Mathematics · Textbook solutions

Statistics

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 69 questions

Sub-divided and Percentage Bar Diagrams

5 q

Solved Examples

Worked · 5
  1. In the neighbouring figure, a percentage bar-diagram is given. Percentage expenses on different items of two families are given. Answer the following questions based on it.
    Bar SolvedEx.1(i)
    Write the percentage expenses of every component for each family.
  2. Bar SolvedEx.1(ii)
    Which family spends more percent of expenses on food as compared to the other and by how much ?
  3. Bar SolvedEx.1(iii)
    What are the percentage expenses on other items ?
  4. Bar SolvedEx.1(iv)
    Which family shows more percentage expenses on electricity ?
  5. Bar SolvedEx.1(v)
    Which family's percentage expense is more on education ?

Practice Set 7.1

2 q
  1. Ex 7.1 Q1
    The following table shows the number of Buses and Trucks in nearest lakh units. Draw percentage bar-diagram. (Approximate the percentages to the nearest integer)
    YearNo. of TrucksNo. of Buses
    2006-2007479
    2007-20085613
    2008-20096016
    2009-20106318
  2. Ex 7.1 Q2
    In the table given below, the information is given about roads. Using this draw sub-divided and percentage bar-diagram (Approximate the percentages to the nearest integer)
    YearPermanent Roads (Lakh km.)Temporary Roads (Lakh km.)
    2000-20011410
    2001-20021511
    2002-20031713
    2003-20042019

Practice Set 7.2

4 q
  1. Classify following information as primary or secondary data.
    Ex 7.2 Q1(i)
    Information of attendance of every student collected by visiting every class in a school.
  2. Ex 7.2 Q1(ii)
    The information of heights of students was gathered from school records and sent to the head office, as it was to be sent urgently.
  3. Ex 7.2 Q1(iii)
    In the village Nandpur, the information collected from every house regarding students not attending school.
  4. Ex 7.2 Q1(iv)
    For science project, information of trees gathered by visiting a forest.

Classification of Data and Frequency Distribution

1 q

Solved Examples

Worked · 1
  1. Frequency SolvedEx.1
    6, 10, 10.5, 11, 15.5, 19, 20, 12, 13 are the given observations. By taking classes 6-10, 11-15, 16-20 prepare grouped frequency distribution table.

Practice Set 7.3

6 q
  1. Ex 7.3 Q1
    For class interval 20-25 write the lower class limit and the upper class limit.
  2. Ex 7.3 Q2
    Find the class-mark of the class 35-40.
  3. Ex 7.3 Q3
    If class mark is 10 and class width is 6 then find the class.
  4. Ex 7.3 Q4
    Complete the following table.
    Classes (age)Tally marksFrequency (No. of students)
    12-13one group of five...
    13-14two groups of five and four singles...
    14-15(not printed)...
    15-16four singles...
    TotalN=∑f=35N = \sum f = 35
    (The book prints the tally marks as strokes; they are written out in words here. The 14-15 row is left blank on purpose - it is to be deduced from the total.)
  5. Ex 7.3 Q5
    In a 'tree plantation' project of a certain school there are 45 students of 'Harit Sena.' The record of trees planted by each student is given below : 3, 5, 7, 6, 4, 3, 5, 4, 3, 5, 4, 7, 5, 3, 6, 6, 5, 3, 4, 5, 7, 3, 5, 6, 4, 4, 3, 5, 6, 6, 4, 3, 5, 7, 3, 4, 5, 7, 6, 4, 3, 5, 4, 4, 7. Prepare a frequency distribution table of the data.
  6. Ex 7.3 Q6
    The value of π\pi upto 50 decimal places is given below : 3.14159265358979323846264338327950288419716939937510 From this information prepare an ungrouped frequency distribution table of digits appearing after the decimal point.

Practice Set 7.4

10 q
  1. Ex 7.4 Q1
    Complete the following cumulative frequency table :
    Class (Height in cm)Frequency (No. of students)Less than type frequency
    150-1530505
    153-15607...
    156-15915...
    159-1621037
    162-1650542
    165-1680345
    TotalN = 45
  2. Ex 7.4 Q2
    Complete the following Cumulative Frequency Table :
    Class (Monthly income in rupees)Frequency (No. of individuals)More than or equal to type cumulative frequency
    1000-500045...
    5000-1000019...
    10000-1500016...
    15000-2000002...
    20000-2500005...
    TotalN = 87
  3. The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare frequency distribution table and cumulative frequency table more than or equal to type. 55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 27, 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49. From the prepared table, answer the following questions :
    Ex 7.4 Q3(i)
    How many students obtained marks 40 or above 40 ?
  4. Ex 7.4 Q3(ii)
    How many students obtained marks 90 or above 90 ?
  5. Ex 7.4 Q3(iii)
    How many students obtained marks 60 or above 60 ?
  6. Ex 7.4 Q3(iv)
    What is the cumulative frequency of equal to or more than type of the class 0-10 ?
  7. Using the data in example (3) above (the mathematics marks of 62 students), prepare a less than type cumulative frequency table and answer the following questions. 55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 27, 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.
    Ex 7.4 Q4(i)
    How many students obtained less than 40 marks ?
  8. Ex 7.4 Q4(ii)
    How many students obtained less than 10 marks ?
  9. Ex 7.4 Q4(iii)
    How many students obtained less than 60 marks ?
  10. Ex 7.4 Q4(iv)
    Find the cumulative frequency of the class 50-60.

Measures of Central Tendency

6 q

Solved Examples

Worked · 6
  1. Central Tendency SolvedEx.1
    Find the mean of numbers 25, 30, 27, 23 and 25.
  2. Central Tendency SolvedEx.2
    The first unit test of 40 marks was conducted for a class of 35 students. The marks obtained by the students were as follows. Find the mean of the marks. 40, 35, 30, 25, 23, 20, 14, 15, 16, 20, 17, 37, 37, 20, 36, 16, 30, 25, 25, 36, 37, 39, 39, 40, 15, 16, 17, 30, 16, 39, 40, 35, 37, 23, 16.
  3. Central Tendency SolvedEx.3
    Find the median of 54, 63, 66, 72, 98, 87, 92.
  4. Central Tendency SolvedEx.4
    Find the median of the data 30, 25, 32, 23, 42, 36, 40, 33, 21, 43.
  5. Central Tendency SolvedEx.5
    Find the mode of 90, 55, 67, 55, 75, 75, 40, 35, 55, 95.
  6. Central Tendency SolvedEx.6
    The ages of workers in a certain factory are given in the following table. Find the mode of their ages.
    Age (Year)1921252730
    Workers51513157

Practice Set 7.5

14 q
  1. Ex 7.5 Q1
    Yield of soyabean per acre in quintal in Mukund's field for 7 years was 10, 7, 5, 3, 9, 6, 9. Find the mean of yield per acre.
  2. Ex 7.5 Q2
    Find the median of the observations, 59, 75, 68, 70, 74, 75, 80.
  3. Ex 7.5 Q3
    The marks (out of 100) obtained by 7 students in Mathematics' examination are given below. Find the mode for these marks. 99, 100, 95, 100, 100, 60, 90
  4. Ex 7.5 Q4
    The monthly salaries in rupees of 30 workers in a factory are given below. 5000, 7000, 3000, 4000, 4000, 3000, 3000, 3000, 8000, 4000, 4000, 9000, 3000, 5000, 5000, 4000, 4000, 3000, 5000, 5000, 6000, 8000, 3000, 3000, 6000, 7000, 7000, 6000, 6000, 4000 From the above data find the mean of monthly salary.
  5. Ex 7.5 Q5
    In a basket there are 10 tomatoes. The weight of each of these tomatoes in grams is as follows 60, 70, 90, 95, 50, 65, 70, 80, 85, 95. Find the median of the weights of tomatoes.
  6. Ex 7.5 Q6
    A hockey player has scored following number of goals in 9 matches. 5, 4, 0, 2, 2, 4, 4, 3, 3. Find the mean, median and mode of the data.
  7. Ex 7.5 Q7
    The calculated mean of 50 observations was 80. It was later discovered that observation 19 was recorded by mistake as 91. What was the correct mean ?
  8. Ex 7.5 Q8
    Following 10 observations are arranged in ascending order as follows. 2, 3, 5, 9, x+1x + 1, x+3x + 3, 14, 16, 19, 20 If the median of the data is 11, find the value of xx.
  9. Ex 7.5 Q9
    The mean of 35 observations is 20, out of which mean of first 18 observations is 15 and mean of last 18 observations is 25. Find the 18th observation.
  10. Ex 7.5 Q10
    The mean of 5 observations is 50. One of the observations was removed from the data, hence the mean became 45. Find the observation which was removed.
  11. Ex 7.5 Q11
    There are 40 students in a class, out of them 15 are boys. The mean of marks obtained by boys is 33 and that for girls is 35. Find out the mean of all students in the class.
  12. Ex 7.5 Q12
    The weights of 10 students (in kg) are given below : 40, 35, 42, 43, 37, 35, 37, 37, 42, 37. Find the mode of the data.
  13. Ex 7.5 Q13
    In the following table, the information is given about the number of families and the siblings in the families less than 14 years of age. Find the mode of the data.
    No. of siblings1234
    Families152555
  14. Ex 7.5 Q14
    Find the mode of the following data.
    Marks353637383940
    No. of students090709040402

Problem Set 7

21 q
  1. Write the correct alternative answer for each of the following questions.
    Prob Q1(i)
    Which of the following data is not primary ?
    1. A.
      By visiting a certain class, gathering information about attendence of students.
    2. B.
      By actual visit to homes, to find number of family members.
    3. C.
      To get information regarding plantation of soyabean done by each farmer from the village Talathi.
    4. D.
      Review the cleanliness status of canals by actually visiting them.
  2. Prob Q1(ii)
    What is the upper class limit for the class 25-35 ?
    1. A.
      25
    2. B.
      35
    3. C.
      60
    4. D.
      30
  3. Prob Q1(iii)
    What is the class-mark of class 25-35 ?
    1. A.
      25
    2. B.
      35
    3. C.
      60
    4. D.
      30
  4. Prob Q1(iv)
    If the classes are 0-10, 10-20, 20-30... then in which class should the observation 10 be included ?
    1. A.
      0-10
    2. B.
      10-20
    3. C.
      0-10 and 10-20 in these 2 classes
    4. D.
      20-30
  5. Prob Q1(v)
    If xˉ\bar{x} is the mean of x1,x2,…,xnx_1, x_2, \ldots, x_n and yˉ\bar{y} is the mean of y1,y2,…,yny_1, y_2, \ldots, y_n and zˉ\bar{z} is the mean of x1,x2,…,xn,y1,y2,…,ynx_1, x_2, \ldots, x_n, y_1, y_2, \ldots, y_n then zˉ=?\bar{z} = ?
    1. A.
      xˉ+yˉ2\dfrac{\bar{x} + \bar{y}}{2}
    2. B.
      xˉ+yˉ\bar{x} + \bar{y}
    3. C.
      xˉ+yˉn\dfrac{\bar{x} + \bar{y}}{n}
    4. D.
      xˉ+yˉ2n\dfrac{\bar{x} + \bar{y}}{2n}
  6. Prob Q1(vi)
    The mean of five numbers is 80, out of which mean of 4 numbers is 46, find the 5th number :
    1. A.
      4
    2. B.
      20
    3. C.
      434
    4. D.
      66
  7. Prob Q1(vii)
    Mean of 100 observations is 40. The 9th observation is 30. If this is replaced by 70 keeping all other observations same, find the new mean.
    1. A.
      40.6
    2. B.
      40.4
    3. C.
      40.3
    4. D.
      40.7
  8. Prob Q1(viii)
    What is the mode of 19, 19, 15, 20, 25, 15, 20, 15 ?
    1. A.
      15
    2. B.
      20
    3. C.
      19
    4. D.
      25
  9. Prob Q1(ix)
    What is the median of 7, 10, 7, 5, 9, 10 ?
    1. A.
      7
    2. B.
      9
    3. C.
      8
    4. D.
      10
  10. Prob Q1(x)
    From following table, what is the cumulative frequency of less than type for the class 30-40 ?
    Class0-1010-2020-3030-4040-50
    Frequency7312132
    1. A.
      13
    2. B.
      15
    3. C.
      35
    4. D.
      22
  11. Prob Q2
    The mean salary of 20 workers is 10,250 rupees. If the salary of office superintendent is added, the mean will increase by 750 rupees. Find the salary of the office superintendent.
  12. Prob Q3
    The mean of nine numbers is 77. If one more number is added to it then the mean increases by 5. Find the number added in the data.
  13. The monthly maximum temperature of a city is given in degree celcius in the following data. By taking suitable classes, prepare the grouped frequency distribution table. 29.2, 29.0, 28.1, 28.5, 32.9, 29.2, 34.2, 36.8, 32.0, 31.0, 30.5, 30.0, 33, 32.5, 35.5, 34.0, 32.9, 31.5, 30.3, 31.4, 30.3, 34.7, 35.0, 32.5, 33.5, 29.0, 29.5, 29.9, 33.2, 30.2 From the table, answer the following questions.
    Prob Q4(i)
    For how many days the maximum temperature was less than 34 degree C ?
  14. Prob Q4(ii)
    For how many days the maximum temperature was 34 degree C or more than 34 degree C ?
  15. Prob Q5
    If the mean of the following data is 20.2, then find the value of pp.
    xix_i1015202530
    fif_i68pp106
  16. There are 68 students of 9th standard from model Highschool, Nandpur. They have scored following marks out of 80, in written exam of mathematics. 70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47 By taking classes 30-40, 40-50, .... prepare the less than type cumulative frequency table. Using the table, answer the following questions :
    Prob Q6(i)
    How many students, have scored marks less than 80 ?
  17. Prob Q6(ii)
    How many students have scored marks less than 40 ?
  18. Prob Q6(iii)
    How many students have scored marks less than 60 ?
  19. By using data in example (6) above (the marks out of 80 of 68 students of model Highschool, Nandpur), and taking classes 30-40, 40-50... prepare equal to or more than type cumulative frequency table and answer the following questions based on it. 70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47
    Prob Q7(i)
    How many students have scored marks 70 or more than 70 ?
  20. Prob Q7(ii)
    How many students have scored marks 30 or more than 30 ?
  21. Prob Q8
    There are 10 observations arranged in ascending order as given below. 45, 47, 50, 52, xx, x+2x + 2, 60, 62, 63, 74. The median of these observations is 53. Find the value of xx. Also find the mean and the mode of the data.