WISKUNDE
GRAAD 11
NOG OEFENINGE
Statistiek
MATHEMATICS
GRADE 11
MORE EXERCISES
Statistics
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 ]
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 :
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 ]
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 |
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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 :
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Gemid / Mean |
Mediaan / Median |
Modus / Mode |
Dogters / Girls |
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Seuns / Boys |
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Klas / Class |
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[ 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 ]
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 ]
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Telling |
Frekwensie (f) |
Kumulatiewe frekwensie |
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Tally |
Frequency (f) |
Cumulative frequency |
0 ≤ m < 10 |
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10 ≤ m < 20 |
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20 ≤ m < 30 |
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30 ≤ m < 40 |
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40 ≤ m ≤ 50 |
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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 ]
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 ]
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Klas middelpunt (x) |
Frekwensie (f) |
Frekwensie (f.x) |
Kumulatiewe frekwensie (kf) |
Kumulatiewe frekwensie pereentasie (kf%) |
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Class centre (x) |
Frequency (f) |
Frequency (f.x) |
Cumulative frequency (cf) |
Cumulatice frequency percentage (cf%) |
40 ≤ m < 50 |
45 |
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50 ≤ m < 60 |
55 |
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60 ≤ m < 70 |
65 |
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70 ≤ m < 80 |
75 |
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80 ≤ m ≤ 90 |
85 |
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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 ]
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;
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Klas middelpunt (x) |
Frekwensie (f) |
Frekwensie (f.x) |
Kumulatiewe frekwensie (kf) |
Kumulatiewe frekwensie pereentasie (kf%) |
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Class centre (x) |
Frequency (f) |
Frequency (f.x) |
Cumulative frequency (cf) |
Cumulatice frequency percentage (cf%) |
150 ≤ m < 160 |
155 |
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160 ≤ m < 170 |
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170 ≤ m ≤ 180 |
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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 ]
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;
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Frekwensie |
Kumulatiewe frekwensie |
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Frequency (f) |
Cumulative frequency |
20 ≤ m < 30 |
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30 ≤ m < 40 |
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40 ≤ m < 50 |
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50 ≤ m < 60 |
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60 ≤ m < 70 |
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70 ≤ m < 80 |
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80 ≤ m ≤ 90 |
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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 ]