WISKUNDE
GRAAD 11
NOG OEFENINGE
  
Statistiek
  
MATHEMATICS
GRADE 11
MORE EXERCISES
  
Statistics
  
  
Vraag  / Question  1  
  
  
        Bereken die gemiddelde, mediaan, modus en
        reikwydte of omvang van die volgende stelle data :
  
        Calculate the mean, median, mode and
        range of the following data sets :
  
    
        1.1   22   ;   24   ;   19   ;   18   ;   20   ;   19   ;   26                                                [ A 1.1 ]
    
        1.2   17   ;   14   ;   11   ;   18   ;   16   ;   17   ;   21   ;   12   ;   22                           [ A 1.2 ]
    
        1.3   57   ;   54   ;   51   ;   58   ;   56   ;   57   ;   61   ;   52   ;   62   ;   57   ;   53      [ A 1.3 ]
    
        1.4   13   ;   10   ;   11   ;   14   ;   12   ;   13   ;   17   ;   12                                      [ A 1.4 ]
    
        1.5   20   ;   22   ;   26   ;   28   ;   24   ;   23   ;   21   ;   22   ;   29   ;   25                 [ A 1.5 ]
    
        1.6   13   ;   15   ;   12   ;   17   ;   12   ;   13   ;   14   ;   18                                      [ A 1.6 ]
    
        1.7   7   ;   4   ;   1   ;   8   ;   5   ;   7   ;   6   ;   5   ;   2   ;   7   ;   3   ;   7                 [ A 1.7 ]
    
        1.8   37   ;   34   ;   31   ;   38   ;   36   ;   37   ;   41   ;   32   ;   42   ;   57   ;   33
                31   ;   28   ;   25   ;   32   ;   30   ;   31   ;   44   ;   26   ;   42   ;   51   ;   33      [ A 1.8 ]
  
Vraag  / Question  2  
  
         Vir een week teken Teboho die
         aantal motors wat per dag
         op 'n parkeerterrein geparkeer
         is aan. Die volgende data
         is aangeteken :
         In one week Teboho notes the number
         of cars that are parked on a
         parking lot. The following data
         is recorded :
  
  
42   21   43   19   37   21   48
  
         2.1  Skryf die data in stygende
                volgorde neer.
                                                         [ A 2.1 ]
  
         2.2  Bereken die omvang
                van die data.                    [ A 2.2 ]
  
         2.3  Bereken die gemiddelde.
                                                         [ A 2.3 ]
  
         2.4  Bereken die mediaan
                  van die data.                  [ A 2.4 ]
  
         2.5  Bereken die modus
                van die data.                    [ A 2.5 ]
  
         2.6  Bereken die aantal dae
                wat die aantal geparkeerde
                motors groter was as
                die gemiddelde.
                                                        [ A 2.6 ]
  
         2.7  Bereken die aantal dae
                wat die aantal geparkeerde
                motors groter was as
                die modus.
                                                        [ A 2.7 ]
  
         2.8  Bereken die aantal dae
                wat die aantal geparkeerde
                motors kleiner was as
                die mediaan.
                                                        [ A 2.8 ]
  
   2.1  Write down the data in
          ascending order.
                                                         [ A 2.1 ]
  
   2.2  Calculate the range of the data.
                                                         [ A 2.2 ]
  
   2.3  Calculate the mean.
                                                         [ A 2.3 ]
  
   2.4  Calculate the median of
          the data.                               [ A 2.4 ]
  
   2.5  Calculate the mode of
          the data.                               [ A 2.5 ]
  
   2.6  Calculate the number of days that
          the number of parked cars in the
          parking lot was greater than
          the mean.
                                                         [ A 2.6 ]
  
   2.7  Calculate the number of days that
          the number of parked cars in the
          parking lot was greater than
          the modus.
                                                         [ A 2.7 ]
  
   2.8  Calculate the number of days that
          the number of parked cars in the
          parking lot was smaller than
          the median.
                                                         [ A 2.8 ]
  
  
Vraag  / Question  3  
  
         Daar is 14 dogters en 11 seuns in 'n Graad 11
         Wiskundige Geletterdheid klas. Hulle het 'n
          toets, maksimum 10 punte, geskryf en hulle
          punte word in die tabel hieronder gegee :
         There are 14 girls and 11 boys in a Grade 11
         Mathematical Literacy class. They wrote a test,
          maximum 10 marks, and their marks are given
          in the table below :
  
  Dogters / Girls    2    4    8    6    7    8    6    8    9    5    8    7    5    1
  Seuns / Boys    7    4    1    8    5    7    6    5    2    7    3         
  
    
    3.1   Voltooi die onderstaande tabel deur die
            punte in stygende orde te rangskik en die
            gemiddelde, mediaan en modus te bereken :
    
    3.1   Complete the table below by arranging the
            marks in ascending order and by
            calculating the mean, median and mode :
  
  
                                                                                 Gemid / Mean    Mediaan / Median    Modus / Mode
  Dogters / Girls                                                                                                                              
  Seuns / Boys                                                                                                                     
  Klas / Class                                                                                                                                                               
  
[ A 3.1 ]
  
         'n Leerling word nou ewekansig uit die klas
         gekies. Bereken die waarskynlikheid dat die
         leerling
    
    3.2   'n dogter sal wees.                     [ A 3.2 ]
    
    3.3   'n seun sal wees met 'n punt kleiner
            as 8?                                          [ A 3.3 ]
    
    3.4   'n punt groter as 6 sal hê?         [ A 3.4 ]
    
    3.5   'n dogter met 'n punt gelyk aan die
            modus van al die punte sal wees?
                                                              [ A 3.5 ]
    
    3.6   'n seun met 'n punt groter as die
            gemiddelde van die seuns se punte
            sal wees?                                   [ A 3.6 ]
    
    3.7   'n punt kleiner as die klasgemiddelde
            sal hê?                                       [ A 3.7 ]
    
    3.8   'n punt groter as die modus van die
            klas sal hê?                               [ A 3.8 ]
    
    3.9   'n seun met 'n punt van 6 sal wees?
                                                              [ A 3.9 ]
         A learner is now chosen radomly from the
         class. Calculate the probability that this
         learner
    
    3.2   will be a girl?                                 [ A 3.2 ]
    
    3.3   will be a boy with a mark smaller
            than 8?                                          [ A 3.3 ]
    
    3.4   will have a mark greater than 6?     [ A 3.4 ]
    
    3.5   will be a girl with a mark equal to
            the mode of all the marks?            [ A 3.5 ]
  
    
    3.6   will be a boy with a mark greater than
            the mean of the marks of the boys?
                                                                  [ A 3.6 ]
    
    3.7   will have a mark smaller than the
            class mean?                                  [ A 3.7 ]
    
    3.8   will have a mark greater than the
            class mode?                                  [ A 3.8 ]
    
    3.9   will be a boy with a mark equal to 6?
                                                                  [ A 3.9 ]
  
Vraag  / Question  4  
  
         Die lys hieronder toon die punte van 45 leerlinge :
  
         The list below shows the marks of 45 pupils :
  
                14;     27;    20;    35;      4;    35;    28;    35;    35;    45;    15;      7;    24;    46;    20
                25;     45;    18;    38;    41;    33;    41;    13;    45;    23;    35;    33;    41;    33;    36
                41;     27;    22;    36;    30;    36;    31;    20;    13;    31;    43;    48;    25;    20;    13
  
         4.1  Voltooi die onderstaande tabel :
                                                              [ A 4.1 ]
         4.1  Complete the table below :
                                                              [ A 4.1 ]
  
  
      Telling    Frekwensie (f)    Kumulatiewe frekwensie
      Tally    Frequency (f)    Cumulative frequency
      0 ≤ m < 10         
      10 ≤ m < 20         
      20 ≤ m < 30         
      30 ≤ m < 40         
      40 ≤ m ≤ 50         
  
         4.2  Is die punte diskreet of kontinu?
                                                              [ A 4.2 ]
         4.3  Wat is die klasgrense van die
                 heel boonste klas?
                                                              [ A 4.3 ]
         4.4  Teken die ogief.
                                                              [ A 4.4 ]
  
         4.5  Lees die volgende van die ogief af :
  
         4.5.1  Hoeveel leerlinge het die toets
                   gedruip? (minder as 10 punte)
                                                              [ A 4.5.1 ]
  
         4.5.2  Hoeveel leerlinge het minder
                   as 15 punte gekry?
                                                              [ A 4.5.2 ]
  
         4.6.3  Hoeveel leerlinge het meer
                   as 19 punte gekry?
                                                              [ A 4.6.3 ]
         4.2  Are the marks discrete or continuous?
                                                              [ A 4.2 ]
         4.3  What are the class boundaries of
                 the top most class?
                                                              [ A 4.3 ]
         4.4  Draw the ogive.
                                                              [ A 4.4 ]
  
         4.5  Read the following from yhe ogive :
  
         4.5.1  How many pupils failed the test?
                   ( less than 10 marks)?
                                                              [ A 4.5.1 ]
  
         4.5.2  How many pupils had less
                   than 15 marks?
                                                              [ A 4.5.2 ]
  
         4.5.3  How many pupils had more
                   than 19 marks?
                                                              [ A 4.5.3 ]
  
  
Vraag  / Question  5  
  
         Die lys hieronder vertoon die
         massa van 50 Graad 11 dogters :
  
         The list below shows the mass
         of 50 Grade 11 girls :
  
                46;     41;    55;    43;    52;    47;    71;    48;    64;    62;    55;    43;    60;    57;    63
                52;     56;    59;    61;    54;    58;    43;    66;    86;    59;    47;    53;    68;    61;    65
                72;     44;    79;    42;    66;    62;    62;    53;    64;    82;    60;    65;    63;    52;    66
                61;     65;    54;    59;    61
  
         5.1  Voltooi die onderstaande tabel :
                                                              [ A 5.1 ]
         5.1  Complete the table below :
                                                              [ A 5.1 ]
  
  
      Klas middelpunt (x)    Frekwensie (f)    Frekwensie (f.x)    Kumulatiewe frekwensie (kf)    Kumulatiewe frekwensie pereentasie (kf%)
      Class centre (x)    Frequency (f)    Frequency (f.x)    Cumulative frequency (cf)    Cumulatice frequency percentage (cf%)
  
40 ≤ m < 50
  
45
  
  
  
  
  
50 ≤ m < 60
  
55
  
  
  
  
  
60 ≤ m < 70
  
65
  
  
  
  
  
70 ≤ m < 80
  
75
  
  
  
  
  
80 ≤ m ≤ 90
  
85
  
  
  
  
  
         5.2  Trek die ogief van die data.
                                                              [ A 5.2 ]
         5.3  Gebruik die ogief om die
                volgende vrae te beantwoord :
  
         5.3.1  Hoeveel dogters het
                'n massa groter as 70 kg?
                                                              [ A 5.3.1 ]
         5.3.2  Hoeveel dogters het
                   'n massa kleiner as 60 kg?
                                                              [ A 5.3.2 ]
         5.3.3  Wat is die maksimum massa
                   van die 25 dogters met
                   die kleinste massa?
                                                              [ A 5.3.3 ]
         5.4  Trek die ogief deur van die
                 kumulatiewe frekwensie
                 persentasie gebruik te maak.
                                                              [ A 5.4 ]
         5.5  Gebruik die ogief om die
                volgende vrae te beantwoord :
  
         5.5.1  Watter persentasie van die
                dogters het 'n massa kleiner
                as 50 kg?
                                                              [ A 5.5.1 ]
         5.5.2  Wat is die minimum massa
                van die swaarste 25% van
                die dogters?
                                                              [ A 5.5.2 ]
         5.5.3  Lees die mediaan af.
                                                              [ A 5.5.3 ]
         5.6  Bereken die gemiddelde massa.
                                                              [ A 5.6 ]
         5.2  Draw the ogive of the data.
                                                              [ A 5.1 ]
         5.3  Use the ogive to answer the
                following questions :
  
         5.3.1  How many girls have a mass
                   greater than 70 kg?
                                                              [ A 5.3.1 ]
         5.3.2  How many girls have a mass
                   smaller than 60 kg?
                                                              [ A 5.3.2 ]
         5.3.3  What is the maximum mass
                   of the 25 girls with the
                   smallest mass?
                                                              [ A 5.3.3 ]
         5.4  Draw the ogive using the
                percentage cumulative frequency.
                                                              [ A 5.4 ]
  
         5.5  Use this ogive to answer the
                following questions :
  
         5.5.1  How percent of the girls have a
                   mass smaller than 50 kg?
                                                              [ A 5.5.1 ]
  
         5.5.2  What is the minimum mass of
                   the heaviest 25% of the girls?
                                                              [ A 5.5.2 ]
  
         5.5.3  Read the median mass.
                                                              [ A 5.5.3 ]
         5.6  Calculate the mean mass.
                                                              [ A 5.6 ]
  
Vraag  / Question  6  
  
     t    Die lys hieronder vertoon die
         lengte, in cm, van 40 leerlinge :
  
         The list below shows the length,
         in cm, of 40 pupils :
  
                163;     158;    161;    171;    162;    165;    159;    156;    167;    166;    162;    173;    177;    157;    165
                178;     175;    179;    166;    165;    154;    179;    151;    153;    173;    172;    168;    151;    164;    159
                151;     165;    152;    158;    165;    172;    153;    163;    164;    179;
  
         6.1  Bereken die
  
         6.1.1  omvang.                        [ A 6.1.1 ]
  
         6.1.2  gemiddelde.                  [ A 6.1.2 ]
  
         6.1.3  mediaan.                       [ A 6.1.3 ]
  
         6.1.4  modus.                          [ A 6.1.4 ]
  
         6.2  Wat is die mees algemene
                lengte van die leerlinge?
                                                        [ A 6.2 ]
         6.3  Voltooi die tabel hieronder.
                                                        [ A 6.3 ]
         6.1  Calculate the
  
         6.1.1  range                                      [ A 6.1.1 ]
  
         6.1.2  mean                                      [ A 6.1.2 ]
  
         6.1.3  median                                   [ A 6.1.3 ]
  
         6.1.4  mode                                      [ A 6.1.4 ]
  
         6.2  What is the most common
                length of the pupils?
                                                                  [ A 6.2 ]
         6.3  Complete the table below :
                                                                  [ A 6.3 ]
  
  
      Klas middelpunt (x)    Frekwensie (f)    Frekwensie (f.x)    Kumulatiewe frekwensie (kf)    Kumulatiewe frekwensie pereentasie (kf%)
      Class centre (x)    Frequency (f)    Frequency (f.x)    Cumulative frequency (cf)    Cumulatice frequency percentage (cf%)
  
150 ≤ m < 160
  
155
  
  
  
  
  
160 ≤ m < 170
  
  
  
  
  
  
170 ≤ m ≤ 180
  
  
  
  
  
  
  
         6.4  Trek die ogief met
                persentasie op die y-as.
                                                              [ A 6.4 ]
  
         6.5.1  Bereken die geskatte
                   gemiddelde.                       [ A 6.5.1 ]
         6.5.2  Vergelyk hierdie waarde met
                   die berekende waarde van 6.1.1
                                                             [ A 6.5.2 ]
         6.6  Gebruik die ogief om die
                volgende vrae te beantwoord :
  
         6.6.1  Wat is die maksimum lengte van
                   die onderste 40 % van die leerlinge?
                                                             [ A 6.6.1 ]
  
         6.6.2  Wat is die minimum lengte van
                   die langste 25 % van die leerlinge?
                                                             [ A 6.6.2 ]
  
         6.6.3  Wat is die minimum lengte van
                   die top 60 % van die leerlinge?
                                                             [ A 6.6.3 ]
  
         6.6.4  60 % van die leerlinge is
                   langer as 162 cm.
                   Is die bewering korrek?
                   Motifeer jou antwoord.
                                                             [ A 6.6.4 ]
  
         6.6.5  55% van die leerlinge is
                   korter as 166 cm.
                   Is die bewering korrek?
                   Sê, met redes, of jy met die
                   bewering saamstem.
                                                             [ A 6.6.5 ]
  
         6.4  Draw the ogive with
                percentages on the y-axis.
                                                              [ A 6.4 ]
  
         6.5.1  Calculate the estimated mean.
                                                              [ A 6.5.1 ]
         6.5.2  Compare this value to the
                   value calculated in 6.1.1
                                                              [ A 6.5.2 ]
         6.6  Use the ogive to answer the
                following questions :
  
         6.6.1  What is the maximum length
                   of the bottom 40 % of the pupils?
                                                              [ A 6.6.1 ]
  
         6.6.2  What is the minimum length
                   of the tallest 25 % of the pupils?
                                                              [ A 6.6.2 ]
  
         6.6.3  What is the minimum length
                   of the top 60 % of the pupils?
                                                              [ A 6.6.3 ]
  
         6.6.4  60 % of the pupils are taller
                   than 162 cm.
                   Is this statement correct?
                   Explain your answer.
                                                              [ A 6.6.4 ]
  
         6.6.5  55 % of the pupils are shorter
                   than 166 cm.
                   Is this statement correct?
                   Say whether you agree and
                   give reasons.
                                                              [ A 6.6.5 ]
  
  
Vraag  / Question  7  
  
         Die lys hieronder stel die
         afstande, in kilometer, voor
         wat 40 leerlinge heen en
         weer na die skool
         gedurende 'n week aflê.
  
         The list below represents the
         distances, in kilometers, that
         40 pupils travel to and from
         school during a week :
  
  
                45;     50;    81;    54;    89;    37;    61;    49;    47;    68;    62;    53;    71;    29;    55
                40;     67;    56;    66;    34;    31;    75;    58;    71;    33;    49;    65;    79;    64;    20
                50;     30;    70;    22;    39;    50;    76;    21;    48;    27;
  
         7.1  Voltooi onderstaande tabel :
                                                          [ A 7.1 ]
  
         7.1  Complete the table below :
                                                              [ A 7.1 ]
  
  
     
Frekwensie
  
Kumulatiewe frekwensie
     
Frequency (f)
  
Cumulative frequency
      20 ≤ m < 30   
  
      30 ≤ m < 40   
  
      40 ≤ m < 50   
  
      50 ≤ m < 60   
  
      60 ≤ m < 70   
  
      70 ≤ m < 80   
  
      80 ≤ m ≤ 90   
  
  
         7.2  Trek die ogief.                   [ A 7.2 ]
  
         7.3  Hoeveel leerlinge reis minder
               as 30 km en 70 km per week?
                                                          [ A 7.3 ]
  
         7.4  Hoeveel leerlinge reis 60 km
               of meer per week?
                                                          [ A 7.4 ]
  
         7.5  Sê of die volgende stellings
               waar of vals is en gee 'n rede
               vir jou gevolgtrekking.
  
         7.5.1  Daar is 5 leerlinge wat minder
                   as 3 km vanaf die skool bly.
                                                       [ A 7.5.1 ]
  
         7.5.2  Agt leerlinge woon tussen
                   10 en 12 km vanaf die skool.
                                                       [ A 7.5.2 ]
  
         7.5.3  Agt leerlinge woon 7 km
                   of meer vanaf die skool.
                                                       [ A 7.5.3 ]
  
         7.5.4  Sewe leerlinge woon tussen
                   6 en 7 km vanaf die skool.
                                                       [ A 7.5.4 ]
  
         7.5.5  Vyf en twintig leerlinge woon nader
                   as 5 km vanaf die skool.
                                                       [ A 7.5.5 ]
  
         7.5.6  Elf leerlinge woon tussen
                   3 en 5 km vanaf die skool.
                                                       [ A 7.5.6 ]
  
         7.5.7  Geen leerling woon verder
                   as 9 km vanaf die skool nie.
                                                       [ A 7.5.7 ]
  
         7.5.8  Sewentien leerlinge woon nader
                   as 50 km van die skool af.
                                                       [ A 7.5.8 ]
  
         7.2  Draw the ogive.                   [ A 7.2 ]
  
         7.3  How many pupils travel less than
                30 and less than 70 km per week?
                                                            [ A 7.3 ]
  
         7.4  How many pupils travel 60 km
                or more per week?
                                                            [ A 7.4 ]
  
         7.5  Say whether the following statements
                are true or false and give a reason
                for your deduction.
  
         7.5.1  There are 5 pupils that stay less
                   than 3 km from the school.
                                                        [ A 7.5.1 ]
  
         7.5.2  Eight pupils stay between 10
                   and 12 km from the school.
                                                        [ A 7.5.2 ]
  
         7.5.3  Eight pupils stay 7 km
                   or more from the school.
                                                        [ A 7.5.3 ]
  
         7.5.4  Seven pupils stay between
                   6 and 7 km from the school.
                                                        [ A 7.5.4 ]
  
         7.5.5  Twenty five pupils stay closer
                   than 5 km from the school.
                                                        [ A 7.5.5 ]
  
         7.5.6  Eleven pupils stay between
                   3 and 5 km from the school.
                                                        [ A 7.5.6 ]
  
         7.5.7  No pupil stays more than
                   9 km from the school.
                                                        [ A 7.5.7 ]
  
         7.5.8  Seventeen pupils stay less than
                   50 km from the school.
                                                        [ A 7.5.8 ]
  
  
  
  
  
  
  
  
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