WISKUNDIGE GELETTERDHEID
GRAAD 12
NOG OEFENINGE
  
Statistiek, mediaan, modus.
  
MATHEMATICAL LITERACY
GRADE 12
MORE EXERCISES
  
Statistics, median, mode.
  
  
Vraag  / Question  1  
  
        Bereken die gemiddelde, mediaan, modus en
        reikwydte van die volgende stelle data :
  
        Calculate the mean, median, mode and
        range of the following data sets :
  
    
        1.1   18   ;   24   ;   19   ;   20   ;   28   ;   19   ;   26   ;   21   ;   22   ;   16   ;   17
                                                                                                                      Ant. / Ans. 1.1
    
        1.2   17   ;   14   ;   11   ;   18   ;   16   ;   17   ;   21   ;   12   ;   22   ;   17
                                                                                                                      Ant. / Ans. 1.2
    
        1.3   38   ;   60   ;   63   ;   57   ;   60   ;   58   ;   59                                Ant. / Ans. 1.3
      
        1.4   50   ;   52   ;   58   ;   51   ;   49   ;   51   ;   80   ;   53   ;   50          Ant. / Ans. 1.4
    
        1.5   14   ;   38   ;   23   ;   18   ;   27   ;   30                                           Ant. / Ans. 1.5
    
        1.6   19   ;   13   ;   23   ;   19   ;   21   ;   19   ;   19                                Ant. / Ans. 1.6
    
        1.7   4   ;   17   ;   15   ;   11   ;   25   ;   15   ;   7   ;   15   ;   11   ;   8
                                                                                                                      Ant. / Ans. 1.7
    
        1.8   37   ;   31   ;   33   ;   34   ;   32   ;   37   ;   31   ;   30   ;   37          Ant. / Ans. 1.8
  
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Vraag  / Question  2  
  
        Sê watter van die volgende waardes,
        gemiddelde, mediaan en modus, beskryf
        die volgende stelle data die beste en
        gee redes :
  
        Say which of the following values, mean,
        median and mode, describe each of the
        following sets of data the best and give
        good reasons:
  
    
        2.1   36   ;   34   ;   31   ;   34   ;   37   ;   32   ;   34                              Ant. / Ans. 2.1
    
        2.2      7   ;     8   ;   31   ;     6   ;     9   ;     7   ;     8   ;     7   ;     6        Ant. / Ans. 2.2
    
        2.3   15   ;   11   ;    3   ;   16   ;   16   ;   15                                          Ant. / Ans. 2.3
    
        2.4   20   ;   17   ;   20   ;   18   ;   23   ;   20                                         Ant. / Ans. 2.4
    
        2.5   22   ;   26   ;   22   ;   62   ;   21   ;   25   ;   24   ;   22                  Ant. / Ans. 2.5
    
        2.6   51   ;   54   ;   92   ;   52   ;   48   ;   53   ;   57   ;   13                  Ant. / Ans. 2.6
    
  
Vraag  / Question  3  
  
        Bereken vir elke stel data die mediaan,
        1ste, 2de en 3de kwartiele, die
        interkwartiel wydte, die 20ste, 25ste,
        75ste, en 80ste persentiele. Skryf ook
        die grense waartussen ons die
        middelste 50% van die data vind, neer.
        Skryf die maksimum waarde van die
        onderste 25% van die data neer.
  
        For each set of data calculate the
        median, 1st, 2nd and 3rd quartiles,
        the inter quartile width, the 20th, 25th,
        75th and 80th percentiles. Also write
        down the boundaries between which
        we find the middle 50% of the data
        values. Write down the maximum value
        for the bottom 25% of the values
  
    
        3.1   16   ;   33   ;   38   ;     3   ;   23   ;   35   ;     8   ;   15   ;   37   ;   24   ;   36   ;
                 37   ;   24   ;   36   ; 21   ;   18   ;   31                                                             Ant. / Ans. 3.1
    
        3.2   48   ;   71   ;   58   ;   49   ;   75   ;   57   ;   96   ;   67   ;   92   ;   51   ;
                63   ;   95   ;   72   ;   51   ;   93                                                                       Ant. / Ans. 3.2
    
        3.3     9   ;   13   ;   42   ;     2   ;   44   ;   15   ;   13   ;   31   ;   18   ;   43   ;
                  3   ;   14   ;   23   ;   16   ;  13     ;   4    ;     5   ;   12   ;     41   ;    7  ;
                25   ;  34   ;   11                                                                                               Ant. / Ans. 3.3
    
        3.4   40   ;   41   ;   31   ;   52   ;   44   ;   32   ;   41   ;   35   ;   49   ;   42   ;
                34   ;   37   ;   36   ;   48   ;  41    ;   35                                                            Ant. / Ans. 3.4
    
  
Vraag  / Question  4  
  
        'n Datastel bestaan uit 5 verskillende
        waardes. Die gemiddelde is 23,2 en
        die mediaan is 24. Die reikwydte is
        10 en die grootste waarde is 28.
    
        4.1   Bereken die kleinste waarde.
                                                      Ant. 4.1
    
        4.2   Skryf die waarde van die modus
                 neer. Verduidelik jou antwoord.
                                                     Ant. 4.2
    
        4.3   Hoeveel waardes is kleiner as
                 die mediaan en hoeveel is
                 groter as die mediaan? Verduidelik.
                                                     Ant. 4.3
    
        4.4   Hoeveel waardes is tussen
                 die mediaan en die grootste
                 waarde? Verduidelik.
                                                     Ant. 4.4
    
        4.5   Bereken die benaderde som
                 van al die data waardes.
                                                     Ant. 4.5
  
        A set of data consists of 5 different
        values. The mean is 23,2 and the
        median is 24. The range is 10 and
        the greatest value is 28.
    
        4.1   Calculate the smallest value.
                                                                 Ans. 4.1
    
        4.2   Write down the value of the mode.
                Explain your answer.
                                                                 Ans. 4.2
    
        4.3   How many values are smaller than
                the median and how many are
                greater than the median? Explain.
                                                                 Ans. 4.3
    
        4.4   How many values are between
                  the median and the greatest
                  value? Explain.
                                                               Ans. 4.4
    
        4.5   Calculate the approximate sum
                 of all the data values.
                                                              Ans. 4.5
  
  
Vraag  / Question  5  
  
        Die gemiddelde van 7 data waardes is
        17,143 en die mediaan is 17.
        Die kleinste waarde is 14, sie wydte
        is 6 en die modus is 19.
    
        5.1   Bereken die grootste waarde.
                                                             Ant. 5.1
    
        5.2   Hoeveel waardes is kleiner
                 as 17 en hoeveel is groter
                 as 17? Verduidelik.
                                                            Ant. 5.2
    
        5.3   Bereken die benaderde som
                 van die data stel.              Ant. 5.3
    
        5.4   Hoeveel waardes is daar
                 tussen 14 en 17?
                                                            Ant. 5.4
    
        5.5   Hoeveel waardes is tussen
                 17 en 20? Kan jy hulle
                 neerskryf? Verduidelik.
                                                           Ant. 5.5
  
        The mean of 7 data values is
        17,143 and the median is 17.
        The smallest value is 14, the range
        is 6 and the mode is 19.
    
        5.1   Calculate the greatest value.
                                                             Ans. 5.1
    
        5.2   How many values are smaller
                 than 17 and how many are
                 greater than 17? Explain.
                                                            Ans. 5.2
    
        5.3   Calculate the approximate sum
                 of the data set.                  Ans. 5.3
    
        5.4   How many values are there
                 between 14 and 17?
                                                            Ans. 5.4
    
        5.5   How many values are
                 between 17 and 20? Can you
                 write them down? Explain.
                                                           Ans. 5.5
  
  
Vraag  / Question  6  
  
        'n Datastel bestaan uit 9 heelgetal
        waardes. Die kleinste waarde is 7 en
        die wydte is 26. Die gemiddelde is 18,
        die mediaan is 17 en die modus is 27.
    
        6.1   Skryf die grootste waarde neer.
                                                               Ant. 6.1
    
        6.2   Hoeveel waardes is kleiner as
                 die mediaan en hoeveel is
                 groter as die mediaan?
                 Verduidelik.                          Ant. 6.2
    
        6.3   Hoeveel waardes is groter as
                 die gemiddelde? Verduidelik.
                                                              Ant. 6.3
    
        6.4   Skryf al die waardes groter
                 as 16 neer.                         Ant. 6.4
    
        6.5   Bereken die benaderde som
                 van al die waardes.           Ant. 6.5
    
        6.6   Bereken die som van die
                 waardes in 6.4                  Ant. 6.6
    
        6.7   Bereken die som van al die
                 waardes kleiner as die
                 mediaan.                           Ant. 6.7
  
        A set of data consists of 9 integer
        values. The smallest value is 7 and
        the range is 26. The mean is 18,
        the median is 17 and the mode is 27.
    
        6.1   Write down the largest value.
                                                               Ans. 6.1
    
        6.2   How many values are smaller
                 than the median and how many
                 are larger than the median?
                 Explain.                                    Ans. 6.2
    
        6.3   How many values are larger
                 than the mean? Explain.
                                                                 Ans. 6.3
    
        6.4   Write down all the values
                 greater than 16.                     Ans. 6.4
    
        6.5   Calculate the approximate sum
                 of all the values.                     Ans. 6.5
    
        6.6   Calculate the sum of the
                 values in 6.4                           Ans. 6.6
    
        6.7   Calculate the sum of al
                 the values smaller than the
                 median.                                 Ans. 6.7
  
  
Vraag  / Question  7  
  
        'n Datastel bestaan uit 10 heeltallige
        waardes. Die mediaan is 9, die
        modus is 8 (frekwensie van2) en
         die gemiddelde is 10,5. Die kleinste.
         getal is 2 en die reikwydte is 19.
    
        7.1   Bereken die grootste waarde.
                                                           Ant. 7.1
    
        7.2   Hoeveel waardes is kleiner as
                 en hoeveel is groter as die
                 mediaan? Verduidelik.
                                                           Ant. 7.2
    
        7.3   Sal dit korrek wees om te beweer
                 dat 50% van die waardes kleiner
                 is as 9? Verduidelik.        Ant. 7.3
    
        7.4   Hoeveel waardes is groter as die
                 gemiddelde? Verduidelik.
                                                          Ant. 7.4
    
        7.5   Bereken die benaderde som
                 van al die waardes.         Ant. 7.5
    
        7.6   Hoeveel waardes is kleiner as
                 die modus? Verduidelik.    Ant. 7.6
  
        A data set contains 10 integer
        values. The median is 9, the
        mod is 8 (frequency of 2) and
        the mean is 10,5. The smallest
        number is 2 and the range is 19.
    
        7.1   Calculate the biggest value.
                                                                 Ans. 7.1
    
        7.2   How many values are smaller
                 than and how many are larger
                 than the median? Explain.
                                                                Ans. 7.2
    
        7.3   Will it be correct to claim that
                 50% of the values are smaller
                 than 9? Explain.                    Ans. 7.3
    
        7.4   How many values are greater
                 than the mean? Explain.
                                                               Ans. 7.4
    
        7.5   Calculate the approximate sum
                 of all the values.                  Ans. 7.5
    
        7.6   How many values are smaller
                 than the mode? Explain.    Ans. 7.6
  
  
Vraag  / Question  8  
  
        'n Kolwer behaal 'n gemiddelde van
        23,1 lopies in 7 wedstryde. Die lopies
        aangeteken in elk van die eerste 6 wedstryde
        is 21 ; 8 ; 6 ; 88 ; 3 ; 5.
    
        8.1   Hoeveel lopies teken hy in die
                 sewende wedstryd aan?
                                                          Ans. 8.1
    
        8.2   Is die gemiddelde van sy tellings
                 'n goeie beskrywing van sy tellings?
                 Verduidelik.                     Ans. 8.2
    
        Die tellings van 'n tweede kolwer is :
         23 ;  18  ;  20  ;  21  ;  17  ;  19  ;  20
    
        8.3   Bereken die gemiddelde van
                sy tellings.                       Ans. 8.3
    
        8.4   As jy 'n bestendige kolwer moet
                 kies, sal jy die eerste of tweede
                 kolwer kies?? Verduidelik.
                                                              Ans. 8.4
  
  
        A batsman scored an average of
        23,1 runs in 7 matches. The runs
        scored in each of the first 6 matches
        were: 21  ; 8 ; 6 ;  88  ; 3 ; 5
    
        8.1   How many runs did he score in
                 the seventh match?
                                                              Ans. 8.1
    
        8.2   Is the average of his scores a good
                 description of his scores? Explain.
                                                               Ans. 8.2
    
        The scores of a second batsman were:
         23 ;  18  ;  20  ;  21  ;  17  ;  19  ;  20
    
        8.3   Calculate the average of his scores.
                                                              Ans. 8.3
    
        8.4   If you were to select a steady batsman,
                 would you choose the first or the
                 second batsman? Explain.
                                                              Ans. 8.4
  
  
  
Vraag  / Question  9  
  
  
   
      Die diagram hierbo stel die
      snor-en-baard diagram van
      'n datastel voor sowel as terme
      wat die verskillende letters op die
      diagram beskryf.
      Die terme, nie noodwendig in die
      korrekte volgorde nie, :
      kwartiel 1, kwartiel 2, kwartiel 3,
      maksimum, mediaan, minimum
      en modus.
    
        9.1   Gee die korrekte terme vir
                 die letters op die
                 snor-baarddiagram deur
                 slegs die letter en die
                 korrekte term neer te skryf.
                                                          Ans. 9.1
  
        9.2   Voltooi deur die korrekte
                 letters in te vul :
  
    
        9.2.1
               Omvang = __ ━ __
                                                          Ans. 9.2.1
    
        9.2.2
               Interkwartielomvang (IKO) = __ ━ __
  
                                                          Ans. 9.2.2
  
   
      The diagram above represents
      the box-and-whisker diagram of
      a set of data as well as terms
      that describe the different letters
      on the diagram .
      The terms, not necessarily in the
      correct order, are :
      quartile 1, quartile 2, quartile 3,
      maximum, median, minimum
      and mode.
    
        9.1   Give the correct terms to
                 identify the letters on the
                 box-and-whisker diagram
                 by writing down only the letter
                 and the correct term.
                                                          Ans. 9.1
  
        9.2   Complete by writing down the
                 letters A to E :
  
    
        9.2.1
               Range = __  ━  __
                                                          Ans. 9.2.1
    
        9.2.2
               Interquartile range (IQR) = __ ━ __
  
                                                          Ans. 9.2.2
  
  
Vraag  / Question  10  
  
      'n Datastel het die volgende waardes :
      gemiddelde = 25, mediaan = 26,
      kleinste waarde = 3, eerste kwartiel = 16,
      tweede kwartiel = 26, derde kwartiel = 36
      modus = 16 en maksimum waarde = 38.
      Verwys na die snor-en-baard diagram van
      Vraag 9 en vul dan die korrekte waardes
      vir die letters, A tot E, in.
                                                                Ans. 10.
  
      A set of data has the following values :
      average = 25, median = 26,
      smallest value = 3, first quartile = 16,
      second quartile = 26, third quartile = 36,
      mode = 16 and maximum value = 38.
      Refer to the box-and-whisker diagram in
      Question 9 and write down the correct
      values for the letters, A to E.
                                                                Ans. 10.
  
  
Vraag  / Question  11  
  
      'n Datastel het die volgende waardes :
      gemiddelde = 25, mediaan = 26,
      kleinste waarde = 3, eerste kwartiel = 16,
      tweede kwartiel = 26, derde kwartiel = 36
      modus = 16 en maksimum waarde = 38.
      Verwys na die snor-en-baard diagram van
      Vraag 9 en vul dan die korrekte waardes
      vir die letters, A tot E, in.
      
                                                                Ans. 11.
  
      A set of data has the following values :
      average = 25, median = 26,
      smallest value = 3, first quartile = 16,
      second quartile = 26, third quartile = 36,
      mode = 16 and maximum value = 38.
      Refer to the box-and-whisker diagram in
      Question 9 and write down the correct
      values for the letters, A to E.
      
                                                                Ans. 11.
  
  
Vraag  / Question  12  
  
      'n Span moet nog twee wedstryde speel.
      Die boomdiagram hieronder stel die
      uitkomstes voor.
      
 
 
 
    
    
      12.1   Vul die 3 ontbrekende uitkomstes in.
                                                              Ans. 12.1
    
      Gee die waarskynlikheid, in die
      eenvoudigste vorm, dat
    
      12.2   die span die eerste westryd sal
                verloor                                  Ans. 12.2
    
      12.3   die span die tweede wedstryd sal wen.
                                                              Ans. 12.3
    
      12.4   die span albei wedstryde sal wen.
                                                              Ans. 12.4
    
      12.5   dat die span ten minste een wedstryd
                sal verloor.                            Ans. 12.5
    
      12.6   ten minste een wedstryd gelykop
                sal wees.                              Ans. 12.6
    
      12.7   dat die span nie 'n wedstryd sal
                verloor nie.                           Ans. 12.7
  
      A team still has to pay two matches.
      The tree-diagram below shows all
      the possible outcomes.
      
 
 
 
    
    
      12.1   Write down the 3 missing outcomes.
                                                              Ans. 12.1
    
      Give the probability, in its
      simplest form, that
    
      12.2   the team will lose the first match.
                                                              Ans. 12.2
    
      12.3   the team will win the second match.
                                                              Ans. 12.3
    
      12.4   the team will win both matches.
                                                              Ans. 12.4
    
      12.5   the team will lose at least one match
                                                              Ans. 12.5
    
      12.6   at least one match will be drawn.
                                                             Ans. 12.6
    
      12.7   the team will not lose a match.
                                                             Ans. 12.7
  
  
Vraag  / Question  13  
  
      Daar is drie kinders in 'n gesin.
      Die boomdiagram hieronder stel die
      uitkomstes voor.
      
 
 
 
    
    
      13.1   Vul die 3 ontbrekende uitkomstes in.
                                                              Ans. 13.1
    
      Gee die waarskynlikheid, in die
      eenvoudigste vorm, dat
    
      13.2   die eerste kind 'n seun sal wees.
                                                             Ans. 13.2
    
      13.3   daar twee dogters in die gesin sal
                wees.                                   Ans. 13.3
    
      13.4   daar net een seun in die gesin sal
                wees.                                   Ans. 13.4
    
      13.5   daar geen dogters in die gesin sal
                wees nie.                             Ans. 13.5
  
      There are three children in a family.
      The tree-diagram below represents
      the outcomes.
      
 
 
 
    
    
      13.1   Write down the three missing
                outcomes.                              Ans. 13.1
    
      Write down the probability, in it's
      simplest form, that
    
      13.2   the first child will be a boy.
                                                             Ans. 13.2
    
      13.3   the family will have two daughters.
                                                             Ans. 13.3
    
      13.4   there will be only one boy in the
                family.                                   Ans. 13.4
    
      13.5   there will be no daughters in the
                family.                                   Ans. 13.5
  
  
Vraag  / Question  14  
  
 
 
 
      'n Dobbelsteen word gerol en 'n muntstuk
      word gelyktydig geskiet.
      Die boomdiagram hierbo stel die
      uitkomstes voor.
    
      14.1   Vul die 4 ontbrekende uitkomstes in.
                                                              Ans. 14.1
    
      Gee die waarskynlikheid, in die
      eenvoudigste vorm, dat
    
      14.2   1 en'n kruis verkry word.
                                                             Ans. 14.2
    
      14.3   'n ewe getal en 'n kruis verkry
                word.                                   Ans. 14.3
    
      14.4   'n getal groter as 3 en 'n munt verkry
                word.                                   Ans. 14.4
    
      14.5   'n onewe getal kleiner as 5 en
                munt verkry word.               Ans. 14.5
    
      14.6   enige getal en munt verkry word.
                                                           Ans. 14.6
    
      14.7   3 en kruis of munt verkry word.
                                                           Ans. 14.6
    
      14.7   2 en nie kruis of munt verkry word nie.
                                                           Ans. 14.6
  
      As a die is cast, a coin is tossed.
      The tree-diagram above represents
      all the possible oucomes.
      
    
      14.1   Write down the 4 missing outcomes.
                                                              Ans. 14.1
    
      Write down, in its simplest form, the
      probability that
    
      14.2   1 and a head are obtained.
                                                             Ans. 14.2
    
      14.3   an even number and a head are
                obtained.                              Ans. 14.3
    
      14.4   a number greater than 3 and a tail
                are obtained.                        Ans. 14.4
    
      14.5   an uneven number smaller than 5 and
                a tail are obtained.               Ans. 14.5
    
      14.6   any number and a tail are obtained.
                                                             Ans. 14.6
    
      14.7   3 and heads or tail are obtained.
                                                             Ans. 14.7
    
      14.7   2 and neither heads or tails are obtained.
                                                             Ans. 14.6
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
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