STATISTIEK 1 E BACH
CONTENTS
Hoofdstuk 1 – Statistiek, gegevens en een kritische houding ................................................................................. 5
1.1 de wetenschap statistiek ....................................................................................................................... 5
1.2 Soorten statistische toepassingen ......................................................................................................... 5
1.3 Basiselementen van de statistiek .......................................................................................................... 5
1.4 Soorten gegevens .................................................................................................................................. 6
1.5 Gegevens verzamelen ............................................................................................................................ 7
1.6 Blijf kritisch ............................................................................................................................................ 8
Werkcollege 1 ..................................................................................................................................................... 8
Oefening 1.1 – Pagina 20 in boek .................................................................................................................... 8
Oefening 1.3 – Pagina 20 in boek .................................................................................................................... 8
Oefening 1.1 – In de cursus ............................................................................................................................. 8
Soorten gegevens/meetschalen...................................................................................................................... 9
Oefening 1.4 – in de cursus ............................................................................................................................. 9
oefening 1.5 – in de cursus ............................................................................................................................. 9
Oefening 1.7 – in boek .................................................................................................................................... 9
Oefening 1.6 – in cursus ................................................................................................................................ 10
Oefening 1.7 – in cursus ................................................................................................................................ 10
Hoofdstuk 2 – het beschrijven van gegevensverzamelingen ................................................................................ 11
2.1 Kwalitatieve gegevens beschrijven ............................................................................................................. 11
2.2 Kwantitatieve gegevens beschrijven met grafische methoden .................................................................. 14
2.3 Sommatienotatie......................................................................................................................................... 15
2.4 Beschrijving van het centrum ...................................................................................................................... 15
2.5 beschrijving van de spreiding ...................................................................................................................... 17
2.7 Hoe ver wijkt een waarneming af van de vorige waarnemingen? .............................................................. 20
2.8 uitschieters opsporen: box-plot en Z-scores ............................................................................................... 20
Werkcollege 2 ................................................................................................................................................... 22
Oefening 2.1 – in cursus ................................................................................................................................ 23
Oefening 2.2 – in cursus ................................................................................................................................ 24
Oefening 2.3 – in cursus ................................................................................................................................ 24
Z-score van een meting ................................................................................................................................. 25
Oefening 2.4 – in cursus ................................................................................................................................ 25
Oefening 2.5 – in cursus ................................................................................................................................ 26
Oefening 2.6 – in cursus ................................................................................................................................ 26
, Oefening 2.1 – Pagina 65 in boek .................................................................................................................. 26
2.6 Betekenis van de standaardafwijking .......................................................................................................... 28
Werkcollege 3 ................................................................................................................................................... 29
interpretatie standaardafwijking .................................................................................................................. 29
oEFENING 8 – in syllabus ............................................................................................................................... 29
Oefening 9 – in syllabus ................................................................................................................................ 29
Oefening 11 – in syllabus .............................................................................................................................. 30
Oefening 5 – pagina 66 in boek ..................................................................................................................... 30
Oefening 10 – pagina 67 in boek ................................................................................................................... 31
Hoofdstuk 3 – Kansrekening ................................................................................................................................. 32
3.1 Gebeurtenissen, uitkomstenruimten en kansen ......................................................................................... 32
3.2 Verenigingen en doorsneden ...................................................................................................................... 35
3.3 complementaire gebeurtenissen ................................................................................................................ 35
3.4 disjuncte gebeurtenissen ............................................................................................................................ 36
conceptvraag ..................................................................................................................................................... 36
Werkcollege 4 ................................................................................................................................................... 37
Oefening 3.3 – in syllabus ............................................................................................................................. 37
Oefening 3.6 – in syllabus ............................................................................................................................. 38
Oefening 3.2 – in boek pagina 103 ................................................................................................................ 38
Oefening 3.4 – in boek pagina 104 ................................................................................................................ 38
Oefening 3.5 – pagina 104 ............................................................................................................................ 38
3.5 Voorwaardelijke kans .................................................................................................................................. 39
3.6 De productregel en onafhankelijke gebeurtenissen ................................................................................... 39
Conceptvraag .................................................................................................................................................... 40
3.7 De regel van Bayes ...................................................................................................................................... 41
3.8 Het trekken van een aselecte steekproef ................................................................................................... 41
werkcollege 5 .................................................................................................................................................... 41
Regel van Bayes ............................................................................................................................................. 41
Oefening 3.5 – in syllabus ............................................................................................................................. 41
oefening 3.11 – in syllabus ............................................................................................................................ 42
Oefening 3.10 – in syllabus ........................................................................................................................... 42
Oefening 3.10 – in boek pagina 105 .............................................................................................................. 42
Oefening 3.11 – in boek pagina 105 .............................................................................................................. 43
Hoofdstuk 4 – Directe kansverdelingen ................................................................................................................ 44
4.1 Twee soorten stochastische variabelen .............................................................................................. 44
4.2 Discrete kansverdelingen .................................................................................................................... 44
4.3 Verwachtingswaarden ......................................................................................................................... 45
, 4.4 De binomiale verdeling ........................................................................................................................ 45
werkcollege 6 .................................................................................................................................................... 46
oefening 4.1 – in syllabus .............................................................................................................................. 46
Oefening 4.2 – in syllabus ............................................................................................................................. 46
Oefening 4.4 – in syllabus ............................................................................................................................. 46
Oefening 4.6 – in syllabus ............................................................................................................................. 47
Oefening 4.2 – pagina 128 in boek ................................................................................................................ 47
Werkcollege 7 ................................................................................................................................................... 48
Oefening 4.5 – uit de syllabus ....................................................................................................................... 48
oefening 4.9 – in syllabus .............................................................................................................................. 48
Oefening 4.10 – in syllabus ........................................................................................................................... 48
Oefening 4.3 – in het boek pagina 128 ......................................................................................................... 49
Oefening 4.4 – in het boek pagina 128 ......................................................................................................... 49
Hoofdstuk 5 – continue kansverdelingen.............................................................................................................. 50
5.1 Continue kansverdelingen ........................................................................................................................... 50
5.2 De uniforme verdeling ................................................................................................................................ 51
5.3 De normale verdeling .................................................................................................................................. 51
5.4 Beschrijvende methoden om te bepalen of een verdeling normaal is ....................................................... 53
5.5 De exponentiële verdeling .......................................................................................................................... 54
5.6 Lineaire combinaties van stochastische variabelen .................................................................................... 54
Werkcollege 8 ................................................................................................................................................... 55
Oefening 5.1 – in syllabus ............................................................................................................................. 55
Oefening 5.2 – in syllabus ............................................................................................................................. 55
Oefening 5.3 – in syllabus ............................................................................................................................. 56
Oefening 5.4 – in syllabus ............................................................................................................................. 56
Hoofdstuk 6 – Verdeling van steekproefgrootheden ............................................................................................ 57
6.1 De verdeling van de steekproefgrootheid................................................................................................... 57
6.2 De centrale limietstelling ............................................................................................................................ 57
Werkcollege 9 ................................................................................................................................................... 58
oEFENING 5.6 – in syllabus ............................................................................................................................ 58
Oefening 5.7 – in syllabus ............................................................................................................................. 59
Oefening 5.8 – in syllabus ............................................................................................................................. 59
Oefening 5.5 – in het boek ............................................................................................................................ 60
Werkcollege 10 ................................................................................................................................................. 60
oefeninG 6.1 – syllabus ................................................................................................................................. 60
Oefening 6.3 – in syllabus ............................................................................................................................. 61
oefening 6.6 – in syllabus .............................................................................................................................. 62
,
CONTENTS
Hoofdstuk 1 – Statistiek, gegevens en een kritische houding ................................................................................. 5
1.1 de wetenschap statistiek ....................................................................................................................... 5
1.2 Soorten statistische toepassingen ......................................................................................................... 5
1.3 Basiselementen van de statistiek .......................................................................................................... 5
1.4 Soorten gegevens .................................................................................................................................. 6
1.5 Gegevens verzamelen ............................................................................................................................ 7
1.6 Blijf kritisch ............................................................................................................................................ 8
Werkcollege 1 ..................................................................................................................................................... 8
Oefening 1.1 – Pagina 20 in boek .................................................................................................................... 8
Oefening 1.3 – Pagina 20 in boek .................................................................................................................... 8
Oefening 1.1 – In de cursus ............................................................................................................................. 8
Soorten gegevens/meetschalen...................................................................................................................... 9
Oefening 1.4 – in de cursus ............................................................................................................................. 9
oefening 1.5 – in de cursus ............................................................................................................................. 9
Oefening 1.7 – in boek .................................................................................................................................... 9
Oefening 1.6 – in cursus ................................................................................................................................ 10
Oefening 1.7 – in cursus ................................................................................................................................ 10
Hoofdstuk 2 – het beschrijven van gegevensverzamelingen ................................................................................ 11
2.1 Kwalitatieve gegevens beschrijven ............................................................................................................. 11
2.2 Kwantitatieve gegevens beschrijven met grafische methoden .................................................................. 14
2.3 Sommatienotatie......................................................................................................................................... 15
2.4 Beschrijving van het centrum ...................................................................................................................... 15
2.5 beschrijving van de spreiding ...................................................................................................................... 17
2.7 Hoe ver wijkt een waarneming af van de vorige waarnemingen? .............................................................. 20
2.8 uitschieters opsporen: box-plot en Z-scores ............................................................................................... 20
Werkcollege 2 ................................................................................................................................................... 22
Oefening 2.1 – in cursus ................................................................................................................................ 23
Oefening 2.2 – in cursus ................................................................................................................................ 24
Oefening 2.3 – in cursus ................................................................................................................................ 24
Z-score van een meting ................................................................................................................................. 25
Oefening 2.4 – in cursus ................................................................................................................................ 25
Oefening 2.5 – in cursus ................................................................................................................................ 26
Oefening 2.6 – in cursus ................................................................................................................................ 26
, Oefening 2.1 – Pagina 65 in boek .................................................................................................................. 26
2.6 Betekenis van de standaardafwijking .......................................................................................................... 28
Werkcollege 3 ................................................................................................................................................... 29
interpretatie standaardafwijking .................................................................................................................. 29
oEFENING 8 – in syllabus ............................................................................................................................... 29
Oefening 9 – in syllabus ................................................................................................................................ 29
Oefening 11 – in syllabus .............................................................................................................................. 30
Oefening 5 – pagina 66 in boek ..................................................................................................................... 30
Oefening 10 – pagina 67 in boek ................................................................................................................... 31
Hoofdstuk 3 – Kansrekening ................................................................................................................................. 32
3.1 Gebeurtenissen, uitkomstenruimten en kansen ......................................................................................... 32
3.2 Verenigingen en doorsneden ...................................................................................................................... 35
3.3 complementaire gebeurtenissen ................................................................................................................ 35
3.4 disjuncte gebeurtenissen ............................................................................................................................ 36
conceptvraag ..................................................................................................................................................... 36
Werkcollege 4 ................................................................................................................................................... 37
Oefening 3.3 – in syllabus ............................................................................................................................. 37
Oefening 3.6 – in syllabus ............................................................................................................................. 38
Oefening 3.2 – in boek pagina 103 ................................................................................................................ 38
Oefening 3.4 – in boek pagina 104 ................................................................................................................ 38
Oefening 3.5 – pagina 104 ............................................................................................................................ 38
3.5 Voorwaardelijke kans .................................................................................................................................. 39
3.6 De productregel en onafhankelijke gebeurtenissen ................................................................................... 39
Conceptvraag .................................................................................................................................................... 40
3.7 De regel van Bayes ...................................................................................................................................... 41
3.8 Het trekken van een aselecte steekproef ................................................................................................... 41
werkcollege 5 .................................................................................................................................................... 41
Regel van Bayes ............................................................................................................................................. 41
Oefening 3.5 – in syllabus ............................................................................................................................. 41
oefening 3.11 – in syllabus ............................................................................................................................ 42
Oefening 3.10 – in syllabus ........................................................................................................................... 42
Oefening 3.10 – in boek pagina 105 .............................................................................................................. 42
Oefening 3.11 – in boek pagina 105 .............................................................................................................. 43
Hoofdstuk 4 – Directe kansverdelingen ................................................................................................................ 44
4.1 Twee soorten stochastische variabelen .............................................................................................. 44
4.2 Discrete kansverdelingen .................................................................................................................... 44
4.3 Verwachtingswaarden ......................................................................................................................... 45
, 4.4 De binomiale verdeling ........................................................................................................................ 45
werkcollege 6 .................................................................................................................................................... 46
oefening 4.1 – in syllabus .............................................................................................................................. 46
Oefening 4.2 – in syllabus ............................................................................................................................. 46
Oefening 4.4 – in syllabus ............................................................................................................................. 46
Oefening 4.6 – in syllabus ............................................................................................................................. 47
Oefening 4.2 – pagina 128 in boek ................................................................................................................ 47
Werkcollege 7 ................................................................................................................................................... 48
Oefening 4.5 – uit de syllabus ....................................................................................................................... 48
oefening 4.9 – in syllabus .............................................................................................................................. 48
Oefening 4.10 – in syllabus ........................................................................................................................... 48
Oefening 4.3 – in het boek pagina 128 ......................................................................................................... 49
Oefening 4.4 – in het boek pagina 128 ......................................................................................................... 49
Hoofdstuk 5 – continue kansverdelingen.............................................................................................................. 50
5.1 Continue kansverdelingen ........................................................................................................................... 50
5.2 De uniforme verdeling ................................................................................................................................ 51
5.3 De normale verdeling .................................................................................................................................. 51
5.4 Beschrijvende methoden om te bepalen of een verdeling normaal is ....................................................... 53
5.5 De exponentiële verdeling .......................................................................................................................... 54
5.6 Lineaire combinaties van stochastische variabelen .................................................................................... 54
Werkcollege 8 ................................................................................................................................................... 55
Oefening 5.1 – in syllabus ............................................................................................................................. 55
Oefening 5.2 – in syllabus ............................................................................................................................. 55
Oefening 5.3 – in syllabus ............................................................................................................................. 56
Oefening 5.4 – in syllabus ............................................................................................................................. 56
Hoofdstuk 6 – Verdeling van steekproefgrootheden ............................................................................................ 57
6.1 De verdeling van de steekproefgrootheid................................................................................................... 57
6.2 De centrale limietstelling ............................................................................................................................ 57
Werkcollege 9 ................................................................................................................................................... 58
oEFENING 5.6 – in syllabus ............................................................................................................................ 58
Oefening 5.7 – in syllabus ............................................................................................................................. 59
Oefening 5.8 – in syllabus ............................................................................................................................. 59
Oefening 5.5 – in het boek ............................................................................................................................ 60
Werkcollege 10 ................................................................................................................................................. 60
oefeninG 6.1 – syllabus ................................................................................................................................. 60
Oefening 6.3 – in syllabus ............................................................................................................................. 61
oefening 6.6 – in syllabus .............................................................................................................................. 62
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