WISKUNDE
GRAAD 11
NOG OEFENINGE
Statistiek : antwoorde
GRAAD 11
NOG OEFENINGE
Statistiek : antwoorde
MATHEMATICS
GRADE 11
MORE EXERCISES
Statistics : answers
GRADE 11
MORE EXERCISES
Statistics : answers
Rangskik / Arrange : 18 ; 19 ; 19 ; 20 ; 22 ; 24 ; 26
18 + 19 + 19 + 20 + 22 + 24 + 26
Gemiddelde / Mean = ──────────────────────
7
148
= ────
7
= 21,143
Mediaan / Median = 20 | Waarde presies in die middel /
Value exactly in the middle
Modus / Mode = 19 | Hoogste frekwensie (2) /
Highest frequency (2)
Reikwydte/Omvang / Range = (maksimum / maximum) ─ minimum
= ( 26 − 18 ) = 8
[ V/Q 1. ]
Rangskik / Arrange : 11 ; 12 ; 14 ; 16 ; 17 ; 17 ; 18 ; 21 ; 22
11 + 12 + 14 + 16 + 17 + 17 + 18 + 21 + 22
Gemiddelde / Mean = ────────────────────────────
9
148
= ───
9
= 16,444
Mediaan / Median = 17 | Waarde presies in die middel /
Value exactly in the middle
Modus / Mode = 17 | Hoogste frekwensie (2) / Highest frequency (2)
Reikwydte/Omvang / Range = (maksimum / maximum) ─ minimum
= ( 22 − 11 ) = 11
[ V/Q 1. ]
Rangskik / Arrange : 51 ; 52 ; 53 ; 54 ; 56 ; 57 ; 57 ; 57 ; 58 ; 61 ; 62
51 + 52 + 53 + 54 + 56 + 57 + 57 + 57 + 58 + 61 + 62
Gemiddelde / Mean = ──────────────────────────────────
11
618
= ─────
11
= 56,182
Mediaan / Median = 57 | Waarde presies in die middel / Value exactly in the middle
Modus / Mode = 57 | Hoogste frekwensie (3) / Highest frequency (3)
Reikwydte/Omvang / Range = (maksimum / maximum) ─ minimum
= ( 62 − 51 ) = 11
[ V/Q 1. ]
Rangskik / Arrange : 10 ; 11 ; 12 ; 12 ; 13 ; 13 ; 14 ; 17
10 + 11 + 12 + 12 + 13 + 13 + 14 + 17
Gemiddelde / Mean = ─────────────────────────
8
102
= ────
8
= 12,75
As daar 'n ewe getal waardes is, is die If the number of values is an even number,
mediaan die gemiddelde van die then the median is the average/mean of the
twee middelste waardes. two values exactly at the middle.
12 + 13
Mediaan / Median = ─────── | Ewe aantal waardes, dus gemiddelde van 2 middelste
2 waardes
= 12,5 | Even number of values, thus average of two values
| exactly in the middle
Modus / Mode = 12 en / and 13 | Hoogste frekwensie (2) / Highest frequency (2)
Reikwydte/Omvang / Range = (maksimum / maximum) ─ minimum
= ( 17 − 10 ) = 7
[ V/Q 1. ]
Rangskik / Arrange : 20 ; 21 ; 22 ; 22 ; 23 ; 24 ; 25 ; 26 ; 28 ; 29
20 + 21 + 22 + 22 + 23 + 24 + 25 + 26 + 28 + 29
Gemiddelde / Mean = ────────────────────────────────
10
240
= ────
10
= 24
23 + 24
Mediaan / Median = ─────── | Ewe aantal waardes, dus gemiddelde van 2 middelste
2 waardes
= 23,5 | Even number of values, thus average of two values
| exactly in the middle
Modus / Mode = 22 | Hoogste frekwensie (2) / Highest frequency (2)
Reikwydte/Omvang / Range = (maksimum / maximum) ─ minimum
= ( 29 − 20 ) = 9
[ V/Q 1. ]
Rangskik / Arrange : 12 ; 12 ; 13 ; 13 ; 14 ; 15 ; 17 ; 18
12 + 12 + 13 + 13 + 14 + 15 + 17 + 18
Gemiddelde / Mean = ──────────────────────────
8
114
= ────
8
= 14,25
13 + 14
Mediaan / Median = ─────── | Ewe aantal waardes, dus gemiddelde van 2 middelste
2 waardes
= 13,5 | Even number of values, thus average of two values
| exactly in the middle
Modus / Mode = 12 en / and 13 | Hoogste frekwensie (2) / Highest frequency (2)
Reikwydte/Omvang / Range = (maksimum / maximum) ─ minimum
= ( 18 − 12 ) = 6
[ V/Q 1. ]
Rangskik / Arrange : 1 ; 2 ; 3 ; 4 ; 5 ; 5 ; 6 ; 7 ; 7 ; 7 ; 7 ; 8
1 + 2 + 3 + 4 + 5 + 5 + 6 + 7 + 7 + 7 + 7 + 8 62
Gemiddelde / Mean = ───────────────────────────── = ────
12 12
= 5,167
5 + 6
Mediaan / Median = ─────── | Ewe aantal waardes, dus gemiddelde van 2 middelste
2 waardes
= 5,5 | Even number of values, thus average of two values
| exactly in the middle
Modus / Mode = 7 | Hoogste frekwensie (4) / Highest frequency (4)
Reikwydte/Omvang / Range = (maksimum / maximum) ─ minimum
= ( 8 − 1 ) = 7
[ V/Q 1. ]
Rangskik / Arrange : 25;26;28;30;31;31;31;32;32;33;33;34;36;37;37;38;41;42;42;44;51;57
Som / Sum = 25+26+28+30+31+31+31+32+32+33+33+34+36+37+37+38+41+42+42+44+51+57
= 791
791
Gemiddelde / Mean = ──── = 35,955
22
33 + 34
Mediaan / Median = ─────── | Ewe aantal waardes, dus gemiddelde van 2 middelste
2 waardes
= 33,5 | Even number of values, thus average of two values
| exactly in the middle
Modus / Mode = 31 | Hoogste frekwensie (3) / Highest frequency (3)
Reikwydte/Omvang / Range = (maksimum / maximum) ─ minimum
= ( 57 − 25 ) = 32
[ V/Q 1. ]
2.1 19 21 21 37 42 43 48 [ V/Q 2. ]
2.2 Omvang / Range = (Maksimum / Maximum) ─ Minimum
= 48 ─ 19
= 29 [ V/Q 2. ]
19 + 21 + 21 + 37 + 42 + 43 + 48 231
2.3 Gemiddelde / Mean = ────────────────────── = ────
7 7
= 33 [ V/Q 2. ]
2.4 Mediaan / Median = 37 . . . middelste waarde / midmost value
[ V/Q 2. ]
2.5 Modus / Mode = 21 . . . hoogste frekwensie (2) / highest frequency (2)
[ V/Q 2. ]
2.6 Aantal dae / Numer of days = 4 . . . gemiddelde / mean = 33 [ V/Q 2. ]
2.7 Aantal dae / Numer of days = 4 . . . modus / mode = 21 [ V/Q 2. ]
2.8 Aantal dae / Numer of days = 3 . . . mediaan / median = 37 [ V/Q 2. ]
3.1
| Gemid / Mean | Mediaan / Median | Modus / Mode | ||||||||||||||||||||||||||
| Dogters / Girls | 1 | 2 | 4 | 5 | 5 | 6 | 6 | 7 | 7 | 8 | 8 | 8 | 8 | 9 | 6,00 | 6,5 | 8 | |||||||||||
| Seuns / Boys | 1 | 2 | 3 | 4 | 5 | 5 | 7 | 7 | 7 | 8 | 8 | 5,18 | 5 | 7 | ||||||||||||||
| Klas / Class | 1 | 1 | 2 | 2 | 3 | 4 | 4 | 5 | 5 | 5 | 5 | 6 | 6 | 7 | 7 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 9 | 5,64 | 6 | 8 |
3.2 Daar is 14 dogters in die klas van 25.
14
P(dogter) = ─── [ V/Q 3. ]
25
3.3 Daar is 9 uit 11 seuns.
9
P(seun + punt < 8) = ─── [ V/Q 3. ]
11
3.4 Daar is 12 uit 25 leerlinge.
12
P(leerling + punt > 6) = ───
25
[ V/Q 3. ]
3.5 Daar is 4 uit 14 dogters.
4
P(dogter + punt = 8) = ───
14
2
= ───
7
[ V/Q 3. ]
3.6 Daar is 5 uit 11 seuns.
5
P(seun + punt > 5,18) = ───
11
[ V/Q 3. ]
3.7 Daar is 11 uit 25 leerlinge.
11
P(leerling + punt < 5,64) = ───
25
[ V/Q 3. ]
3.8 Daar is 1 uit 25 leerlinge.
1
P(leerling + punt > 8) = ───
25
[ V/Q 3. ]
3.9 Daar is geen seuns nie, 0 uit 11.
0
P(seun + punt = 6) = ─── = 0
11
[ V/Q 3. ]
3.2 There are 14 girls in the class of 25.
14
P(girl) = ─── [ V/Q 3. ]
25
3.3 There are 9 from 11 boys.
9
P(boy + mark < 8) = ─── [ V/Q 3. ]
11
3.4 There are 12 from 25 learners.
12
P(learner + mark > 6) = ───
25
[ V/Q 3. ]
3.5 There are 4 from 14 girls.
4
P(girl + mark = 8) = ───
14
2
= ──
7
[ V/Q 3. ]
3.6 There are 5 from 11 boyss.
5
P(boy + mark > 5,18) = ───
11
[ V/Q 3. ]
3.7 There are 11 from 25 learners.
11
P(learner + mark < 5,64) = ───
25
[ V/Q 3. ]
3.8 There is 1 from 25 learners.
1
P(learner + mark > 8) = ───
25
[ V/Q 3. ]
3.9 There are no boys, 0 from 11.
0
P(boy + mark = 6) = ─── = 0
11
[ V/Q 3. ]
4.1
[ V/Q 4. ]
| Telling | Frekwensie (f) | Kumulatiewe Frekwensie | |
| Tally | Frequency (f) | Cumulative Frequency | |
| 0 ≤ m < 10 | ││ | 2 | 2 |
| 10 ≤ m < 20 | ┼┼┼┼ │ | 6 | 8 |
| 20 ≤ m < 30 | ┼┼┼┼ ┼┼┼┼ ││ | 12 | 20 |
| 30 ≤ m < 40 | ┼┼┼┼ ┼┼┼┼ ┼┼┼┼ | 15 | 35 |
| 40 ≤ m ≤ 50 | ┼┼┼┼ ┼┼┼┼ | 10 | 45 |
4.2 Punte is diskreet, kan net
sekere waardes besit.
[ V/Q 4. ]
4.3 Onderste klasgrens = 0 en
boonste klasgrens = <10
[ V/Q 4. ]
4.2 The marks are discrete, they
can only have certain values.
[ V/Q 4. ]
4.3 Bottom class bounadry = 0 and
top class boundary = < 10
[ V/Q 4. ]
5.1
[ V/Q 5. ]
5.2
[ V/Q 5. ]
| 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%) | |
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5.2
5.5.1 20 %
[ A 5. ]
5.5.2 70 kg
[ A 5. ]
5.5.3 mediaan = 60 kg
[ A 5. ]
∑fx
5.6 gemiddelde = ────
∑n
2 970
= ──────
50
= 59,4
[ A 5. ]
5.5.1 20 %
[ A 5. ]
5.5.2 70 kg
[ A 5. ]
5.5.3 median = 60 kg
[ A 5. ]
∑fx 2970
5.6 mean = ──── = ─────
∑cf 50
= 59,4
[ A 5. ]
6.1 Rangskik die lengtes / Arrange the lengths :
151 151 151 152 153 153 154 156 157 158 158 159 159
161 162 162 163 163 164 164 165 165 165 165 165 166 166 167 168
171 172 172 173 173 175 177 178 179 179 179
6.1.1 Minimum = 151; Maksimum / Maximum = 179
Omvang / Range = Maksimum / Maximum = 179 ─ 151 = 48 [ A 6. ]
6571
6.1.2 Gemiddelde / Mean = ───── = 164,275
40 [ A 6. ]
6.1.3 Mediaan is die gemiddelde van die 2 middelste waardes (ewe aantal waardes)
Median is the mean ot the 2 values in the middle (even number of valies)
164 + 165
Mediaan / Median = ──────── = 164,5
2 [ A 6. ]
6.1.4 Modus is die waarde wat die meeste voorkom.
Mode is the value wat appears most often.
Modus / Mode = 165 (kom 5 keer voor / appears 5 times)
[ A 6. ]
6.2 Mees algemene lengte = 165 cm (Modus)
Most common length = 165 cm (Mode)
[ A 6. ]
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%) | |
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6.4
∑fx 6580
6.5.1 Geskatte gemiddelde / Estimated mean = ──── = ─────
∑f 40
= 164,5 [ A 6. ]
6.5.2 Die berekende waarde = 164,275 en die geskatte waarde = 164,5. Die twee waardes is
dus byna gelyk.
The calculated value = 162,275 and the estimated value = 164,5. The two values are
therefore nearly equal.
[ A 6. ]
6.6.1 Maksimum lengte korste 40 % / Maximum length of shortest 40 % = 162 cm [ A 6. ]
6.6.2 Minimum lengte langste 25 % / Minimum length of tallest 25 % = 171 cm [ A 6. ]
6.6.3 Minimum lengte langste 60 % / Minimum length of tallest 60 % = 162 cm [ A 6. ]
6.6.4 Stelling is korrek. Die maksimum lengte van korste 40 % is 162 cm.
60 % is dus langer as 162 cm.
The statement is true. The maximum length of the shortest 40 % is 162 cm.
60 % ate therefore taller. [ A 6. ]
6.6.5 Stelling is korrek. 55 % is korter as 166 cm. /
The statement is true. 55 % are shorter than 166 cm.
[ A 6. ]
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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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| 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
7.3 5 leerlinge reis minder as
30 km per week en
32 reis minder as 70 km
per week.
[ V 7. ]
7.4 15 leerlinge reis 60 km
per week.
[ V 7. ]
7.5 NB Die afstande wat gegee word is
die afstand wat 'n leerling per week aflê.
Die leerling reis die afstand 10 keer
per week. Die gegewe afstand is dus
10 keer die afstand van die skool af.
7.5.1 Waar. 5 leerlinge reis minder as
30 km per week en is dus minder
as 3 km van die skool af.
[ V 7. ]
7.5.2 Vals. Tussen 10 en 12 km van die
skool af beteken tussen 100 en
120 km per week en daar is geen
leerling wat meer as 90 km reis nie.
[ V 7. ]
7.5.3 Waar. 8 leerlinge reis tussen
70 en 90 km per week en is dus
tussen 7 en 9 km van die skool af.
[ V 7. ]
7.5.4 Waar. Sewe leerlinge reis tussen
60 en 70 km per week en is dus
tussen 6 en 7 km van die skool af.
[ V 7. ]
7.5.5 Vals. Nader as 5 km beteken
minder as 50 km per week.
Daar is 17 leerlinge wat minder
as 50 km per week reis.
[ V 7. ]
7.5.6 Vals. Twaalf leerlinge reis 30 km
en meer maar minder as 50 km
per week en dus is hulle tussen
3 en 5 km van die skool af.
[ V 7. ]
7.5.7 Waar. Geen leerling reis meer
as 90 km per week nie en is
dus minder as 9 km van die skool af.
[ V 7. ]
7.5.8 Vals. Geen leerling is meer as
9 km van die skool af nie, verwys
na 7.5.7. Al die leerlinge is dus
nader as 9 km van die skool af.
[ V 7. ]
7.3 Five pupils travel less than
30 km per week and
32 travel less than 70 km
per week.
[ Q 7. ]
7.4 Fifteen pupils travel 60 km
per week.
[ Q 7. ]
7.5 NB The distances given are the
distances travelled per week.
The pupil travels this distance 10 times
per week. Thus the given distance is
10 times the distance from the school.
7.5.1 True. 5 pupils travel less than
30 km per week and thus are less
than 3 km from the school.
[ Q 7. ]
7.5.2 False. Between 10 and 12 km
from the school implies that more
than 100 km and less than 120 km
must be travelled in a week and
no pupil travels more then 90 km.
[ Q 7. ]
7.5.3 True. Eight pupils travel between 70
and 90 km per week and thus are
between 7 and 9 km from the school.
[ Q 7. ]
7.5.4 True. Seven pupils travel between 60
and 70 km per week and thus are
between 6 and 7 km from the school.
[ Q 7. ]
7.5.5 False. Closer than 5 km implies less
than 50 km per week. There are
17 pupils that travel less than 50 km
per week.
[ Q 7. ]
7.5.6 False. Twelve pupils travel 30 km and
more but less than 50 km per week
and thus live between 3 and 5 km
from the school.
[ Q 7. ]
7.5.7 True. No pupil travels more than
90 km per week and thus lives
less than 9 km from the school.
[ Q 7. ]
7.5.8 False. No pupil lives more than
9 km from the school, refer to 7.5.7.
All pupils thus live closer than
9 km from the school.
[ Q 7. ]