WISKUNDE
GRAAD 10
NOG OEFENINGE
Statistiek : antwoorde.
GRAAD 10
NOG OEFENINGE
Statistiek : antwoorde.
MATHEMATICS
GRAAD 10
NOG OEFENINGE
Statistics : answers.
GRAAD 10
NOG OEFENINGE
Statistics : answers.
Σ x 676
1.2.1 Gemiddelde / Mean = ──── = ───
n 13
= 52 Vr. / Qu. 1.2.1
1.2.2 Modus / Mode = 47 (2 keer / twice) Vr. / Qu. 1.2.2
1.2.3 Omvang / Range = maks. / max − min.
= 84 − 25
= 59 Vr. / Qu. 1.2.3
1.2.1 Gemiddelde / Mean = ──── = ───
n 13
= 52 Vr. / Qu. 1.2.1
1.2.2 Modus / Mode = 47 (2 keer / twice) Vr. / Qu. 1.2.2
1.2.3 Omvang / Range = maks. / max − min.
= 84 − 25
= 59 Vr. / Qu. 1.2.3
1.2.4 Lys die getalle van klein na groot. / List the numbers is ascending order :
25 26 27 34 45 47 47 53 62 68 75 83 84
Q1 Q2 Q3
Q2 is die middelste getal. / Q2 is the number exactly in the middle.
∴ Q2 = 47
OF / OR met die formule: / using the formulae :
2(n + 1) 2(13 + 1) 2 × 14
Posisie van / Position of Q2 = ────── = ────── = ───── = 7
4 4 4
∴ Q2 is die 7de getal / Q2 is the 7th number d.i. / i.e. Q2 = 47 Vr. / Qu. 1.2.4
1.2.5 Q1 verdeel die linkerkantse helfte van die getalle in die helfte, / Q1 divides the lefthand half into two equal parts.
Q1 is die getal halfpad tussen 27 en 34, die gemiddelde van 27 en 34. /
Q1 is the number halfway between 27 and 34, i.e. the average of 27 and 34.
27 + 34
Q1 = ────── = 30,5
2
Q3 verdeel die regterkantse helfte van die getalle in die helfte, /
Q3 divides the righthand half into two equal parts.
Q3 is die getal halfpad tussen 68 en 75, die gemiddelde van 68 en 75. /
Q3 is the number halfway between 68 and 75, i.e. the average of 68 and 75.
68 + 75
Q3 = ────── = 71,5
2
OF / OR gebruik die formules: / use the formulae :
(n + 1) 3(n + 1)
Posisie van / Position of Q1 = ────── Posisie van / Position of Q3 = ──────
4 4
(13 + 1) 3(13 + 1)
= ────── = ──────
4 4
14 3 × 14
= ─── = 3,5 = ───── = 10,5
4 4
∴ Q1 is die 3de getal, 27, plus die helfte van die verskil tussen die derde getal (27) en die vierde getal (34) /
Q1 is the 3rd number, 27, plus half of the difference between the third number (27) and the fourth number (34)
34 − 27
∴ Q1 = 27 + ────── = 30,5
2
∴ Q3 is die 10de getal, 68, plus die helfte van die verskil tussen die tiende getal (68) en die elfde getal (75) /
Q3 is the 10th number, 28, plus half of the difference between the tenth number (68) and the eleventh number (75)
75 − 68
∴ Q3 = 68 + ────── = 71,5
2 Vr. / Qu. 1.2.5
1.2.6 IKVW / IQR = Q3 − Q1 = 71,5 − 30,5 = 41 Vr. / Qu. 1.2.6
1.3 Vyfpuntopsomming / Five number summary :
Minimum = 25; Q1 = 30,5; Q2 = 47; Q3 = 71,5; maksimum / maximum = 86 Vr. / Qu. 1.3
1.4
Vr. / Qu. 1.4
25 26 27 34 45 47 47 53 62 68 75 83 84
Q1 Q2 Q3
Q2 is die middelste getal. / Q2 is the number exactly in the middle.
∴ Q2 = 47
OF / OR met die formule: / using the formulae :
2(n + 1) 2(13 + 1) 2 × 14
Posisie van / Position of Q2 = ────── = ────── = ───── = 7
4 4 4
∴ Q2 is die 7de getal / Q2 is the 7th number d.i. / i.e. Q2 = 47 Vr. / Qu. 1.2.4
1.2.5 Q1 verdeel die linkerkantse helfte van die getalle in die helfte, / Q1 divides the lefthand half into two equal parts.
Q1 is die getal halfpad tussen 27 en 34, die gemiddelde van 27 en 34. /
Q1 is the number halfway between 27 and 34, i.e. the average of 27 and 34.
27 + 34
Q1 = ────── = 30,5
2
Q3 verdeel die regterkantse helfte van die getalle in die helfte, /
Q3 divides the righthand half into two equal parts.
Q3 is die getal halfpad tussen 68 en 75, die gemiddelde van 68 en 75. /
Q3 is the number halfway between 68 and 75, i.e. the average of 68 and 75.
68 + 75
Q3 = ────── = 71,5
2
OF / OR gebruik die formules: / use the formulae :
(n + 1) 3(n + 1)
Posisie van / Position of Q1 = ────── Posisie van / Position of Q3 = ──────
4 4
(13 + 1) 3(13 + 1)
= ────── = ──────
4 4
14 3 × 14
= ─── = 3,5 = ───── = 10,5
4 4
∴ Q1 is die 3de getal, 27, plus die helfte van die verskil tussen die derde getal (27) en die vierde getal (34) /
Q1 is the 3rd number, 27, plus half of the difference between the third number (27) and the fourth number (34)
34 − 27
∴ Q1 = 27 + ────── = 30,5
2
∴ Q3 is die 10de getal, 68, plus die helfte van die verskil tussen die tiende getal (68) en die elfde getal (75) /
Q3 is the 10th number, 28, plus half of the difference between the tenth number (68) and the eleventh number (75)
75 − 68
∴ Q3 = 68 + ────── = 71,5
2 Vr. / Qu. 1.2.5
1.2.6 IKVW / IQR = Q3 − Q1 = 71,5 − 30,5 = 41 Vr. / Qu. 1.2.6
1.3 Vyfpuntopsomming / Five number summary :
Minimum = 25; Q1 = 30,5; Q2 = 47; Q3 = 71,5; maksimum / maximum = 86 Vr. / Qu. 1.3
1.4
Vr. / Qu. 1.4
2.1 Stingel / Stem Blaar / Leave
14 8;
15 1; 4; 5; 7; 9
16 3; 3; 7;
17 2; 2; 2; 3;
18 2; 4
Vr. / Qu. 2.1
14 8;
15 1; 4; 5; 7; 9
16 3; 3; 7;
17 2; 2; 2; 3;
18 2; 4
Vr. / Qu. 2.1
Σ x 2 427
2.2.1 Gemiddelde / Mean = ──── = ───
n 15
= 164,8 Vr. / Qu. 2.2.1
2.2.2 Modus / Mode = 172 (3 keer / thrice) Vr. / Qu. 2.2.2
2.2.3 Omvang / Range = maks. / max − min.
= 184 − 148
= 36 Vr. / Qu. 2.2.3
2.2.1 Gemiddelde / Mean = ──── = ───
n 15
= 164,8 Vr. / Qu. 2.2.1
2.2.2 Modus / Mode = 172 (3 keer / thrice) Vr. / Qu. 2.2.2
2.2.3 Omvang / Range = maks. / max − min.
= 184 − 148
= 36 Vr. / Qu. 2.2.3
2.2.4 Lys die getalle van klein na groot. / List the numbers is ascending order :
148 151 154 155 157 159 163 163 167 172 172 172 173 182 184
Q1 Q2 Q3
Q2 is die middelste getal. / Q2 is the number exactly in the middle.
∴ Q2 = 163
OF / OR met die formule: / using the formulae :
2(n + 1) 2(15 + 1) 2 × 16
Posisie van / Position of Q2 = ────── = ────── = ───── = 8
4 4 4
∴ Q2 is die 8ste getal / Q2 is the 8th number d.i. / i.e. Q2 = 163 Vr. / Qu. 2.2.4
2.2.5 Q1 verdeel die linkerkantse helfte van die getalle in die helfte. / Q1 divides the lefthand half into two equal parts.
Q1 is die vierde getal, d.i. Q1 = 155. / Q1 is the fourth number, i.e. Q1 = 155.
Q3 verdeel die regterkantse helfte van die getalle in die helfte, / Q3 divides the righthand half into two equal parts.
Q3 is die 12de getal, d.i. Q3 = 172 / Q3 is the 12th number, i.e. Q3 = 172.
OF / OR gebruik die formules: / use the formulae :
(n + 1) 3(n + 1)
Posisie van / Position of Q1 = ────── Posisie van / Position of Q3 = ──────
4 4
(15 + 1) 3(15 + 1)
= ────── = ──────
4 4
16 3 × 16
= ─── = 4 = ───── = 12
4 4
∴ Q1 is die 4de getal, 155 / Q1 is the 4th number, 155
∴ Q3 is die 12de getal, 172 / Q3 is the 12th number, 172 Vr. / Qu. 2.2.5
2.2.6 IKVW / IQR = Q3 − Q1 = 71,5 − 30,5 = 41 Vr. / Qu. 2.2.6
2.3 Vyfpuntopsomming / Five number summary :
Minimum = 25; Q1 = 30,5; Q2 = 47; Q3 = 71,5; maksimum / maximum = 86 Vr. / Qu. 2.2.6
2.4
Vr. / Qu. 2.4
148 151 154 155 157 159 163 163 167 172 172 172 173 182 184
Q1 Q2 Q3
Q2 is die middelste getal. / Q2 is the number exactly in the middle.
∴ Q2 = 163
OF / OR met die formule: / using the formulae :
2(n + 1) 2(15 + 1) 2 × 16
Posisie van / Position of Q2 = ────── = ────── = ───── = 8
4 4 4
∴ Q2 is die 8ste getal / Q2 is the 8th number d.i. / i.e. Q2 = 163 Vr. / Qu. 2.2.4
2.2.5 Q1 verdeel die linkerkantse helfte van die getalle in die helfte. / Q1 divides the lefthand half into two equal parts.
Q1 is die vierde getal, d.i. Q1 = 155. / Q1 is the fourth number, i.e. Q1 = 155.
Q3 verdeel die regterkantse helfte van die getalle in die helfte, / Q3 divides the righthand half into two equal parts.
Q3 is die 12de getal, d.i. Q3 = 172 / Q3 is the 12th number, i.e. Q3 = 172.
OF / OR gebruik die formules: / use the formulae :
(n + 1) 3(n + 1)
Posisie van / Position of Q1 = ────── Posisie van / Position of Q3 = ──────
4 4
(15 + 1) 3(15 + 1)
= ────── = ──────
4 4
16 3 × 16
= ─── = 4 = ───── = 12
4 4
∴ Q1 is die 4de getal, 155 / Q1 is the 4th number, 155
∴ Q3 is die 12de getal, 172 / Q3 is the 12th number, 172 Vr. / Qu. 2.2.5
2.2.6 IKVW / IQR = Q3 − Q1 = 71,5 − 30,5 = 41 Vr. / Qu. 2.2.6
2.3 Vyfpuntopsomming / Five number summary :
Minimum = 25; Q1 = 30,5; Q2 = 47; Q3 = 71,5; maksimum / maximum = 86 Vr. / Qu. 2.2.6
2.4
Vr. / Qu. 2.4
Σ x 220
3.2.1 Gemiddelde / Mean = ──── = ───
n 10
= 22 Vr. / Qu. 3.2.1
3.2.2 Modus / Mode = geen / no
(al die getalle kom net een keer voor /
(all the numbers have a frequency of 1) Vr. / Qu. 3.2.2
3.2.3 Omvang / Range = maks. / max − min.
= 29 − 16
= 13 Vr. / Qu. 3.2.3
3.2.1 Gemiddelde / Mean = ──── = ───
n 10
= 22 Vr. / Qu. 3.2.1
3.2.2 Modus / Mode = geen / no
(al die getalle kom net een keer voor /
(all the numbers have a frequency of 1) Vr. / Qu. 3.2.2
3.2.3 Omvang / Range = maks. / max − min.
= 29 − 16
= 13 Vr. / Qu. 3.2.3
3.2.4 Lys die getalle van klein na groot. / List the numbers is ascending order :
16 18 19 20 21 22 23 24 28 29
(n + 1) (10 + 1) 11
Posisie van / Position of Q1 = ────── = ────── = ───── = 2,75
4 4 4
∴ Q1 = getal 2 + 0,75(getal 3 − getal 2) / number 2 + 0,75(number 3 − number 2)
= 18 + 0,75(19 − 18) = 18,75
2(n + 1) 2(10 + 1) 2 × 11
Posisie van / Position of Q2 = ────── = ────── = ───── = 5,5
4 4 4
∴ Q2 = getal 5 + 0,5(getal6 − getal5) / number5 + 0,5(number6 − number5)
= 21 + 0,5(22 − 21) = 21,5
3(n + 1) 3(10 + 1) 3 × 11
Posisie van / Position of Q3 = ────── = ────── = ───── = 8,25
4 4 4
∴ Q3 = getal 8 + 0,25(getal 9 − getal 8) / number 8 + 0,25(number 9 − number 8)
= 24 + 0,25(28 − 24) = 25 Vr. / Qu. 3.2.4
3.2.5 IKVW / IQR = Q3 − Q1 = 25 − 18,75 = 6,25 Vr. / Qu. 3.2.5
3.3 Vyfpuntopsomming / Five number summary :
Minimum = 16; Q1 = 18,75; Q2 = 21,5; Q3 = 25; maksimum / maximum = 29 Vr. / Qu. 3.3
3.4
Vr. / Qu. 3.4
16 18 19 20 21 22 23 24 28 29
(n + 1) (10 + 1) 11
Posisie van / Position of Q1 = ────── = ────── = ───── = 2,75
4 4 4
∴ Q1 = getal 2 + 0,75(getal 3 − getal 2) / number 2 + 0,75(number 3 − number 2)
= 18 + 0,75(19 − 18) = 18,75
2(n + 1) 2(10 + 1) 2 × 11
Posisie van / Position of Q2 = ────── = ────── = ───── = 5,5
4 4 4
∴ Q2 = getal 5 + 0,5(getal6 − getal5) / number5 + 0,5(number6 − number5)
= 21 + 0,5(22 − 21) = 21,5
3(n + 1) 3(10 + 1) 3 × 11
Posisie van / Position of Q3 = ────── = ────── = ───── = 8,25
4 4 4
∴ Q3 = getal 8 + 0,25(getal 9 − getal 8) / number 8 + 0,25(number 9 − number 8)
= 24 + 0,25(28 − 24) = 25 Vr. / Qu. 3.2.4
3.2.5 IKVW / IQR = Q3 − Q1 = 25 − 18,75 = 6,25 Vr. / Qu. 3.2.5
3.3 Vyfpuntopsomming / Five number summary :
Minimum = 16; Q1 = 18,75; Q2 = 21,5; Q3 = 25; maksimum / maximum = 29 Vr. / Qu. 3.3
3.4
Vr. / Qu. 3.4
4.2.2 Lys die getalle van klein na groot. / List the numbers is ascending order :
38 43 45 48 51 52 53 54 56 58 61 62 63 65 71 72
(n + 1) (16 + 1) 17
Posisie van / Position of Q1 = ────── = ────── = ───── = 4,25
4 4 4
∴ Q1 = getal 4 + 0,25(getal 5 − getal 4) / number 4 + 0,25(number 5 − number 4)
= 48 + 0,25(51 − 48) = 48,75
2(n + 1) 2(16 + 1) 2 × 17
Posisie van / Position of Q2 = ────── = ────── = ───── = 8,5
4 4 4
∴ Q2 = getal 8 + 0,5(getal9 − getal8) / number8 + 0,5(number9 − number8)
= 54 + 0,5(56 − 54) = 55
3(n + 1) 3(16 + 1) 3 × 17
Posisie van / Position of Q3 = ────── = ────── = ───── = 12,75
4 4 4
∴ Q3 = getal 12 + 0,75(getal 13 − getal 12) / number 12 + 0,75(number 13 − number 12)
= 62 + 0,75(63 − 62) = 62,75 Vr. / Qu. 4.2.2
4.2.3 IKVW / IQR = Q3 − Q1 = 62,75 − 48,75 = 14 Vr. / Qu. 4.2.3
4.3 Vyfpuntopsomming / Five number summary :
Minimum = 16; Q1 = 18,75; Q2 = 21,5; Q3 = 25; maksimum / maximum = 29 Vr. / Qu. 4.3
4.4
Vr. / Qu. 4.4
omvang / range = maksimum / maximum − minimum
a = minimum = 38 − 24
= 14
d = Q3 = 2 × minimum
= 2 × 14 = 28
IKVW / IQR = Q3 − Q1
b = Q1 = Q3 − IKVW / IQR
= 28 − 8 = 20
c = Q2 = Q1 + 4
= 20 + 4 = 24
a = 14; b = 20; c = 24; d = 28; e = 38
omvang / range = maksimum / maximum − minimum
36 = e − 18
e = 36 + 18 = 54
c = Q2 = e − 18
= 54 − 18 = 36
d = Q3 = Q2 + 6
= 36 + 6 = 42
IKVW / IQR = Q3 − Q1
b = Q1 = Q3 − IKVW / IQR
= 42 − 11 = 31
a = 18; b = 31; c = 36; d = 42; e = 54
omvang / range = maksimum / maximum − minimum
32 = e − 33
e = 32 + 33 = 65
c = e − 12
= 65 − 12 = 53
d = 2a − 4
= 2 × 33 − 4 = 62
b = d − 20
= 62 − 20 = 42
a = 33; b = 42; c = 53; d = 62; e = 65
8.1 25%
8.2 50%
8.3 omvang / range = 68 − 4 = 64
8.4 IKVW / IQR = Q3 − Q1
= 50 − 32 = 18
9.1
|
Σfx 1 375
9.2 gemiddelde / mean = ──── = ───── = 30,56
n 45
9.3 modale klas /
modal class = 30 ≤ m < 40 ( f = 15 )
9.2 gemiddelde / mean = ──── = ───── = 30,56
n 45
9.3 modale klas /
modal class = 30 ≤ m < 40 ( f = 15 )
n
9.4.1 Posisie van / Position of Q2 = ───
4
45
= ────
4
= 11,25
Q2 is die 12de getal en dus in die
interval 20 ≤ m < 30 /
Q2 is the 12th number and thus in
the interval 20 ≤ m < 30
3n
9.4.3 Posisie van / Position of D3 = ───
10
3 × 45
= ─────
10
= 13,5
Die derde desiel is die 14de getal en is
in die interval 20 ≤ m < 30 /
The third decile is the 14th number and thus
in the interval 20 ≤ m < 30
9.4.1 Posisie van / Position of Q2 = ───
4
45
= ────
4
= 11,25
Q2 is die 12de getal en dus in die
interval 20 ≤ m < 30 /
Q2 is the 12th number and thus in
the interval 20 ≤ m < 30
3n
9.4.3 Posisie van / Position of D3 = ───
10
3 × 45
= ─────
10
= 13,5
Die derde desiel is die 14de getal en is
in die interval 20 ≤ m < 30 /
The third decile is the 14th number and thus
in the interval 20 ≤ m < 30
70n
9.4.2 Posisie van / Position of P70 = ───
100
70 × 45
= ──────
100
= 31,5
Die 70ste persentiel is die 32ste getal en is
in die interval 30 ≤ m < 40 /
The 70th percentile is the 32nd number and thus
in the interval 30 ≤ m < 40
9.4.2 Posisie van / Position of P70 = ───
100
70 × 45
= ──────
100
= 31,5
Die 70ste persentiel is die 32ste getal en is
in die interval 30 ≤ m < 40 /
The 70th percentile is the 32nd number and thus
in the interval 30 ≤ m < 40
10.1
|
Σfx 1 610
10.2 gemiddelde / mean = ──── = ───── = 57,5
n 28
10.3 modale interval /
modal interval = 50 ≤ m < 60 ( f = 11 )
10.2 gemiddelde / mean = ──── = ───── = 57,5
n 28
10.3 modale interval /
modal interval = 50 ≤ m < 60 ( f = 11 )
2n
10.4.1 Posisie van / Position of Q2 = ───
4
2 × 28
= ─────
4
= 14
Q2 is die 14de getal en dus in die interval
50 ≤ m < 60 /
Q2 is the 14th number and thus in the interval
50 ≤ m < 60
2n
10.4.3 Posisie van / Position of D2 = ───
10
2 × 28
= ─────
10
= 5,6
D2 is die 6de getal en dus in die interval
40 ≤ m < 50 /
D2 is the 6th number and thus in the interval
40 ≤ m < 50
10.4.1 Posisie van / Position of Q2 = ───
4
2 × 28
= ─────
4
= 14
Q2 is die 14de getal en dus in die interval
50 ≤ m < 60 /
Q2 is the 14th number and thus in the interval
50 ≤ m < 60
2n
10.4.3 Posisie van / Position of D2 = ───
10
2 × 28
= ─────
10
= 5,6
D2 is die 6de getal en dus in die interval
40 ≤ m < 50 /
D2 is the 6th number and thus in the interval
40 ≤ m < 50
80n
10.4.2 Posisie van / Position of P80 = ───
100
80 × 28
= ─────
100
= 22,4
P80 is die 23ste getal en dus in die interval
60 ≤ m < 70 /
P80 is the 23rd number and thus in the interval
60 ≤ m < 70
10.4.2 Posisie van / Position of P80 = ───
100
80 × 28
= ─────
100
= 22,4
P80 is die 23ste getal en dus in die interval
60 ≤ m < 70 /
P80 is the 23rd number and thus in the interval
60 ≤ m < 70
11.1
|
Σfx 5 040
11.2 gemiddelde / mean = ──── = ───── = 157,5
n 28
11.3 modale interval /
modal interval = 140 ≤ h < 160 ( f = 15 )
11.2 gemiddelde / mean = ──── = ───── = 157,5
n 28
11.3 modale interval /
modal interval = 140 ≤ h < 160 ( f = 15 )
11.4.1 Die gemiddelde is in die interval 140 ≤ h < 160 /
The mean is in the interval 140 ≤ h < 160
3n
11.4.3 Posisie van / Position of Q3 = ───
4
3 × 32
= ──────
4
= 24
Q3 is die 24ste getal en dus in die
interval 160 ≤ h < 180 /
Q3 is the 24th number and thus in the
interval 160 ≤ h < 180
8n
11.4.5 Posisie van / Position of D8 = ───
10
8 × 32
= ─────
10
= 25,6
D8 is die 26ste getal en dus in die
interval 160 ≤ h < 180 /
D8 is the 26th number and thus in the
interval 160 ≤ h < 180
The mean is in the interval 140 ≤ h < 160
3n
11.4.3 Posisie van / Position of Q3 = ───
4
3 × 32
= ──────
4
= 24
Q3 is die 24ste getal en dus in die
interval 160 ≤ h < 180 /
Q3 is the 24th number and thus in the
interval 160 ≤ h < 180
8n
11.4.5 Posisie van / Position of D8 = ───
10
8 × 32
= ─────
10
= 25,6
D8 is die 26ste getal en dus in die
interval 160 ≤ h < 180 /
D8 is the 26th number and thus in the
interval 160 ≤ h < 180
n
11.4.2 Posisie van / Position of Q1 = ───
4
32
= ───
4
= 8
Q1 is die 8ste getal en is in
die interval 140 ≤ h < 160 /
Q1 is the 8th number and thus
in interval 140 ≤ h < 160
30n
11.4.4 Posisie van / P30 = ───
100
30 × 32
= ─────
100
= 9,6
P30 is die 10de waarde en is in die
interval 140 ≤ h < 160 /
P30 is the 10th value and thus
in interval 140 ≤ h < 160
11.4.2 Posisie van / Position of Q1 = ───
4
32
= ───
4
= 8
Q1 is die 8ste getal en is in
die interval 140 ≤ h < 160 /
Q1 is the 8th number and thus
in interval 140 ≤ h < 160
30n
11.4.4 Posisie van / P30 = ───
100
30 × 32
= ─────
100
= 9,6
P30 is die 10de waarde en is in die
interval 140 ≤ h < 160 /
P30 is the 10th value and thus
in interval 140 ≤ h < 160
12.1
|
Σfx 355
12.2 gemiddelde / mean = ──── = ───── = 17,75
n 20
12.3 modale interval / modal interval = 15 ≤ t < 20
( f = 8 )
12.2 gemiddelde / mean = ──── = ───── = 17,75
n 20
12.3 modale interval / modal interval = 15 ≤ t < 20
( f = 8 )
n
12.4.1 Posisie van / Position of Q1 = ───
4
20
= ───
4
= 5
Q1 is die 5de waarde en is in
die interval 10 ≤ t < 15 //
Q1 is the 5th value and thus in
interval 10 ≤ t < 15
4n
12.4.3 Posisie van / Position of D4 = ───
10
4 × 16
= ─────
10
= 6,4
D4 is die 7de waarde en is in
die interval 15 ≤ t < 20 /
D4 is the 7th value and thus
in interval 15 ≤ t < 20
12.4.1 Posisie van / Position of Q1 = ───
4
20
= ───
4
= 5
Q1 is die 5de waarde en is in
die interval 10 ≤ t < 15 //
Q1 is the 5th value and thus in
interval 10 ≤ t < 15
4n
12.4.3 Posisie van / Position of D4 = ───
10
4 × 16
= ─────
10
= 6,4
D4 is die 7de waarde en is in
die interval 15 ≤ t < 20 /
D4 is the 7th value and thus
in interval 15 ≤ t < 20
80n
12.4.2 Posisie van / Position of P80 = ────
100
80 × 20
= ───────
100
= 16
P80 is die 16de waarde en is in
die interval 20 ≤ t < 25 /
P80 is the 16th value and thus in
interval 20 ≤ t < 25
12.4.2 Posisie van / Position of P80 = ────
100
80 × 20
= ───────
100
= 16
P80 is die 16de waarde en is in
die interval 20 ≤ t < 25 /
P80 is the 16th value and thus in
interval 20 ≤ t < 25