WISKUNDIGE GELETTERDHEID
NOG OEFENINGE

Statistiek.

MATHEMATICAL LITERACY
MORE EXERCISES

Statistics.

Vraag  / Question  1

Die Telling en Frekensie tabel hieronder,
stel die punte uit 10 vir 'n taak oor
Wiskundige Geletterheid voor.

 Punt Telling Frekwensie, f 1 │││ A 2 B 4 3 │││ 3 4 ││ 2 5 │││ 3 6 ││ 2 7 C D 8 │ 1 9 ││ 2

1.1  Skryf die waardes van
A, B, C en D neer.
[ A 1.1 ]

1.2  Is hierdie data diskrete of
kontinue data? Verduidelik.
[ A 1.2 ]

1.3  Wat is die swakste punt en
wat is die beste punt?
[ A 1.3 ]

1.4  Hoeveel leerlinge het 2 punte
gekry?
[ A 1.4 ]

1.5  Wat is die frekwensie van
6 punte?
[ A 1.5 ]

1.6  Watter punt(e) het 'n frekwensie
van 3?
[ A 1.6 ]

1.7  Watter punt(e) het die laagste
frekwensie en wat is hierdie
frekwensie?
[ A 1.7 ]

1.8  Watter punt(e) het die hoogste
frekwensie en wat is hierdie
frekwensie?
[ A 1.8 ]
The Tally and Frequency table
below represents the marks out
of 10 for a task in Mathematical Literacy.

 Mark Tally Frequency, f 1 │││ A 2 B 4 3 │││ 3 4 ││ 2 5 │││ 3 6 ││ 2 7 C D 8 │ 1 9 ││ 2

1.1  Write down the values of
A, B, C and D.
[ A 1.1 ]

1.2  Is this data discrete or
continuous? Explain.
[ A 1.2 ]

1.3  What is the lowest mark and
which is the best mark?
[ A 1.3 ]

1.4  How many pupils have 2 marks?

[ A 1.4 ]

1.5  What is the frequency of
6 marks?
[ A 1.5 ]

1.6  Which mark(s) has a frequency
of 3?
[ A 1.6 ]

1.7  Which mark(s) has the lowest
frequency and what is this
frequency?
[ A 1.7 ]

1.8  Which mark(s) has the highest
frequency and what is thhs
frequency?
[ A 1.8 ]

Vraag  / Question  2

Die Telling en Frekensie tabel hieronder,
stel die getalle wat verkry is as 'n
dobbelsteen 'n aantal kere gerol word.

 Getal Telling Frekwensie, f 1 │││ 3 2 A B 3 ││││ 4 4 │││ 3 5 ││ 2 6 │││ 3
Σf = 20

2.1  Skryf die waardes van
A en B neer.
[ A 2.1 ]

2.2  Is hierdie data diskrete of
kontinue data? Verduidelik.
[ A 2.2 ]

2.3  Wat is die frekwensie van 1?
[ A 2.3 ]

2.4   4 is die frekwensie van
watter getal(le)?
[ A 2.4 ]

2.5  Watter getal kom die meeste
kere voor? Verduidelik.
[ A 2.5 ]

2.6  Nommer 5 kom die minste
kere voor. Verduidelik.
[ A 2.6 ]
The Tally and Frequency table below
represents the numbers obtained when
a die was rolled a certain number of times.

 Number Tally Frequency, f 1 │││ 3 2 A B 3 ││││ 4 4 │││ 3 5 ││ 2 6 │││ 3
Σf = 20

2.1  Write down the values of
A and B.
[ A 2.1 ]

2.2  Is this data discrete or
continuous? Explain.
[ A 2.2 ]

2.3  What is the frequency of 1?
[ A 2.3 ]

2.4   4 is the frequency of
which number(s)?
[ A 2.4 ]

2.5  Which number appeared
most? Explain.
[ A 2.5 ]

2.6  Number 5 appeared least
often. Explain.
[ A 2.6 ]

Vraag  / Question  3

Die massa van 35 leerlinge in 'n klas
is bepaal en die volgende massas
word aangeteken : 61, 45, 73, 46,
52, 66, 74, 46, 57, 61, 49, 45, 45,
62, 67, 64, 58, 52, 49, 63, 55, 52,
47, 68, 71, 49, 58, 52, 63, 72, 53,
49, 47, 54, 74

3.1  Maak 'n frekwensietabel van
die data en gebruik 6
klasse, begin met 45 - 49,
50 - 54, en eindig met
70 - 74. Gebruik 3 kolomme
getiteld massa, telling
en frekwensie, f.
[ A 3.1 ]

3.2  Verduidelik die betekenis van
die getalle 45 - 49 in
die massakolom.
[ A 3.2 ]

3.3  Verduidelik die betekenis van
die getal 11 in
die frekwensiekolom.
[ A 3.3 ]

3.4  Skryf die klasgrense van die
eerste klas (die klas
bo-aan die tabel) neer.
[ A 3.4 ]

3.5  Wat is die frekwensie van
die klas 65 - 69 ?
[ A 3.5 ]

3.6  Watter klas het 'n
frekwensie van 4?
[ A 3.6 ]

3.7  Wat is die laagste frekwensie en
watter klas het die frekwensie?
[ A 3.7 ]

3.8  Wat is die hoogste frekwensie en
watter klas het die frekwensie?
[ A 3.8 ]

3.9  Die data in bostaande lys is diskreet.
Stem jy saam? Verduidelik.
[ A 3.9 ]
The mass of 35 pupils in a class was
determined and the following masses
were noted : 61, 45, 73, 46,
52, 66, 74, 46, 57, 61, 49, 45, 45,
62, 67, 64, 58, 52, 49, 63, 55, 52,
47, 68, 71, 49, 58, 52, 63, 72, 53,
49, 47, 64, 74

3.1  Make a frequency table of the data
and use 6 classes,starting with
45 - 49, 50 -54, and ending with
70 - 74. Use 3 columns titled mass,
tally and frequency, f.

[ A 3.1 ]

3.2  Explain the meaning of the
numbers 45 - 49 in
the mass column.
[ A 3.2 ]

3.3  Explain the meaning of the
number 11 in the
frequency column.
[ A 3.3 ]

3.4  Write down the class boundaries
for the first class, i.e. the class at
the top of the table.
[ A 3.4 ]

3.5  What is the frequency of the
class 65 - 69?
[ A 3.5 ]

3.6  Which class has a frequency of 4?
[ A 3.6 ]

3.7  What is the lowest frequency and
which class has this frequency?
[ A 3.7 ]

3.8  What is the highest frequency and
which class has this frequency?
[ A 3.8 ]

3.9  The data in the list above is discrete.
Do you agree? Explain.
[ A 3.9 ]

Vraag  / Question  4

'n Boer meet die hoogte van 50
eucalyptus bome op sy plaas en
noteer die hoogtes as volg :

A farmer measures the height of
50 eucalyptus trees on his farm
and records it as follows :

 2,4 5,3 2,6 3,8 4,4 3,8 1,3 2,5 3,5 2,9 5,1 4,7 5,3 1,4 3,8 4,1 4,6 3,9 2,4 3,1 4,6 4,7 3,8 5,1 3,6 4,8 2,6 2,7 5,1 3,3 4,4 2,0 1,4 2,4 3,4 1,6 5,2 1,7 5,3 4,5 2,2 3,4 5,3 3,6 2,4 1,7 3,5 5,4 4,3 4,8

4.1  Maak 'n frekwensietabel van
die data en gebruik 5
klasse, begin met 1,0 - 1,9,
2,0 - 2,9, en eindig met
5,0 - 5,9. Gebruik 3 kolomme
getiteld hoogte, (m), telling
en frekwensie, f.
[ A 4.1 ]

4.2  Watter klas het die
meeste bome?
[ A 4.2 ]

4.3  Hoeveel bome is korter
as 2,0 m?
[ A 4.3 ]

4.4  Hoeveel bome is langer
as 4,0 m?
[ A 4.4 ]

4.1  Make a frequency table of the data
and use 5 classes,starting with
1,0 - 1,9, 2,0 -2,9, and ending with
5,0 - 5,9. Use 3 columns titled height (m),
tally and frequency, f.

[ A 4.1 ]

4.2  Which class contains the most trees?

[ A 4.2 ]

4.3  How many trees are shorter
than 2,0 m?
[ A 4.3 ]

4.4  How many trees are taller
than 4,0 m?
[ A 4.4 ]

Vraag  / Question  5

Die lengte van 40 Graad 10 leerlinge
is bepaal en as volg noteer :

The lengths of 40 Grade 10 pupils
were determined and noted as follows :

1,12        1,32        1,92        1,25        1,63        1,83        1,15        1,23        1,42        1,63
1,53        1,36        1,78        1,57        1,76        1,81        1,18        1,28        1,37        1,72
1,42        1,55        1,67        1,73        1,45        1,73        1,58        1,62        1,73        1,52
1,63        1,58        1,69        1,78        1,37        1,52        1,73        1,84        1,76        1,63

5.1  Maak 'n frekwensietabel van
die data en gebruik 5
klasse, begin met 1,00 - 1,19,
1,20 - 1,29, en eindig met
1,90 - 1,99. Gebruik 3 kolomme
getiteld lengte, (m), telling
en frekwensie, f.
[ A 5.1 ]

5.2  Skryf die kleinste en grootste
hoogte neer.
[ A 5.2 ]

5.3  Watter goep het die
kleinste frekwensie?
[ A 5.3 ]

5.4  Hoeveel leerlinge is
korter as 1,40 m?
[ A 5.4 ]

5.5  Wat is die kleinste lengte van
die groep met die meeste leerlinge?
[ A 5.5 ]

5.6  Watter persentasie leerlinge is
langer as 1,59 m?
[ A 5.6 ]

5.1  Make a frequency table of the data
and use 5 classes,starting with
1,00 - 1,19, 1,20 -1,29, and ending with
1,90 - 1,99. Use 3 columns titled length (m),
tally and frequency, f.

[ A 5.1 ]

5.2  Write down the shortest and
the tallest length.
[ A 5.2 ]

5.3  Which class has the
lowest frequency?
[ A 5.3 ]

5.4  How many pupils are shorter
than 1,40 m?
[ A 5.4 ]

5.5  What is the smallest length of
the class with the most pupils?
[ A 5.5 ]

5.6  What percentage of the
pupils are taller than 1,59 m?
[ A 5.6 ]

Vraag  / Question  6

Die punte wat vir 'n toets bepaal is,
word hieronder getoon :

The marks ontained for a test is
given below :

54        63        42        67        12        86        34        57        54        78        38        43
52        59        45        32        23        37        47        58        63        59        64        61
74        96        45        62        58        56        18        29        13        56        54

6.1  Maak 'n frekwensietabel van
die data en gebruik 5
klasse, begin met 0 - 19,
20 - 39, en eindig met
80 - 100. Gebruik 3 kolomme
getiteld punt, telling
en frekwensie, f.
[ A 6.1 ]

6.2  Skryf die laagste en
die hoogste punt neer.
[ A 6.2 ]

6.3  Hoeveel leerlinge het
minder as 40 punte?
[ A 6.3 ]

6.4  Hoeveel leerlinge het
meer as 80 punte?
[ A 6.4 ]

6.5  Watter persentasie van die
leerlinge het tussen 39 en 80 punte?
[ A 6.5 ]

6.6  Bereken die omvang van die
data.
[ A 6.6 ]

6.1  Make a frequency table of the data
and use 5 classes,starting with
0 - 19, 20 - 39, and ending with
80 - 100. Use 3 columns titled mark,
tally and frequency, f.

[ A 6.1 ]

6.2  Write down the lowest and
the highest mark.
[ A 6.2 ]

6.3  How many pupils have less
than 40 marks?
[ A 6.3 ]

6.4  How many pupils have more
than 80 marks?
[ A 6.4 ]

6.5  What percentage of the pupils have
more than 39 and less than 80 marks?
[ A 6.5 ]

6.6  Calculate the rangge of the data.

[ A 6.6 ]

Vraag  / Question  7

7.1  Maak 'n staafgrafiek van
die data in Vraag 1.
[ A 7.1 ]

7.1  Make a bargraph of the
data in Question 1.
[ A 7.1 ]

Vraag  / Question  8

8.1  Maak 'n staafgrafiek van
die data in Vraag 2.
[ A 8.1 ]

8.1  Make a bargraph of the
data in Question 2.
[ A 8.1 ]

Vraag  / Question  9

9.1  Maak 'n histogram van
die data in Vraag 5.
[ A 9.1 ]

9.1  Make a histogram of the
data in Question 5.
[ A 9.1 ]

Vraag  / Question  10

Die ouderdom, in jare, van graad 10
leerlinge word hieronder getoon :

The age, in years, of Grade 10
pupils are given below :

12        17        15        16        15        14        17        14        13        18
15        19        15        19        16        19        16        14        20        14
17        20        16        19        14        17        18        21        18        13

10.1  Maak 'n frekwensietabel van
die data en gebruik 4
klasse, begin met 11,5 - 14,5 ,
14,5 - 17,5 , 17,5 - 20,5 en eindig met
80 - 100. Gebruik 3 kolomme
getiteld punt, telling
en frekwensie, f.
[ A 10.1 ]

10.2  Skryf die laagste en
die hoogste punt neer.
[ A 10.2 ]

10.1  Make a frequency table of
the data and use 5
classes, beginning with 0 - 19,
20 - 39, and stopping with
80 - 100. Use 3 columns
titled mark, tally
and frequency, f.
[ A 10.1 ]

10.2  Write down the lowest and the
highest mark.
[ A 10.2 ]

Vraag  / Question  11

Die LMI (Liggaammassa indeks) van
'n persoon word gebruik om te bepaal
in watter kategorie die gewig van die
persoon val. Die LMI van 'n aantal
leerlinge word bepaal en word hieronder
getoon :

The BMI (Bodymass index) of a
person is used to classify the weight
of the person. The BMI of a number
of pupils is determined and
is given below :

30,1        23,5        21,5        18,4        28,1        22,9        20,8        21,2
26,5        24,2        18,4        18,3        26,0        22,6        19,6        19,7
28,4        22,5        20,2        18,4        23,5        21,6        18,6        28,3
25,3        26,1        19,8        24,0        23,8        19,3        30,8        17,3
24,3        26,1        18,3        19,6        31,2        27,8        30,4        26,5

11.1  Bepaal die gemiddelde gewig
van die leerlinge.
[ A 11.1 ]

11.2  Maak 'n frekwensietabel van
die data en gebruik 4
klasse, begin met 17, - 18,5 ,
18,5 - 25,0 , 25,0 - 30,0 en eindig met
30,0 - 40,0. Gebruik 3 kolomme
getiteld LMI, telling
en frekwensie, f.
[ A 11.2 ]

11.3  In watter klas val die gemiddelde
gewig van die leerlinge?
[ A 11.3 ]

11.4  Bepaal die persentasie van die
leerlinge wat

11.4.1  ondergewig is.            [ A 11.4.1 ]

11.4.2  normale gewig het.     [ A 11.4.2 ]

11.4.3  geset is.                      [ A 11.4.3 ]

11.4.4  oorgewig is.                [ A 11.4.4 ]

11.1  Determine the mean weight
of the pupils.
[ A 11.1 ]

11.2  Make a frequenct table of the
data and use 4 classes, starting
with 17,0 - 18,5, 18,5 - 25,0,
25,0 - 30,0 and stopping with
30,0 - 40,0. Use 3 columns
titled BMI, tally and frequency, f

[ A 11.2 ]

11.3  In which class does the mean
weight of the pupils fall?
[ A 11.3 ]

11.4  Determine the percentage of
the pupils who

11.4.1  are under weight.         [ A 11.4.1 ]

11.4.2  have normal weight.     [ A 11.4.2 ]

11.4.3  are obese.                    [ A 11.4.3 ]

11.4.4  are over weight.           [ A 11.4.4 ]

Vraag  / Question  12

Die punte wat vir 'n toets bepaal is,
word hieronder getoon :

The marks ontained for a test is
given below :

54        63        42        67        12        86        34        57        54        78        38        43
52        59        45        32        23        37        47        58        63        59        64        61
74        96        45        62        58        56        18        29        13        56        54

12.1  Rangskik die data in
stygende volgorde.
[ A 12.1 ]

12.2  Skryf die kleinste en die
grootste punt neer.
[ A 12.2 ]

12.3  Bereken die omvang van
die punte.
[ A 12.3 ]

12.4  Bereken die rekenkundige
gemiddelde van die punte.
[ A 12.4 ]

12.5  Bereken die mediaan.
[ A 12.5 ]

12.5  Bereken die modus.
[ A 12.6 ]

12.1  Arrange the marks in
ascending order.
[ A 12.1 ]

12.2  Write down the lowest and the
highest mark.
[ A 12.2 ]

12.3  Calculate the range of
the marks.
[ A 12.3 ]

12.4  Calculate the mean of
the marks.
[ A 12.4 ]

12.5  Calculate the median.
[ A 12.5 ]

12.6  Calculate the mode.
[ A 12.6 ]

Vraag  / Question  13

Beskou die onderstaande datastel.

Study the data set shown below.

38        42        53        31        37        42        58        32        45        61        55        42
67        33        46

13.1  Rangskik die data in
stygende volgorde.
[ A 13.1 ]

13.2  Stel hierdie data met 'n
stingel-en-blaar tabel voor.
[ A 13.2 ]

13.3  Skryf die minimum en
maksimum waardes neer.
[ A 13.3 ]

13.4  Bereken die omvang
van die data.
[ A 13.4 ]

13.5  Bereken die rekenkundige
gemiddelde van die data.
[ A 13.5 ]

13.6  Bepaal die mediaan vir die data.
[ A 13.6 ]

13.7  Bepaal die modus van die data.
[ A 13.7 ]

13.1  Arrange the data in
ascending order.
[ A 13.1 ]

13.2  Represent the data with
a stem and leave tabel.
[ A 13.2 ]

13.3  Write down the minimum
and maximum of the data.
[ A 13.3 ]

13.4  Calculate the range of
the data.
[ A 13.4 ]

13.5  Calculate the arithmetic mean of
the data.
[ A 13.5 ]

13.6  Determine the median for the data.
[ A 13.6 ]

13.7  Determine the mode for the data.
[ A 13.7 ]

Vraag  / Question  14

Die massa van 20 leerlinge in 'n klas
word bepaal en die volgende massas
word aangeteken :
55   43   55   57   59   55   60   70   66   55
66   55   53   46   53   49   51   78   47   53

The mass of 20 pupils in a class
is determined and the following
masses are recorded :
55   43   55   57   59   55   60   70   66   55
66   55   53   46   53   49   51   78   47   53

14.1  Rangskik die data in
stygende volgorde.
[ A 14.1 ]

14.2  Stel hierdie data met 'n
stingel-en-blaar tabel voor.
[ A 14.2 ]

14.3  Skryf die minimum en
maksimum waardes neer.
[ A 14.3 ]

14.4  Bereken die omvang
van die data.
[ A 14.4 ]

14.5  Bereken die rekenkundige
gemiddelde van die data.
[ A 14.5 ]

14.6  Bepaal die mediaan vir die data.
[ A 14.6 ]

14.7  Bepaal die modus van die data.
[ A 14.7 ]

14.1  Arrange the data in
ascending order.
[ A 14.1 ]

14.2  Represent the data with
a stem and leave tabel.
[ A 14.2 ]

14.3  Write down the minimum
and maximum of the data.
[ A 14.3 ]

14.4  Calculate the range of
the data.
[ A 14.4 ]

14.5  Calculate the arithmetic mean of
the data.
[ A 14.5 ]

14.6  Determine the median for the data.
[ A 14.6 ]

14.7  Determine the mode for the data.
[ A 14.7 ]

Vraag  / Question  15

Sommige van die Gr. 10 lerlinge het die
aantal oproepe wat hulle gesin oor 'n
week ontvang, opgeteken.
Die aantal oproepe was :
27   14     5   16   17   12   14   25   30
17   14   12     6   14     9   25

Some of the Grad 10 pupils recorded
the number of phone calls that the
The numbers were :
27   14     5   16   17   12   14   25   30
17   14   12     6   14     9   25

15.1  Rangskik die data in
stygende volgorde.
[ A 15.1 ]

15.2  Skryf die minimum en
maksimum neer.
[ A 15.2 ]

15.3  Bereken die omvang
van die data.                   [ A 15.3 ]

15.4  Bereken die rekenkundige
gemiddelde van die data.
[ A 15.4 ]

15.5  Bepaal die mediaan vir die data.
[ A 15.5 ]

15.6  Bepaal die modus van die data.
[ A 15.6 ]

15.1  Arrange the data in
ascending order.
[ A 15.1 ]

15.2  Write down the minimum
and maximum of the data.
[ A 15.2 ]

15.3  Calculate the range of
the data.                               [ A 15.3 ]

15.4  Calculate the arithmetic mean of
the data.
[ A 15.4 ]

15.5  Determine the median for the data.
[ A 15.5 ]

15.6  Determine the mode for the data.
[ A 15.6 ]

Vraag  / Question  16

Beskou die volgende datastel :
a   7   9   b   c   16   17   20   23

Die omvang van die data is 18.
Die som van al die data waardes
is 126.
Die waarde b is die gemiddelde
van die stel.
Bepaal die waardes van a, b en c.
[ A 16 ]

Study the following data set :
a   7   9   b   c   16   17   20   23

The range of the data is 18.
The sum of all the data values
is 126.
The value b = the mean of
the set.
Determine the value of a, b and c.
[ A 16 ]

Vraag  / Question  17

Beskou die volgende datastel :
Study the following data set :

35   36   38   a   40   44   45   49   b   c   d   63   73   79   87   88

c stel die omvang van die data voor.
Die som van al die data waardes
is 880.
Die waarde d is die gemiddelde
van die stel.
Die mediaan van die data is 50.
Bepaal die waardes van a, b, c en d.
[ A 17 ]

The range of the data is represented by c.
The sum of all the data values
is 880.
The value d is the mean of
the set.
The median of the set is 50.
Determine the value of a, b, c and d.
[ A 17 ]

Vraag  / Question  18

Vir een week teken Teboho die
aantal vragmotors wat per dag
op 'n parkeerterrein geparkeer
is aan. Die volgende data
is aangeteken :
In one week Teboho notes the number
of trucks that are parked on a
parking lot. The following data
is recorded :

8   11   14   9   10   11   7

18.1  Skryf die data in stygende
volgorde neer.
[ A 18.1 ]

18.2  Skryf die minimum en
maksimum waardes neer.
[ A 18.2 ]

18.3  Bereken die omvang
van die data.                  [ A 18.3 ]

18.4  Bereken die gemiddelde.
[ A 18.4 ]

18.5  Bereken die mediaan
van die data.                  [ A 18.5 ]

18.6  Bereken die modus
van die data.                  [ A 18.6 ]

18.7  Bereken die aantal dae
waar die aantal geparkeerde
vragmotors groter was as
die gemiddelde.
[ A 18.7 ]

18.8  Bereken die aantal dae
waar die aantal geparkeerde
vragmotors groter was as
die modus.
[ A 18.8 ]

18.9  Bereken die aantal dae
waar die aantal geparkeerde
vragmotors kleiner was as
die mediaan.
[ A 18.9 ]

18.1  Write down the data in
ascending order.
[ A 18.1 ]

18.2  Write down the minimum and
maximum of the data..
[ A 18.2 ]

18.3  Calculate the range of the data.
[ A 18.3 ]

18.4  Calculate the mean.
[ A 18.4 ]

18.5  Calculate the median of
the data.                               [ A 18.5 ]

18.6  Calculate the mode of
the data.                               [ A 18.6 ]

18.7  Calculate the number of days that
the number of parked trucks in the
parking lot was greater than
the mean.
[ A 18.7 ]

18.8  Calculate the number of days that
the number of parked trucks in the
parking lot was greater than
the modus.
[ A 18.8 ]

18.9  Calculate the number of days that
the number of parked trucks in the
parking lot was smaller than
the median.
[ A 18.9 ]