Page 1 IX Mathematics C.B.S.E. Practice Papers Page 94 14. Statistics Q 1 Define array or arrayed data. Mark (1) Q 2 Define frequency. Mark (1) Q 3 Write the relation between class mark, lower limit and upper limit of a class interval. Mark (1) Q 4 Define primary data. Marks (2) Q 5 Define secondary data. How it is differ from the primary data? Marks (2) Q 6 Find the mode of the following data : Marks Number of students 48 4 49 10 50 12 51 10 52 10 How many students are there whose marks are less than the modal value? Marks (2) Q 7 Following data represents the favourite fruit liked by 20 children. P G A M M P A M G M A M M M M M A A P G. Make a frequency table to find how many more children chose apple as their favourite fruit than pomegranate. Marks (2) Q 8 Make a bar graph of the given data. Marks (2) Q 9 Following frequency table represents the number of students in each section of class 9th of ABC school. Find the mean number of students per sections. Number of Student Per Section Section A 20 Section B 18 Section C 25 Section D 22 Section E 20 Marks (2) Instrument Frequency clarinet 11 flute 18 trumpet 7 violin 5 Page 2 IX Mathematics C.B.S.E. Practice Papers Page 94 14. Statistics Q 1 Define array or arrayed data. Mark (1) Q 2 Define frequency. Mark (1) Q 3 Write the relation between class mark, lower limit and upper limit of a class interval. Mark (1) Q 4 Define primary data. Marks (2) Q 5 Define secondary data. How it is differ from the primary data? Marks (2) Q 6 Find the mode of the following data : Marks Number of students 48 4 49 10 50 12 51 10 52 10 How many students are there whose marks are less than the modal value? Marks (2) Q 7 Following data represents the favourite fruit liked by 20 children. P G A M M P A M G M A M M M M M A A P G. Make a frequency table to find how many more children chose apple as their favourite fruit than pomegranate. Marks (2) Q 8 Make a bar graph of the given data. Marks (2) Q 9 Following frequency table represents the number of students in each section of class 9th of ABC school. Find the mean number of students per sections. Number of Student Per Section Section A 20 Section B 18 Section C 25 Section D 22 Section E 20 Marks (2) Instrument Frequency clarinet 11 flute 18 trumpet 7 violin 5 IX Mathematics C.B.S.E. Practice Papers Page 95 Q 10 The table below shows the age of seven students participating in a music recital. Find the median and mode of the data. Marks (2) Q 11 Find the median and mode of the speeds displayed in the graph. Marks (2) Q 12 Make the frequency polygon of the given data. Class-Intervals Frequency 0 â€“ 10 9 10 â€“ 20 14 20 â€“ 30 8 30 â€“ 40 10 40 â€“ 50 9 Marks (2) Q 13 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 1. Determine the range. 2. How many babies have weight below 2.5 kg. 3. How many babies have weight more than 2.8 kg. Marks (3) Q 14 The class- marks of a distribution are 26,31,36,41,46,51,56,61,66,71.Find the true class limits. Marks (3) Q 15 The bar graph shown in figure represents the circulation of newspaper in 5 languages. Study the bar graph and answer the following questions: (i) What is the total number of newspapers published in Hindi, English,Urdu, Punjabi and Bengali? Age (years) 12 10 9 10 11 8 13 Page 3 IX Mathematics C.B.S.E. Practice Papers Page 94 14. Statistics Q 1 Define array or arrayed data. Mark (1) Q 2 Define frequency. Mark (1) Q 3 Write the relation between class mark, lower limit and upper limit of a class interval. Mark (1) Q 4 Define primary data. Marks (2) Q 5 Define secondary data. How it is differ from the primary data? Marks (2) Q 6 Find the mode of the following data : Marks Number of students 48 4 49 10 50 12 51 10 52 10 How many students are there whose marks are less than the modal value? Marks (2) Q 7 Following data represents the favourite fruit liked by 20 children. P G A M M P A M G M A M M M M M A A P G. Make a frequency table to find how many more children chose apple as their favourite fruit than pomegranate. Marks (2) Q 8 Make a bar graph of the given data. Marks (2) Q 9 Following frequency table represents the number of students in each section of class 9th of ABC school. Find the mean number of students per sections. Number of Student Per Section Section A 20 Section B 18 Section C 25 Section D 22 Section E 20 Marks (2) Instrument Frequency clarinet 11 flute 18 trumpet 7 violin 5 IX Mathematics C.B.S.E. Practice Papers Page 95 Q 10 The table below shows the age of seven students participating in a music recital. Find the median and mode of the data. Marks (2) Q 11 Find the median and mode of the speeds displayed in the graph. Marks (2) Q 12 Make the frequency polygon of the given data. Class-Intervals Frequency 0 â€“ 10 9 10 â€“ 20 14 20 â€“ 30 8 30 â€“ 40 10 40 â€“ 50 9 Marks (2) Q 13 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 1. Determine the range. 2. How many babies have weight below 2.5 kg. 3. How many babies have weight more than 2.8 kg. Marks (3) Q 14 The class- marks of a distribution are 26,31,36,41,46,51,56,61,66,71.Find the true class limits. Marks (3) Q 15 The bar graph shown in figure represents the circulation of newspaper in 5 languages. Study the bar graph and answer the following questions: (i) What is the total number of newspapers published in Hindi, English,Urdu, Punjabi and Bengali? Age (years) 12 10 9 10 11 8 13 IX Mathematics C.B.S.E. Practice Papers Page 96 (ii) State the language in which the largest number of news papers is published. (iii) State the language in which the number of newspapers published is minimum. Marks (3) Q 16 Prepare a frequency distribution from the following data by taking the class intervals. Mid points Frequency 5 3 15 9 25 15 35 10 45 6 55 4 Total = 47 Marks (3) Q 17 Mean of 18 numbers is 57. If 9 is added to each number, find the new mean. Marks (3) Q 18 Prove that the sum of the deviations of individual observations from their mean is zero. Marks (3) Q 19 The median of the following observation arranged in ascending order is 22. Find x. 8, 11, 13, 15, x+1, x+3, 30,35,40,43 Marks (3) Q 20 1. If the mean of the following data is 20.2, find the value of p: X 10 15 20 25 30 f 6 8 p 10 6 Marks (4) Q 21 The water bills of 32 houses in a colony for a period is given below : 56, 43, 32, 38, 56, 22 ,68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 59 . Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals. Marks (4) Q 22 Construct a frequency polygon for the following data: Age ( in years) Frequency 0-2 4 2-4 2 4-6 12 6-8 18 8-10 25 Marks (4) Q 23 The population of a state in different census years is as given below: Census year 1981 1982 1983 1984 1985 Population in Lakhs 30 50 70 110 150 Represent the above information with the help of bar graph. Marks (4) Page 4 IX Mathematics C.B.S.E. Practice Papers Page 94 14. Statistics Q 1 Define array or arrayed data. Mark (1) Q 2 Define frequency. Mark (1) Q 3 Write the relation between class mark, lower limit and upper limit of a class interval. Mark (1) Q 4 Define primary data. Marks (2) Q 5 Define secondary data. How it is differ from the primary data? Marks (2) Q 6 Find the mode of the following data : Marks Number of students 48 4 49 10 50 12 51 10 52 10 How many students are there whose marks are less than the modal value? Marks (2) Q 7 Following data represents the favourite fruit liked by 20 children. P G A M M P A M G M A M M M M M A A P G. Make a frequency table to find how many more children chose apple as their favourite fruit than pomegranate. Marks (2) Q 8 Make a bar graph of the given data. Marks (2) Q 9 Following frequency table represents the number of students in each section of class 9th of ABC school. Find the mean number of students per sections. Number of Student Per Section Section A 20 Section B 18 Section C 25 Section D 22 Section E 20 Marks (2) Instrument Frequency clarinet 11 flute 18 trumpet 7 violin 5 IX Mathematics C.B.S.E. Practice Papers Page 95 Q 10 The table below shows the age of seven students participating in a music recital. Find the median and mode of the data. Marks (2) Q 11 Find the median and mode of the speeds displayed in the graph. Marks (2) Q 12 Make the frequency polygon of the given data. Class-Intervals Frequency 0 â€“ 10 9 10 â€“ 20 14 20 â€“ 30 8 30 â€“ 40 10 40 â€“ 50 9 Marks (2) Q 13 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 1. Determine the range. 2. How many babies have weight below 2.5 kg. 3. How many babies have weight more than 2.8 kg. Marks (3) Q 14 The class- marks of a distribution are 26,31,36,41,46,51,56,61,66,71.Find the true class limits. Marks (3) Q 15 The bar graph shown in figure represents the circulation of newspaper in 5 languages. Study the bar graph and answer the following questions: (i) What is the total number of newspapers published in Hindi, English,Urdu, Punjabi and Bengali? Age (years) 12 10 9 10 11 8 13 IX Mathematics C.B.S.E. Practice Papers Page 96 (ii) State the language in which the largest number of news papers is published. (iii) State the language in which the number of newspapers published is minimum. Marks (3) Q 16 Prepare a frequency distribution from the following data by taking the class intervals. Mid points Frequency 5 3 15 9 25 15 35 10 45 6 55 4 Total = 47 Marks (3) Q 17 Mean of 18 numbers is 57. If 9 is added to each number, find the new mean. Marks (3) Q 18 Prove that the sum of the deviations of individual observations from their mean is zero. Marks (3) Q 19 The median of the following observation arranged in ascending order is 22. Find x. 8, 11, 13, 15, x+1, x+3, 30,35,40,43 Marks (3) Q 20 1. If the mean of the following data is 20.2, find the value of p: X 10 15 20 25 30 f 6 8 p 10 6 Marks (4) Q 21 The water bills of 32 houses in a colony for a period is given below : 56, 43, 32, 38, 56, 22 ,68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 59 . Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals. Marks (4) Q 22 Construct a frequency polygon for the following data: Age ( in years) Frequency 0-2 4 2-4 2 4-6 12 6-8 18 8-10 25 Marks (4) Q 23 The population of a state in different census years is as given below: Census year 1981 1982 1983 1984 1985 Population in Lakhs 30 50 70 110 150 Represent the above information with the help of bar graph. Marks (4) IX Mathematics C.B.S.E. Practice Papers Page 97 Q 24 The average marks of boys in an examination are 65 and that of girls is 74. If the average of marks of all candidates in that examination is 70, find the ratio of the number of boys to the number of girls that appeared in the examination. Marks (4) Q 25 1. The marks obtained (out of 100) by a class of 80 students are given below: Marks Number of students 10-20 6 20-30 17 30-50 15 50-70 16 70-100 26 Construct a histogram to represent the data above. Marks (4) Q 26 1. Draw a histogram for the following distribution: Marks obtained 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 No. of Students 7 10 6 8 12 3 2 2 Marks (4) Most Important Questions Q 1 List the different types of statistical data. Q 2 List the different types of frequency distribution. Q 3 List the different ways for the presentation of raw data. Q 4 Given below are the ages of 25 students of class IX in a school. Prepare a discrete frequency distribution. 15, 16, 16, 14, 17, 17, 16, 15, 15, 16, 16, 17, 15, 16, 16, 14, 16, 15, 14, 15, 16, 16, 15, 14, 15. Q 5 What is data? Explain the types of statistical data? Q 6 The class marks of a distribution are 26, 31, 36, 41, 46, 51, 56, 61, 66, 71. Determine the true class limits. Q 7 Form a grouped frequency distribution from the following data by inclusive method taking 4 as the magnitude of class intervals. 31, 23, 19, 29, 22, 20, 16, 10, 13, 34, 38, 33, 28, 21, 15, 18, 36, 24, 18, 15, 12, 30, 27, 23, 20, 17, 14, 32, 26, 25, 18, 29, 24, 19, 16, 11, 22, 15, 17, 10. Q 8 The marks obtained by 40 students of Class IX in an examination are given below : 18, 8, 12, 6, 8, 16, 12, 5, 23, 2, 16, 23, 2, 10, 20, 12, 9, 7, 6, 5, 3, 5, 13, 21, 13, 15, 20, 24, 1, 7, 21, 16, 13, 18, 23, 7, 3, 18, 17, 16. Present the data in the form of a frequency distribution using the same class size, one such class being 20-25 (where 25 is not included). Q 9 The class marks of a distribution are : 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102. Determine the class size, the class limits and the true class limits. Page 5 IX Mathematics C.B.S.E. Practice Papers Page 94 14. Statistics Q 1 Define array or arrayed data. Mark (1) Q 2 Define frequency. Mark (1) Q 3 Write the relation between class mark, lower limit and upper limit of a class interval. Mark (1) Q 4 Define primary data. Marks (2) Q 5 Define secondary data. How it is differ from the primary data? Marks (2) Q 6 Find the mode of the following data : Marks Number of students 48 4 49 10 50 12 51 10 52 10 How many students are there whose marks are less than the modal value? Marks (2) Q 7 Following data represents the favourite fruit liked by 20 children. P G A M M P A M G M A M M M M M A A P G. Make a frequency table to find how many more children chose apple as their favourite fruit than pomegranate. Marks (2) Q 8 Make a bar graph of the given data. Marks (2) Q 9 Following frequency table represents the number of students in each section of class 9th of ABC school. Find the mean number of students per sections. Number of Student Per Section Section A 20 Section B 18 Section C 25 Section D 22 Section E 20 Marks (2) Instrument Frequency clarinet 11 flute 18 trumpet 7 violin 5 IX Mathematics C.B.S.E. Practice Papers Page 95 Q 10 The table below shows the age of seven students participating in a music recital. Find the median and mode of the data. Marks (2) Q 11 Find the median and mode of the speeds displayed in the graph. Marks (2) Q 12 Make the frequency polygon of the given data. Class-Intervals Frequency 0 â€“ 10 9 10 â€“ 20 14 20 â€“ 30 8 30 â€“ 40 10 40 â€“ 50 9 Marks (2) Q 13 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 1. Determine the range. 2. How many babies have weight below 2.5 kg. 3. How many babies have weight more than 2.8 kg. Marks (3) Q 14 The class- marks of a distribution are 26,31,36,41,46,51,56,61,66,71.Find the true class limits. Marks (3) Q 15 The bar graph shown in figure represents the circulation of newspaper in 5 languages. Study the bar graph and answer the following questions: (i) What is the total number of newspapers published in Hindi, English,Urdu, Punjabi and Bengali? Age (years) 12 10 9 10 11 8 13 IX Mathematics C.B.S.E. Practice Papers Page 96 (ii) State the language in which the largest number of news papers is published. (iii) State the language in which the number of newspapers published is minimum. Marks (3) Q 16 Prepare a frequency distribution from the following data by taking the class intervals. Mid points Frequency 5 3 15 9 25 15 35 10 45 6 55 4 Total = 47 Marks (3) Q 17 Mean of 18 numbers is 57. If 9 is added to each number, find the new mean. Marks (3) Q 18 Prove that the sum of the deviations of individual observations from their mean is zero. Marks (3) Q 19 The median of the following observation arranged in ascending order is 22. Find x. 8, 11, 13, 15, x+1, x+3, 30,35,40,43 Marks (3) Q 20 1. If the mean of the following data is 20.2, find the value of p: X 10 15 20 25 30 f 6 8 p 10 6 Marks (4) Q 21 The water bills of 32 houses in a colony for a period is given below : 56, 43, 32, 38, 56, 22 ,68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 59 . Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals. Marks (4) Q 22 Construct a frequency polygon for the following data: Age ( in years) Frequency 0-2 4 2-4 2 4-6 12 6-8 18 8-10 25 Marks (4) Q 23 The population of a state in different census years is as given below: Census year 1981 1982 1983 1984 1985 Population in Lakhs 30 50 70 110 150 Represent the above information with the help of bar graph. Marks (4) IX Mathematics C.B.S.E. Practice Papers Page 97 Q 24 The average marks of boys in an examination are 65 and that of girls is 74. If the average of marks of all candidates in that examination is 70, find the ratio of the number of boys to the number of girls that appeared in the examination. Marks (4) Q 25 1. The marks obtained (out of 100) by a class of 80 students are given below: Marks Number of students 10-20 6 20-30 17 30-50 15 50-70 16 70-100 26 Construct a histogram to represent the data above. Marks (4) Q 26 1. Draw a histogram for the following distribution: Marks obtained 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 No. of Students 7 10 6 8 12 3 2 2 Marks (4) Most Important Questions Q 1 List the different types of statistical data. Q 2 List the different types of frequency distribution. Q 3 List the different ways for the presentation of raw data. Q 4 Given below are the ages of 25 students of class IX in a school. Prepare a discrete frequency distribution. 15, 16, 16, 14, 17, 17, 16, 15, 15, 16, 16, 17, 15, 16, 16, 14, 16, 15, 14, 15, 16, 16, 15, 14, 15. Q 5 What is data? Explain the types of statistical data? Q 6 The class marks of a distribution are 26, 31, 36, 41, 46, 51, 56, 61, 66, 71. Determine the true class limits. Q 7 Form a grouped frequency distribution from the following data by inclusive method taking 4 as the magnitude of class intervals. 31, 23, 19, 29, 22, 20, 16, 10, 13, 34, 38, 33, 28, 21, 15, 18, 36, 24, 18, 15, 12, 30, 27, 23, 20, 17, 14, 32, 26, 25, 18, 29, 24, 19, 16, 11, 22, 15, 17, 10. Q 8 The marks obtained by 40 students of Class IX in an examination are given below : 18, 8, 12, 6, 8, 16, 12, 5, 23, 2, 16, 23, 2, 10, 20, 12, 9, 7, 6, 5, 3, 5, 13, 21, 13, 15, 20, 24, 1, 7, 21, 16, 13, 18, 23, 7, 3, 18, 17, 16. Present the data in the form of a frequency distribution using the same class size, one such class being 20-25 (where 25 is not included). Q 9 The class marks of a distribution are : 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102. Determine the class size, the class limits and the true class limits. IX Mathematics C.B.S.E. Practice Papers Page 98 Q 10 100 plants each were planted in 100 schools during Van Mahotsava. After one month, the number of plants that survived were recorded as : 95 67 28 32 65 65 69 33 98 96 76 42 32 38 42 40 40 69 95 92 75 83 76 83 85 62 37 65 63 42 89 65 73 81 49 52 64 76 83 92 93 68 52 79 81 83 59 82 75 82 86 90 44 62 31 36 38 42 39 83 87 56 58 23 35 76 83 85 30 68 69 83 86 43 45 39 83 75 66 83 92 75 89 66 91 27 88 89 93 42 53 69 90 55 66 49 52 83 34 36 Represent the above data in a frequency distribution table. Q 11 Consider the marks obtained (out of 100 marks) by 30 students of Class IX of a school: 10 20 36 92 95 40 50 56 60 70 92 88 80 70 72 70 36 40 36 40 92 40 50 50 56 60 70 60 60 88 Construct a frequency distribution table. Q 12 For the following data of daily wages(in rupees) received by 30 labourers in a certain factory, construct a grouped frequency distribution table by dividing the range into class intervals of equal width, each corresponding to 2 rupees, in such a way that the mid- value of the first class interval corresponds to 12 rupees. 14, 16, 16, 14, 22, 13, 15, 24, 12, 23, 14, 20, 17, 21, 22, 18, 18, 19, 20,17, 16, 15, 11, 12, 21, 20 ,17, 18, 19, 23. Q 13 Form a discrete frequency distribution from the following scores : 15, 18, 16, 20, 25, 24, 25, 20, 16, 15, 18, 18, 16, 24, 15, 20, 28, 30, 27, 16, 24, 25, 20, 18, 28, 27, 25, 24, 24, 18, 18, 25, 20 ,16, 15, 20, 27, 28, 29, 16. Q 14 The weights in grams of 50 oranges picked at random from a consignment are as follows : 131, 113, 82, 75, 204, 81, 84, 118, 104, 110, 80, 107, 111, 141, 136, 123, 90, 78, 90, 115, 110, 98, 106, 99, 107, 84, 76, 186, 82, 100, 109, 128, 115, 107, 115, 119, 93, 187, 139, 129, 130, 68, 195, 123, 125, 111, 92, 86, 70, 126. Form the grouped frequency table by dividing the variable range into intervals of equal width, each corresponding to 20 gms in such a way that the mid-value of the first class corresponds to 70 gms. Q 15 The marks obtained by 35 students in an examination are given below:Read More