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MATHEMATICS, , UNIT 5, , DATA HANDLING, (A) Main Concepts and Results, , ed, , • The data can be arranged in a tabular form using tally marks., • A pictograph represents data through pictures of objects., , ©, o, be NC, re ER, pu T, bl, is, h, , • Interpretation of a pictograph and drawing a pictograph., , • Representation of data using a bar diagram or bar graph., • In a bar graph, bars of uniform width are drawn horizontally or, vertically with equal spacing between them. Length of each bar gives, the required information., • Interpretation of a bar graph and drawing a bar graph., , no, tt, , (B) Solved Examples, , Write the correct answer from the given four options:, Example 1:, , Using tally marks which one of the following represents, the number five?, (A), , (B) ÖÖÖÖÖ, , (C), , (D), , Solution:, , Answer is (D)., , Example 2:, , State whether the following statements are true or false:, (a) A tabular form of data is also a pictorial representation, of the data., (b) A pictograph represents data in the form of pictures, of objects or parts of objects., , Solution:, , (a) False, , (b) True, , 20052014
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UNIT-5, Example 3:, , The blood groups of 25 students are recorded as under:, A, B, O, A, AB, O, A, O, B, A, O, B, A, AB, AB, A, A, B, B,, O, B, AB, O, A, B., Arrange the information in a table using tally marks., Tally marks, , Number of students, , A, , 8, , B, , 7, , O, , 6, , AB, , 4, , In a school, there are five sections of Class VI. The number, of students in each section is given below:, , ed, , Example 4:, , Blood group, , C, , D, , E, , ©, o, be NC, re ER, pu T, bl, is, h, , Solution:, , 42, , 36, , 32, , Section, , A, , Number of, students, , 40, , B, 44, , Represent the above data using a bar graph., First of all, draw a horizantal line and a vertical line., Choose a suitable scale along the vertical line, say 1 unit, length= 4 students. On the horizontal line, write the, sections A, B, C, D and E. Draw vertical bars on the, respective section showing the number of students in, that section., , Number of students, , no, tt, , Solution:, , 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, A B C, Sections, , 70, , D, , E, , EXEMPLAR PROBLEMS, , 20052014
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MATHEMATICS, Example 5:, , The number of vistors in a science exhibition on different, days of a week is shown below:, Look at the above pictograph and answer the following, questions:, Day, , Number of Visitors, , = 100 visitors, , Monday, , ©, o, be NC, re ER, pu T, bl, is, h, , Wednesday, , ed, , Tuesday, , Thursday, , Friday, , Saturday, , no, tt, , (a) What is the total number of visitors from Monday to, Saturday?, (b) On which day was the number of visitors maximum?, What was their total number?, (c) On which day was the number of visitors minimum?, (d) On which day was the number of visitors same as, the number of visitors on two days taken together?, Solution:, , Number of visitors on Monday, Tuesday, Wednesday,, Thursday, Friday and Saturday were 550, 700, 1000,, 900, 900, and 1250 respectively., (a) The total number of visitors from Monday to Saturday, = 550 + 700 + 1000 + 900 + 900 + 1250 = 5300, DATA HANDLING, , 71, , 20052014
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UNIT-5, (b) The number of visitors was maximum on Saturday, and the number was 1250., (c) The number of visitors was minimum on Monday, and the number was 550., (d) The number of visitors on Saturday was 1250 which, was equal to the total number of visitors on Monday, (550) and Tuesday (700)., , (C) Exercise, , ed, , In questions 1 to 5, out of the four options, only one is correct. write, the correct answer., , ©, o, be NC, re ER, pu T, bl, is, h, , 1. Using tally marks, which one of the following represents the number, eight:, (A), , (B), , (C), , (D), , 2. The marks (out of 10) obtained by 28 students in a Mathematics, test are listed as below:, 8, 1, 2, 6, 5, 5, 5, 0, 1, 9, 7, 8, 0, 5, 8, 3, 0, 8, 10, 10, 3, 4, 8, 7, 8, 9,, 2, 0, , no, tt, , The number of students who obtained marks more than or equal to, 5 is, (A) 13, , (B) 15, , (C) 16, , (D) 17, , 3. In question 2 above, the number of students who scored marks less, than 4 is, (A) 15, , (B) 13, , (C) 12, , (D) 10, , 4. The choices of the fruits of 42 students in a class are as follows:, , 72, , A , O , B , M ,, , A ,, , G ,, , B , G , A , G ,, , B , M , A , G ,, , M , A ,, , B , G , M , B ,, , A , O , M , O ,, , G , B ,, , O , M , G , A ,, , A , B , M , O ,, , M , G ,, , B , A , M , O , M , O,, , EXEMPLAR PROBLEMS, , 20052014
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MATHEMATICS, where A, B, G, M and O stand for the fruits Apple, Banana, Grapes,, Mango and Orange respectively., Which two fruits are liked by an equal number of students?, (A) A and M, , (B) M and B, , (C) B and O, , (D) B and G, , 5. According to data of question 4, which fruit is liked by most of the, students?, (A) O, , (B) G, , (C) M, , (D) A, , In questions 6 to 13, state whether the given statements are true (T) or, false (F)., , ed, , 6. In a bar graph, the width of bars may be unequal., , ©, o, be NC, re ER, pu T, bl, is, h, , 7. In a bar graph, bars of uniform width are drawn vertically only., 8. In a bar graph, the gap between two consecutive bars may not be the, same., 9. In a bar graph, each bar (rectangle) represents only one value of the, numerical data., 10. To represent the population of different towns using bar graph, it is, convenient to take one unit length to represent one person., , no, tt, , 11. Pictographs and bar graphs are pictorial representations of the, numerical data., 12. An observation occurring five times in a data is recorded as, | | | | |, using tally marks., 13. In a pictograph, if a symbol, shelf, then the symbol, , represents 50 books in a library, represents 25 books., , In questions 14 to 20, fill in the blanks to make the statements true:, 14. A _______ is a collection of numbers gathered to give some meaningful, information., 15. The data can be arranged in a tabular form using _______ marks., 16. A _______ represents data through pictures of objects., , DATA HANDLING, , 73, , 20052014
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UNIT-5, 17. In a bar graph, ________ can be drawn horizontally or vertically., 18. In a bar graph, bars of ________ width can be drawn horizontally or, vertically with ________ spacing between them., 19. An observation occurring seven times in a data is represented as, ________ using tally marks., 20. In a pictograph, if a symbol, then, , represents 20 flowers in a basket, , stands for ________ flowers., , 21. On the scale of 1 unit length = 10 crore, the bar of length 6 units, will represent ________ crore and of ——— units will represent 75, crore., , ©, o, be NC, re ER, pu T, bl, is, h, , ed, , 22. In an examination, the grades achieved by 30 students of a class are, given below. Arrange these grades in a table using tally marks:, B, C, C, E, A, C, B, B, D, D, D, D, B, C, C, C, A, C, B, E, A, D,, C, B, E, C, B, E, C, D, 23. The number of two wheelers owned individually by each of 50 families, are listed below. Make a table using tally marks., 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 0, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3,, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 1, 4, 1, 3, 1, 1, 2, 1, 1, 1, 1,, 2, 3, 2, 1, 1, , no, tt, , Find the number of families having two or more, two wheelers., 24. The lengths in centimetres (to the nearest centimetre) of 30 carrots, are given as follows:, 15,, 20,, , 22,, 22,, , 21,, 21,, , 20,, , 22,15,, , 20,, 15,, , 21,, 21,, , 18,, 18,, , 21,, 20, , 18,, , 15,, , 20,, , 20,, , 18,, , 20,15,, , 21,, , 18,, , 20,, , 18,, , 22,, , 20,, , Arrange the data given above in a table using tally marks and answer, the following questions., (a), , 74, , What is the number of carrots which have length more than 20 cm?, , EXEMPLAR PROBLEMS, , 20052014
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MATHEMATICS, (b), , Which length of the carrots occur maximum number of times?, Minimum number of times?, , 25. Thirty students were interviewed to find out what they want to be in, future. Their responses are listed as below:, doctor, engineer, doctor, pilot, officer, doctor, engineer, doctor, pilot,, officer, pilot, engineer, officer, pilot, doctor, engineer, pilot, officer,, doctor, officer, doctor, pilot, engineer, doctor, pilot, officer, doctor,, pilot, doctor, engineer, Arrange the data in a table using tally marks., 26. Following are the choices of games of 40 students of Class VI:, , ed, , football, cricket, football, kho-kho, hockey, cricket, hockey, kho-kho,, , ©, o, be NC, re ER, pu T, bl, is, h, , tennis, tennis, cricket, football, football, hockey, kho-kho, football,, cricket, tennis, football, hockey, kho-kho, football, cricket, cricket,, football, hockey, kho-kho, tennis, football, hockey, cricket, football,, hockey, cricket, football, kho-kho, football, cricket, hockey, football., (a), , Arrange the choices of games in a table using tally marks., , (b), , Which game is liked by most of the students?, , (c), , Which game is liked by minimum number of students?, , Shirt size, 30, , no, tt, , 27. Fill in the blanks in the following table which represents shirt size, of 40 students of a school., Tally Marks, , Number of students, 3, , 32, 34, , 8, , 36, 38, , 10, , 40, , 7, , DATA HANDLING, , 75, , 20052014
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UNIT-5, 28. Following pictograph represents some surnames of people listed in, the telephone directory of a city, , Surname, , Number of people, , = 100 people, , Khan, , ed, , Patel, , Roy, , Saikia, , no, tt, , Singh, , ©, o, be NC, re ER, pu T, bl, is, h, , Rao, , Observe the pictograph and answer the following questions:, (a), , How many people have surname ‘Roy’?, , (b), , Which surname appears the maximum number of times in the, telephone directory?, , (c), , Which surname appears the least number of times in the, directory?, , (d), , Which two surnames appear an equal number of times?, , 29. Students of Class VI in a school were given a task to count the, number of articles made of different materials in the school. The, information collected by them is represented as follows:, 76, , EXEMPLAR PROBLEMS, , 20052014
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MATHEMATICS, Material used, , Articles, , = 20 articles, , Wood, Glass, Metal, Rubber, Plastic, Observe the pictograph and answer the following questions:, Which material is used in maximum number of articles?, , (b), , Which material is used in minimum number of articles?, , (c), , Which material is used in exactly half the number of articles as, those made up of metal?, , (d), , What is the total number of articles counted by the students?, , ©, o, be NC, re ER, pu T, bl, is, h, , ed, , (a), , 30. The number of scouts in a school is depicted by the following, pictograph:, , VI, , Number of scouts, , = 10 scouts, , no, tt, , Class, , VII, , VIII, , IX, , X, , DATA HANDLING, , 77, , 20052014
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UNIT-5, Observe the pictograph and answer the following questions:, (a), , Which class has the minimum number of scouts?, , (b), , Which class has the maximum number of scouts?, , (c), , How many scouts are there in Class VI?, , (d), , Which class has exactly four times the scouts as that of Class, X?, , (e), , What is the total number of scouts in the Classes VI to X?, , Hindi, , English, , Number of Students, , ©, o, be NC, re ER, pu T, bl, is, h, , Subject, , ed, , 31. A survey was carried out in a certain school to find out the popular, school subjects among students of Classes VI to VIII. The data in, this regard is displayed as pictograph given below:, , = 50 students, , no, tt, , Mathematics, , Science, , Social Studies, , 78, , (a), , Which subject is most popular among the students?, , (b), , How many students like Mathematics?, , (c), , Find the number of students who like subjects other than, Mathematics and Science., , EXEMPLAR PROBLEMS, , 20052014
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MATHEMATICS, 32. The following pictograph depicts the information about the areas in, sqkm (to nearest hundred) of some districts of Chhattisgarh State:, Area (in km2), , District, , = 1000sqkm, , Raigarh, Rajnandgaon, Koria, Mahasamund, , ed, , Kabirdham, , ©, o, be NC, re ER, pu T, bl, is, h, , Jashpur, (a), , What is the area of Koria district?, , (b), , Which two districts have the same area?, , (c), , How many districts have area more than 5000 square kilometres?, , 33. The number of bottles of cold drinks sold by a shopkeeper on six, consecutive days is as follows:, Day, Number of, bottles, , no, tt, , Sunday Monday Tuesday Wednesday Thursday Friday, 350, , 200, , 300, , 250, , 100, , 150, , Prepare a pictograph of the data using one symbol to represent 50, bottles., 34. The following table gives information about the circulation of, newspapers (dailies) in a town in five languages., Language, Number of, newspapers, , English, , Hindi, , Tamil, , Punjabi, , Gujarati, , 5000, , 8500, , 500, , 2500, , 1000, , Prepare a pictograph of the above data, using a symbol of your choice,, each representing 1000 newspapers., DATA HANDLING, , 79, , 20052014
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UNIT-5, 35. Annual expenditure of a company in the year 2007-2008 is given, below:, Expenditure, (Rs in lakh), , Salaries of employees, , 65, , Advertisement, , 10, , Purchase of machinery, , 85, , Electricity and water, , 15, , Transportation, , 25, , Other expenses, , 30, , ed, , Items, , ©, o, be NC, re ER, pu T, bl, is, h, , Prepare a pictograph of the above data using an appropriate symbol, to represent Rs 10 lakh., 36. The following bar graph shows the number of houses (out of 100) in, a town using different types of fuels for cooking., Read the bar graph and answer the following questions:, , no, tt, , Scale: 1 unit length = 5 houses, , 80, , (a), , Which fuel is used in maximum number of houses?, , (b), , How many houses are using coal as fuel?, , (c), , Suppose that the total number of houses in the town is 1 lakh., From the above graph estimate the number of houses using, electricity., , EXEMPLAR PROBLEMS, , 20052014
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MATHEMATICS, 37. The following bar graph represents the data for different sizes of, shoes worn by the students in a school. Read the graph and answer, the following questions., Scale : 1 unit length = 50 students, , Find the number of, students whose shoe, sizes have been collected., , (b), , What is the number of, students wearing shoe, size 6?, , (c), , What are the different, sizes of the shoes worn by, the students?, , (d), , Which shoe size is worn by the maximum number of students?, , (e), , Which shoe size is worn by minimum number of students?, , (f), , State whether true or false:, , ©, o, be NC, re ER, pu T, bl, is, h, , ed, , (a), , The total number of students wearing shoe sizes 5 and 8 is the same, as the number of students wearing shoe size 6., Scale : 1 unit length = 10 tickets, , no, tt, , 38. The following graph gives the, information about the, number of railway tickets sold, for different cities on a railway, ticket counter between 6.00, am to 10.00 am. Read the bar, graph and answer the, following questions., (a), , How many tickets were, sold in all?, , (b), , For which city were the, maximum number of, tickets sold?, , DATA HANDLING, , 81, , 20052014
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UNIT-5, (c), , For which city were the minimum number of tickets sold?, , (d), , Name the cities for which the number of tickets sold is more, than 20., , (e), , Fill in the blanks:, , Number of tickets sold for Delhi and Jaipur together exceeds the, total number of tickets sold for Patna and Chennai by _______., 39. The bar graph given below represents approximate length, (in kilometres) of some National Highways in India. Study the bar, graph and answer the following questions:, , no, tt, , ©, o, be NC, re ER, pu T, bl, is, h, , ed, , Scale : 1 unit length = 200km, , (a), , Which National Highway (N.H.) is the longest among the above?, , (b), , Which National Highway is the shortest among the above?, , (c), , What is the length of National Highway 9?, , (d), , Length of which National Highway is about three times the, National Highway10?, , 40. The bar graph given below represents the circulation of newspapers, in different languages in a town. Study the bar graph and answer, the following questions:, , 82, , EXEMPLAR PROBLEMS, , 20052014
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MATHEMATICS, Scale : 1 unit length = 200 Newspapers, , What is the, circulation of, English, newspaper?, , (b), , Name the two, languages in, which, circulation of, newspaper is, the same., , (c), , By how much is the circulation of newspaper in Hindi more, than the newspaper in Bengali?, , ©, o, be NC, re ER, pu T, bl, is, h, , ed, , (a), , 41. Read the bar graph given below and answer the following questions:, Scale : 1 unit = 50 students, , What information is given by the bar graph?, , (b), , In which year is the, number of students, maximum?, , (c), , In which year is the, number of students, twice as that of, 2001-02?, , (d), , In which year did the, number of students, decrease as compared, to previous year?, , (e), , In which year is the increase in number of students maximum, as compared to the previous year?, , no, tt, , (a), , DATA HANDLING, , 83, , 20052014
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UNIT-5, 42. The lengths in km (rounded to nearest hundred) of some major, rivers of India is given below:, River, , Length (in km), , Narmada, , 1300, , Mahanadi, , 900, , Brahmputra, , 2900, , Ganga, , 2500, , Kaveri, , 800, , Krishna, , 1300, , ed, , Draw a bar graph to represent the above information., , Bank, , ©, o, be NC, re ER, pu T, bl, is, h, , 43. The number of ATMs of different banks in a city is shown below:, , Syndicate Bank, , Number of ATMs, 5, , Dena Bank, , 15, , Indian Bank, , 20, , State Bank of India, , 25, , Vijaya Bank, , 10, , no, tt, , Draw a bar graph to represent the above information by choosing, the scale of your choice., 44. Number of mobile phone users in various age groups in a city is, listed below:, Age group (in years), , Number of mobile users, , 1—20, , 25000, , 21—40, , 40000, , 41—50, , 35000, , 61—80, , 10000, , Draw a bar graph to represent the above information., , 84, , EXEMPLAR PROBLEMS, , 20052014
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MATHEMATICS, 45. The following table gives the number of vehicles passing through a, toll gate, every hour from 8.00 am. to 1.00 pm:, Time, Interval, , 8.00, to, 9.00, , 9.00, to, 10.00, , 10.00, to, 11.00, , 11.00, to, 12.00, , 12.00, to, 1.00, , Number, of vehicles, , 250, , 450, , 300, , 250, , 150, , Draw a bar graph representing the above data., , ed, , 46. The following table represents income of a Gram Panchayat from, different sources in a particular year:, Income (in Rs.), , ©, o, be NC, re ER, pu T, bl, is, h, , Sources, Income from local taxes, , Funds received from government, Donations, , 75000, , 150000, 25000, , Income from other resources, , 50000, , Draw a bar graph to represent the above information., , Stage, Primary, , no, tt, , 47. The following table gives the data of number of schools (stage-wise), of a country in the year 2002., Number of schools (in thousands), 80, , Upper Primary, , 55, , Secondary, , 30, , Higher Secondary, , 20, , Draw a bar graph to represent the above data:, , DATA HANDLING, , 85, , 20052014
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UNIT-5, 48. Home appliances sold by a shop in one month are given as below:, Home appliance, , Number of home appliances, , Refrigerator, , 75, , Television, , 45, , Washing Machine, , 30, , Cooler, , 60, , DVD Player, , 30, , Draw a bar graph to represent the above information., , ©, o, be NC, re ER, pu T, bl, is, h, , ed, , 49. In a botanical garden, the number of different types of plants are, found as follows:, Type of the plant, Herb, Shrub, , Number of plants, 50, 60, , Creeper, , 20, , Climber, , 45, , Tree, , 95, , no, tt, , Draw a bar graph to represent the above information and answer, the following questions:, (a) Which type of plant is maximum in number in the garden?, (b) Which type of plant is minimum in number in the garden?, 50. Prepare a bar graph of the data given in question 28., 51. Refer to question 39. Prepare a pictograph of the data by taking a, suitable symbol to represent 200 kilometers., 52. Prepare a pictograph of the information given in question 38., 53. Refer to question 23. Prepare a bar graph of the data., , 86, , EXEMPLAR PROBLEMS, , 20052014
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MATHEMATICS, 54. The following table shows the area of the land on which different, crops were grown., Crop, , Area of land (in million hectares), , Rice, , 50, , Wheat, , 30, , Pulses, , 20, , Sugarcane, , 25, , Cotton, , 15, , ed, , Prepare a pictograph by choosing a suitable symbol to represent 10, million hectares., , no, tt, , ©, o, be NC, re ER, pu T, bl, is, h, , 55. Refer to question 54. Prepare a bar graph of the data., , DATA HANDLING, , 87, , 20052014
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UNIT-5, , no, tt, , ©, o, be NC, re ER, pu T, bl, is, h, , ed, , Rough Work, , 88, , EXEMPLAR PROBLEMS, , 20052014
