 45, 47, 30, 22, 17. If we make a frequency distribution table for each observation, then the table would be too long, so, for convenience, we make groups of observations say, 0-10, 10-20 and so on, and obtain a frequency distribution of the number of observations falling in each Page 5 DATA HANDLING 69 5.1 Looking for Information In your day-to-day life, you might have come across information, such as: (a) Runs made by a batsman in the last 10 test matches. (b) Number of wickets taken by a bowler in the last 10 ODIs. (c) Marks scored by the students of your class in the Mathematics unit test. (d) Number of story books read by each of your friends etc. The information collected in all such cases is called data. Data is usually collected in the context of a situation that we want to study . For example, a teacher may like to know the average height of students in her class. T o find this, she will write the heights of all the students in her class, organise the data in a systematic manner and then interpret it accordingly. Sometimes, data is represented graphically to give a clear idea of what it represents. Do you remember the different types of graphs which we have learnt in earlier classes? 1. A Pictograph: Pictorial representation of data using symbols. Data Handling CHAPTER 5 = 100 cars ? One symbol stands for 100 cars July = 250 denotes 1 2 of 100 August = 300 September = ? (i) How many cars were produced in the month of July? (ii) In which month were maximum number of cars produced? 70 MATHEMATICS 2. A bar graph: A display of information using bars of uniform width, their heights being proportional to the respective values. Bar heights give the quantity for each category. Bars are of equal width with equal gaps in between. (i) What is the information given by the bar graph? (ii) In which year is the increase in the number of students maximum? (iii) In which year is the number of students maximum? (iv) State whether true or false: â€˜The number of students during 2005-06 is twice that of 2003-04.â€™ 3. Double Bar Graph: A bar graph showing two sets of data simultaneously. It is useful for the comparison of the data. (i) What is the information given by the double bar graph? (ii) In which subject has the performance improved the most? (iii) In which subject has the performance deteriorated? (iv) In which subject is the performance at par? DATA HANDLING 71 THINK, DISCUSS AND WRITE If we change the position of any of the bars of a bar graph, would it change the information being conveyed? Why? 1. Month July August September October November December Number of 1000 1500 1500 2000 2500 1500 watches sold 2. Children who prefer School A School B School C W alking 40 55 15 Cycling 45 25 35 3. Percentage wins in ODI by 8 top cricket teams. Teams From Champions Last 10 Trophy to World Cup-06 ODI in 07 SouthAfrica 75% 78% Australia 61% 40% Sri Lanka 54% 38% New Zealand 47% 50% England 46% 50% Pakistan 45% 44% W est Indies 44% 30% India 43% 56% TRY THESE Draw an appropriate graph to represent the given information. 5.2 Organising Data Usually , data available to us is in an unorganised form called raw data. T o draw meaningful inferences, we need to organise the data systematically . For example, a group of students was asked for their favourite subject. The results were as listed below: Art, Mathematics, Science, English, Mathematics, Art, English, Mathematics, English, Art, Science, Art, Science, Science, Mathematics, Art, English, Art, Science, Mathematics, Science,Art. Which is the most liked subject and the one least liked? 72 MATHEMATICS TRY THESE It is not easy to answer the question looking at the choices written haphazardly . W e arrange the data in T able 5.1 using tally marks. Table 5.1 Subject Tally Marks Number of Students Art | | | | | | 7 Mathematics | | | | 5 Science | | | | | 6 English | | | | 4 The number of tallies before each subject gives the number of students who like that particular subject. This is known as the frequency of that subject. Frequency gives the number of times that a particular entry occurs. From Table 5.1, Frequency of students who like English is 4 Frequency of students who like Mathematics is 5 The table made is known as frequency distribution table as it gives the number of times an entry occurs. 1. A group of students were asked to say which animal they would like most to have as a pet. The results are given below: dog, cat, cat, fish, cat, rabbit, dog, cat, rabbit, dog, cat, dog, dog, dog, cat, cow, fish, rabbit, dog, cat, dog, cat, cat, dog, rabbit, cat, fish, dog. Make a frequency distribution table for the same. 5.3 Grouping Data The data regarding choice of subjects showed the occurrence of each of the entries several times. For example, Art is liked by 7 students, Mathematics is liked by 5 students and so on (Table 5.1). This information can be displayed graphically using a pictograph or a bargraph. Sometimes, however, we have to deal with a large data. For example, consider the following marks (out of 50) obtained in Mathematics by 60 students of Class VIII: 21, 10, 30, 22, 33, 5, 37, 12, 25, 42, 15, 39, 26, 32, 18, 27, 28, 19, 29, 35, 31, 24, 36, 18, 20, 38, 22, 44, 16, 24, 10, 27, 39, 28, 49, 29, 32, 23, 31, 21, 34, 22, 23, 36, 24, 36, 33, 47, 48, 50, 39, 20, 7, 16, 36, 45, 47, 30, 22, 17. If we make a frequency distribution table for each observation, then the table would be too long, so, for convenience, we make groups of observations say, 0-10, 10-20 and so on, and obtain a frequency distribution of the number of observations falling in each DATA HANDLING 73 group. Thus, the frequency distribution table for the above data can be. Table 5.2 Groups Tally Marks Frequency 0-10 | | 2 10-20 | | | | | | | | 10 20-30 | | | | | | | | | | | | | | | | | 21 30-40 | | | | | | | | | | | | | | | | 19 40-50 | | | | | | 7 50-60 | 1 Total 60 Data presented in this manner is said to be grouped and the distribution obtained is called grouped frequency distribution. It helps us to draw meaningful inferences like â€“ (1) Most of the students have scored between 20 and 40. (2) Eight students have scored more than 40 marks out of 50 and so on. Each of the groups 0-10, 10-20, 20-30, etc., is called a Class Interval (or briefly a class). Observe that 10 occurs in both the classes, i.e., 0-10 as well as 10-20. Similarly, 20 occurs in classes 10-20 and 20-30. But it is not possible that an observation (say 10 or 20) can belong simultaneously to two classes. T o avoid this, we adopt the convention that the common observation will belong to the higher class, i.e., 10 belongs to the class interval 10-20 (and not to 0-10). Similarly, 20 belongs to 20-30 (and not to 10-20). In the class interval, 10-20, 10 is called the lower class limit and 20 is called the upper class limit. Similarly , in the class interval 20-30, 20 is the lower class limit and 30 is the upper class limit. Observe that the difference between the upper class limit and lower class limit for each of the class intervals 0-10, 10-20, 20-30 etc., is equal, (10 in this case). This difference between the upper class limit and lower class limit is called the width or size of the class interval. TRY THESE 1. Study the following frequency distribution table and answer the questions given below. Frequency Distribution of Daily Income of 550 workers of a factory Table 5.3 Class Interval Frequency (Daily Income in Rupees) (Number of workers) 100-125 45 125-150 25Read More