WISKUNDIGE GELETTERDHEID
GRAAD 10
NOG OEFENINGE
  
Statistiek : antwoorde
  
MATHEMATICAL LITERACY
GRADE 10
MORE EXERCISES
  
Statistics : answers
  
  
Antwoorde  / Answers  1  
  
    
         1.1  A = 3; B = ││││
                C = ┼┼┼┼ en D = 1.
                                                         [ V 1.1 ]
    
         1.2  Die data is diskreet. 'n Leerling
                kan net 'n heelgetal punte hê
                'n Leerling kan 3 punte hê, maar
                nie 3,2 punte nie. Uitsondering
                is waar punte uit bv. 10 gegee
                word maar die oorspronklike punt
                is uit bv, 100
                                                         [ V 1.2 ]
    
         1.3  Die swakste punt is 1 en
                die hoogste punt is 9.
                                                         [ V 1.3 ]
    
         1.4  4 leerlinge het 2 punte.
                                                         [ V 1.4 ]
    
         1.5  Die frekwensie van 6 punte is 2
                                                         [ V 1.5 ]
    
         1.6  1, 3 en 5 punte het 'n
                frekwensie van 3.
                                                         [ V 1.6 ]
    
         1.7  Die laagste frekwensie is 1 en
                dit is die frekwensie van 8 punte.
                                                         [ V 1.7 ]
    
         1.8  Die hoogste frekwensie is 5 en
                dit is die frekwensie van 7 punte.
                                                         [ V 1.8 ]
    
         1.1  A = 3; B = ││││
                C = ┼┼┼┼ and D = 1.
                                                         [ Q 1.1 ]
    
         1.2  The data is discrete. A pupil can
                only have a whole number of marks.
                A Pupil can have 3 marks but not
                3,2 marks. An exception is where
                marks are allocated out of 10 but
                the original mark is given out
                of 100.
                                                         [ Q 1.2 ]
    
         1.3  The lowest mark is 1 and the
                best mark is 9.
                                                         [ Q 1.3 ]
    
         1.4  4 pupils have 2 marks.
                                                         [ Q 1.4 ]
    
         1.5  The frquency of 6 marks is 2.
                                                         [ Q 1.5 ]
    
         1.6  1, 3 and 5 marks have a
                frequency of 3.
                                                         [ Q 1.6 ]
    
         1.7  The lowest frequency is 1 and
                that is the frequency of 8 marks.
                                                         [ Q 1.7 ]
    
         1.8  7 marks have the highest
                frequency which is 5.
                                                         [ Q 1.8 ]
  
Antwoorde  / Answers  2  
  
    
         2.1  A = ┼┼┼┼  en B = 5
                                                         [ V 2.1 ]
    
         2.2  Die data is diskreet. Die dobbelsteen
                vertoon net heelgetalle.
                                                         [ V 2.2 ]
    
         2.3  Die frekwensie van 1 = 3
                                                         [ V 2.3 ]
    
         2.4  Die getal 3 het 'n frekwensie van 4
                                                         [ V 2.4 ]
    
         2.5  Getal 2 verskyn die meeste omdat
                sy frekwensie die hoogste is.
                                                         [ V 2.5 ]
    
         2.6  Getal 5 verskyn die minste omdat
                sy frekwensie die laagste is.
                                                         [ V 2.6 ]
    
         2.1  A = ┼┼┼┼  and B = 5.
                                                         [ Q 2.1 ]
    
         2.2  The data is discrete.
                The die shows only whole numbers.
                                                         [ Q 2.2 ]
    
         2.3  The frequency of 1 = 3.
                                                         [ Q 2.3 ]
    
         2.4  The number 3 has a frequency of 4.
                                                         [ Q 2.4 ]
    
         2.5  Number 2 appeared most because
                it has the highest frequency.
                                                         [ Q 2.5 ]
    
         2.6  Number 5 appeared least because
                it has the lowest frequency.
                                                         [ Q 2.6 ]
  
Antwoorde  / Answers  3  
  
    
     Massa / Mass      Telling / Tally      Frekwensie, f / Frequency, f
    45 ─ 49     ┼┼┼┼  ┼┼┼┼  │     11
    50 ─ 54     ┼┼┼┼  │     6
    55 ─ 59     ││││     4
    60 ─ 64     ┼┼┼┼  │     6
    65 ─ 69     │││     3
    70 ─ 74     ┼┼┼┼     5
                                                                                                                                       Σf = 35
  
                                                                                                                                       [ V 3.1 ]
    
         3.2  Die 45 is die onderste of laagste
                klasgrens en die 49 is die
                boonste of hoogste klasgrens.
                Enige massa tussen 45 en 49,
                beide ingesluit, hoort in die klas.
                                                         [ V 3.2 ]
    
         3.3  Die 11 is die frekwensie van
                daardie klas, 45 - 49.
                Dit beteken dat daar 11
                massas groter as 44 en
                kleiner as 50 is.
                                                         [ V 3.3 ]
    
         3.4  Die laagste of onderste klasgrens
                is 45 en die boonste of hoogste
                klasgrens is 48.
                                                         [ V 3.4 ]
    
         3.5  Frekwensie van klas 65 - 69 is 3.
                                                         [ V 3.5 ]
    
         3.6  Frekwensie van klas 55 - 59 is 4.
                                                         [ V 3.6 ]
    
         3.7  Die laagste frekwensie is 3
                en klas 65 - 69 het daardie
                frekwensie.
                                                         [ V 3.7 ]
    
         3.8  Die hoogste frekwensie is 11
                en klas 45 - 49 het daardie
                frekwensie.
                                                         [ V 3.8 ]
    
         3.9  Ja omdat die massa korrek tot
                die naaste kilogram aangeteken
                is sodat die data uit heelgetalle
                bestaan. Geen massa van
                bv. 46,345 kg, alhoewel moontlik,
                is aangeteken nie.
                                                         [ V 3.9 ]
    
         3.2  The 45 is the bottom or lower
                boundary and the 49 is the
                upper or higher boundary.
                Any mass between 45 and 49,
                both included, belongs to this class.
                                                         [ Q 3.2 ]
    
         3.3  The 11 is the frequency of that
                class, 45 - 49.That means that there
                are 11 masses greater than 44 and
                smaller than 50
               
                                                         [ Q 3.3 ]
    
         3.4  Lower/bottom boundary 45 and
                upper/higher 49.
               
                                                         [ Q 3.4 ]
    
         3.5  Frequency of class 65 - 69 is 3.
                                                         [ Q 3.5 ]
    
         3.6  Frequency of class 55 - 59 is 4.
                                                         [ Q 3.6 ]
    
         3.7  The smallest frequency is 3 and
                that is the frequency of class 65 - 69.
               
                                                         [ Q 3.7 ]
    
         3.8  The highest frequency is 11 and
                that is the frequency of class 45 - 49.
               
                                                         [ Q 3.8 ]
    
         3.9  Yes because the mass is noted correct
                to the nearest kilogram, the data
                consists of whole numbers. No mass
                of e.g. 46,345 kg is noted,
                although it can exist.
  
                                                         [ Q 3.9 ]
  
Antwoorde  / Answers  4  
  
    
         4.1  
  
     Hoogte / Height      Telling / Tally      Frekwensie, f / Frequency, f
    1,0 ─ 1,9     ┼┼┼┼  ││     7
    2,0 ─ 2,9     ┼┼┼┼  ┼┼┼┼  │     11
    3,0 ─ 3,9     ┼┼┼┼  ┼┼┼┼  │││     13
    4,0 ─ 4,9     ┼┼┼┼  │     6
    5,0 ─ 5,9     │││     3
                                                                                                                       Σf = 35

                                                                                                                             [ V / Q 4.1 ]
    
         4.2  Klas 3,0 - 3,9 het die
                meeste bome, 13
                                                         [ V 4.2 ]
    
         4.3  7 + 11 = 18 bome is
                korter as 2 m.
                                                         [ V 4.3 ]
    
         4.4  6 + 3 = 9 bome is
                langerer as 4 m.
                                                         [ V 4.4 ]
    
         4.2  Class 3,0 - 3,9 has the most
                trees, 13.
                                                         [ Q 4.2 ]
    
         4.3  7 + 11 = 18 trees
                are shorter than 2 m.
                                                         [ Q 4.3 ]
    
         4.4  6 + 3 = 9 trees
                are taller than 4 m.
                                                         [ Q 4.4 ]
  
Antwoorde  / Answers  5  
  
    
         5.1  
  
     Lengte / Height      Telling / Tally      Frekwensie, f / Frequency, f
    1,00 ─ 1,19     │││     3
    1,20 ─ 1,39     ┼┼┼┼  ││     7
    1,40 ─ 1,59     ┼┼┼┼  ┼┼┼┼     10
    1,60 ─ 1,79     ┼┼┼┼  ┼┼┼┼  ┼┼┼┼  │     16
    1,80 ─ 2,00     ││││     4
                                                                                                                       Σf = 40

                                                                                                                             [ V / Q 5.1 ]
    
         5.2  Kleinste lengte = 1,12 m en
                grootste lengte = 1,84 m
                                                         [ V 5.2 ]
    
         5.3  Klas 1,00 - 1,19 het die
                laagste frekwensie, 3
                                                         [ V 5.3 ]
    
         5.4  3 + 7 = 10 leerlinge is
                korter as 1,40 m
                                                         [ V 5.4 ]
    
         5.5  1,60 maar kortste leerling
                in die klas, volgens die tabel,
                is 1,62 m.
                                                         [ V 5.5 ]
    
         5.6  20 leerlinge is langer as 1,59 m.
  
                                           20            100
                Persentasie  =  ───  X  ─────  %
                                           40              1
                                    =  50  %
                                                         [ V 5.6 ]
    
         5.2  Smallest length = 1,12 m and
                greatest length = 1,84 m..
                                                         [ Q 5.2 ]
    
         5.3  Class 1,00 - 1,19 has the smallest
                frequency, 3.
                                                         [ Q 5.3 ]
    
         5.4  3 + 7 = 10 pupils
                are shorter than 1,40 m.
                                                         [ Q 5.4 ]
    
         5.5  1,60 but according to the
                tabel the shortest pupil
                is 1,62 m.
                                                         [ Q 5.5 ]
    
         5.6  20 pupils are taller than 1,59 m.
  
                                          20            100
                Percentage  =  ───  X  ─────  %
                                          40              1
                                    =  50  %
                                                         [ Q 5.6 ]
  
Antwoorde  / Answers  6  
  
    
         6.1  
  
     Punt / Mark      Telling / Tally      Frekwensie, f / Frequency, f
    0 ─ 19     │││     3
    20 ─ 39     ┼┼┼┼  │     6
    40 ─ 59     ┼┼┼┼  ┼┼┼┼  ┼┼┼┼  │     16
    60 ─ 79     ┼┼┼┼  │││     8
    80 ─ 100     ││     2
                                                                                                                       Σf = 35

                                                                                                                             [ V / Q 6.1 ]
    
         6.2  Laagste punt = 12 en
                hoogste punt = 96
                                                         [ V 6.2 ]
    
         6.3  26 leerlinge het meer
                as 39 punte.
                                                         [ V 6.3 ]
    
         6.4  2 leerlinge het meer
                as 79 punte.
                                                         [ V 6.4 ]
    
         6.5  24 leerlinge se punte is groter
                as 39 en kleiner as 80
                                           24        100
                Persentasie  =  ─── X ────  %
                                           35          1
                                     =  68,56  %
                                                         [ V 6.5 ]
    
         6.6  omvang  =  maksimum  ─  minimum
                               =  96  ─  12
                               =  84
                                                         [ V 6.6 ]
    
         6.2  Smallest mark = 12 and
                highest mark = 96.
                                                         [ Q 6.2 ]
    
         6.3  26 pupils have more than
                39 marks.
                                                         [ Q 6.3 ]
    
         6.4  2 pupils have more than
                79 marks.
                                                         [ Q 6.4 ]
    
         6.5  24 pupils have marks more than
                39 and less than 80.
                                          24          100
                Percentage  =  ───  X  ────  %
                                          35            1
                                    =  68,56  %
                                                         [ Q 6.5 ]
    
         6.6  range  =  maximum  ─  minimum
                           =  96  ─  12
                           =  84
                                                         [ Q 6.6 ]
  
Antwoorde  / Answers  7  
  
    
         7.1  
  
  

  
                                                                                                                             [ V / Q 7.1 ]
  
Antwoorde  / Answers  8  
  
    
         8.1  
  
  

  
                                                                                                                             [ V / Q 8.1 ]
  
Antwoorde  / Answers  9  
  
    
         9.1  
  
  

  
                                                                                                                             [ V / Q 9.1 ]
  
Antwoorde  / Answers  10  
  
    
         10.1  
  
     LMI / BMI      Telling / Tally      Frekwensie, f / Frequency, f
    x < 18,5     ││││     4
    18,5 < x < 25     ┼┼┼┼  ┼┼┼┼  ┼┼┼┼  ┼┼┼┼     20
    25 < x < 30     ┼┼┼┼  ┼┼┼┼     10
    x > 30     ││││     4
                                                                                                                       Σf = 40

                                                                                                                             [ V / Q 10.1 ]
    
         10.2  Laagste punt = 12 en
                  hoogste punt = 96
                                                         [ V 10.2 ]
    
         10.2  Lowest mark = 12 and
                  highest mark = 96
                                                         [ V 10.2 ]
  
Antwoorde  / Answers  11  
  
    
                                                      943,4 ????
         11.1  Gemiddelde / Mean  =  ──────
                                                          40
  
                                                =  23,6                                                            [ V / Q 11.1 ]
    
         11.2  
  
     LMI / BMI      Telling / Tally      Frekwensie, f / Frequency, f
    17,0 ─ 18,5     ││││     4
    18,5 ─ 25,0     ┼┼┼┼  ┼┼┼┼  ┼┼┼┼  ┼┼┼┼     20
    25,0 ─ 30,0     ┼┼┼┼  ┼┼┼┼     10
    30,0 ─ 40,0     ││││     4
                                                                                                                       Σf = 40

                                                                                                                           [ V / Q 11.2 ]
    
         11.3  Die gemiddelde gewig val in
                  die normale gewig kategorie.
                                                         [ V 11.32 ]
    
         11.4.1  6 leerlige is onder gewig.
                                                 6        100
                     Persentasie  =  ─── X ─── %
                                               40          1
                                          =  15 %
                                                       [ V 11.4.1 ]
    
         11.4.2  20 leerlige is normale gewig.
                                               20        100
                     Persentasie  =  ─── X ─── %
                                               40          1
                                          =  50 %
                                                       [ V 11.4.2 ]
    
         11.4.3  10 leerlige is geset.
                                               10        100
                     Persentasie  =  ─── X ─── %
                                               40          1
                                          =  25 %
                                                       [ V 11.4.3 ]
    
         11.4.4  4 leerlige is geset.
                                                 4        100
                     Persentasie  =  ─── X ─── %
                                               40          1
                                          =  10 %
                                                       [ V 11.4.4 ]
    
         11.3  The mean weight falls in the
                  normal weight category.
                                                         [ Q 11.3 ]
    
         11.4.1  6 pupils are under weight.
                                                 6            100
                      Percentage  =  ───  X  ──── %
                                                40             1
                                          =  15 %
                                                         [ Q 11.4.1 ]
    
         11.4.2  20 pupils have normal weight.
                                                20          100
                      Percentage  =  ───  X  ──── %
                                                40             1
                                          =  50 %
                                                         [ Q 11.4.2 ]
    
         11.4.3  10 pupils are obese.
                                                10          100
                      Percentage  =  ───  X  ──── %
                                                40             1
                                          =  25 %
                                                         [ Q 11.4.3 ]
    
         11.4.4  4 pupils are over weight.
                                                 4            100
                      Percentage  =  ───  X  ──── %
                                                40             1
                                          =  10 %
                                                         [ Q 11.4.4 ]
  
Antwoord  / Answer  12  
  
  
  
    
         12.1   12   13   18   23   29   32   34   37   38   42   43   45   45   47   52   54   54   54
                  56   56   57   58   58   59   59   61   62   63   63   64   67   74   78   86   96
                                                                                                                                [ V / Q 12.1 ]
    
         12.2  kleinste / lowest  =  12  en / grootste / highest  =  96                                 [ V / Q 12.2 ]
    
         12.3  omvang / range  =  grootste / highest  ─  kleinste / lowest
                                           =  96  ─  12
                                           =  84                                                                             [ V / Q 12.3 ]
    
                                                                            som van al die punte / sum of all the marks
         12.4  Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
                                                                                aantal puntee / number of marks
  
                                                                            1789
                                                                      =  ─────
                                                                             35
  
                                                                      =  51,114                                             [ V / Q 12.4 ]
    
         12.5  Die mediaan is die waarde presies in die middel / 
                 The median is the value exactly in the middle.
  
                 Die mediaan / The median  =  54                                                               [ V / Q 12.5 ]
    
         12.6  Die modus is die waarde wat die meeste voorkom. / 
                 The mode is the value that has the highest frequency / that appears most often.
  
                 Die modus  =  54  . . . kom die meeste, drie keer, voor  / 
                 The mode  =  54  . . . appears most often, three times
                                                                                                                                [ V / Q 12.6 ]
  
Antwoord  / Answer  13  
  
    
         13.1   31   32   33   37   38   42   42   42   45   46   53   55   58   61   67           [ V / Q 13.1 ]
    
           
     13.2      Stingel / Stem      Blare / Leaves
                       3     1   2   3   7   8
                       4     2   2   2   5   6
                       5     3   5   8
                       6     1   7

                                                                                                                           [ V / Q 13.2 ]
    
         13.3  Minimum  =  31  ;   Maksimum / Maximum  =  67                                 [ V / Q 13.3 ]
    
         13.4  Omvang / Range  =  Maksimum / Maximum  ─  Minimum
                                             =  67  ─  31
                                             =  36                                                                      [ V / Q 13.4 ]
    
                                                                            som van al die punte / sum of all the marks
         13.5  Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
                                                                                aantal punte / number of marks
  
                                                                            682
                                                                      =  ─────
                                                                             15
  
                                                                      =  45,467                                      [ V / Q 13.5 ]
    
         13.6  Mediaan / Median  =  42                                                                    [ V / Q 13.6 ]
    
         13.7  Modus / Mode  =  42                                                                         [ V / Q 13.7 ]
  
Antwoord  / Answer  14  
  
    
         14.1   43   46   47   49   51   53   53   53   55   55   55   55   55   57   59   60   66
                  66   70   78                                                                                       [ V / Q 14.1 ]
    
           
     14.2      Stingel / Stem      Blare / Leaves
                       4     3   6   7   9
                       5     1   3   3   3   5   5   5   5   5   7   9
                       6     0   6   6
                       7     0   8
                                                                                                                           [ V / Q 14.2 ]
    
         14.3  Minimum  =  43  ;   Maksimum / Maximum  =  78                                 [ V / Q 14.3 ]
    
         14.4  Omvang / Range  =  Maksimum / Maximum  ─  Minimum
                                             =  78  ─  43
                                             =  35                                                                      [ V / Q 14.4 ]
    
                                                                            som van al die punte / sum of all the marks
         14.5  Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
                                                                                aantal punte / number of marks
  
                                                                            1 126
                                                                      =  ─────
                                                                             20
  
                                                                      =  5,300                                      [ V / Q 14.5 ]
    
         14.6                                    55 + 55
                 Mediaan / Median  =  ───────
                                                        2
  
                                              =  55                                                                     [ V / Q 14.6 ]
    
         14.7  Modus / Mode  =  55                                                                          [ V / Q 14.7 ]
  
Antwoord  / Answer  15  
  
    
         15.1   5   6   9   12   12   14   14   14   14   16   17   17   25   25   27   30
                                                                                                                           [ V / Q 15.1 ]
    
         15.2  Minimum  =  5  ;   Maksimum / Maximum  =  30                                 [ V / Q 15.2 ]
    
         15.3  Omvang / Range  =  Maksimum / Maximum  ─  Minimum
                                             =  30  ─  5
                                             =  25                                                                      [ V / Q 15.3 ]
    
                                                                            som van al die punte / sum of all the marks
         15.4  Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
                                                                                aantal punte / number of marks
  
                                                                            257
                                                                      =  ─────
                                                                             16
  
                                                                      =  16,063                                      [ V / Q 15.4 ]
    
         15.5                                    14 + 14
                 Mediaan / Median  =  ───────
                                                        2
  
                                              =  14                                                                     [ V / Q 15.5 ]
    
         15.6  Modus / Mode  =  14                                                                          [ V / Q 15.6 ]
  
Antwoord  / Answer  16  
  
         Omvang / Range  =  Maksimum / Maximum  ─  Minimum / Minimum
                              18  =  23  ─  a
                                a  =  23  ─  18
                                a  =  5
  
                                                                   som van al die punte / sum of all the marks
         Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
                                                                        aantal punte / number of marks
  
                                                                    126
                                                         b  =  ─────
                                                                      9
  
                                                             =  14
  
         c  =  126  ─  (5   7   9   14   16   17   20   23)
           =  15
         a = 5 ;   b  =  14   en / and   c  =  15
                                                                                                                             [ V / Q 16 ]
  
Antwoord  / Answer  17  
  
         Omvang / Range  =  Maksimum / Maximum  ─  Minimum / Minimum
                                 c  =  88  ─  35
                                     =  53
  
                                                                   som van al die punte / sum of all the marks
         Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
                                                                        aantal punte / number of marks
  
                                                                    880
                                                         d  =  ─────
                                                                    16
  
                                                             =  55
  
                                           49 + b
         Mediaan / Median  =  ─────      . . .  ewe aantal waardes  /  even number of values              
                                                2
  
                                           49 + b
                                50  =  ─────      . . .  ewe aantal waardes  /  even number of values              
                                                2
  
                                b  =  2 X 50  ─  49
                                    =  51
  
         a  =  880  ─  (35 + 36 + 38 + 39 + 43 + 45 + 49 + 51 + 53 + 55 + 61 + 68 + 73 + 79 + 87 + 88)
             =  39
         a = 39 ;   b  =  51 ;   c  =  53   en / and   d  =  55
                                                                                                                             [ V / Q 17 ]
  
Antwoord  / Answer  18  
  
    
         18.1  Gerangskik / Arranged   :    7    8    9    10    11    11    14          [ V / Q 18. ]
  
  
    
         18.2  Minimum = 7 ;      Maksimum / Maximum =  14                           [ V / Q 18. ]
  
  
    
         18.3  Omvang / Range  =  Maksimum / Maximum   ─   Minimum
  
                                               =  14  ─  7
  
                                               =  7                                                                 [ V / Q 18. ]
  
    
                                                       7 + 8 + 9 + 10 + 11 + 11 + 14             70
         18.4  Gemiddelde / Mean  =  ───────────────────     =  ─── 
                                                                          7                                       7
  
  
                                                    =  10                                                          [ V / Q 18. ]
  
    
         18.5  Mediaan / Median  =  10  . . . middelste waarde  /  midmost value
  
                                                                                                                       [ V / Q 18. ]
  
  
    
         18.6  Modus = 11  (2 waardes)    /  Mode   =  11     (2 values)             [ V / Q 18. ]
  
  
    
         18.7  3 dae   /   3 days    gemiddelde / mean =  10                              [ V / Q 18. ]
  
  
    
         18.8  1 dag   /   1 day    modus / mode =  11                                        [ V / Q 18. ]
  
  
    
         18.9  3 dae   /   3 days    mediaan / median =  10                                [ V / Q 18. ]
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
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