Te Pāngarau me te Tauanga, Kaupae 1, 2020

1910375

SUPERVISOR’S USE ONLY

91037M

© Mana Tohu Mātauranga o Aotearoa, 2020. Pūmau te mana.Kia kaua rawa he wāhi o tēnei tuhinga e tāruatia ki te kore te whakaaetanga a te Mana Tohu Mātauranga o Aotearoa.

Te Pāngarau me te Tauanga, Kaupae 1, 202091037M Te whakaatu māramatanga ki te tūponotanga,

raraunga hoki

9.30 i te ata Rāmere 20 Whiringa-ā-rangi 2020 Ngā whiwhinga: Whā

Paetae Kaiaka KairangiTe whakaatu māramatanga ki te tūponotanga, raraunga hoki.

Te whakaatu māramatanga ki te tūponotanga, raraunga hoki me te parahau i ngā kīanga me ngā kitenga.

Te whakaatu māramatanga ki te tūponotanga, raraunga hoki me te whakaatu i te matatau ki te tauanga.

Tirohia mēnā e rite ana te Tau Ākonga ā-Motu (NSN) kei runga i tō puka whakauru ki te tau kei runga i tēnei whārangi.

Me whakautu e koe ngā pātai KATOA kei roto i te pukapuka nei.

Tuhia ō mahinga KATOA.

Mēnā ka hiahia whārangi atu anō mō ō tuhinga, whakamahia te wāhi wātea kei muri o tēnei pukapuka.

Tirohia mēnā e tika ana te raupapatanga o ngā whārangi 2-31 kei roto i tēnei pukapuka, ka mutu, kāore tētahi o aua whārangi i te takoto kau.

ME HOATU RAWA KOE I TĒNEI PUKAPUKA KI TE KAIWHAKAHAERE Ā TE MUTUNGA O TE WHAKAMĀTAUTAU.

MĀ TE KAIMĀKA ANAKE

TAPEKE

Tohua tēnei pouaka mēnā kāore he tuhituhi i

roto i tēnei pukapuka

Te Pāngarau me te Tauanga 91037M, 2020

MĀ TE KAIMĀKA

ANAKE

TŪMAHI TUATAHI

He manu iti noa te tūturiwhatu nō Aotearoa. Kitea noatia ana i ngā takutai, ngā wahapū me ngā kūkūpango. Ka rerekē te taupori o ēnei manu i ētahi wā o te tau i te wā e nekeneke haere ana i roto o Aotearoa, ā, atu ki Ahitereiria hoki.

E whakaatu te kauwhata i raro i te taupori o ngā tūturiwhatu i tētahi wāhi i Aotearoa i waenga i te Kohitātea 2015 me te Whiringa-ā-nuku 2020.

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(a) Nōnahea i kitea ai te rahinga iti rawa o te tūturiwhatu?

Parahautia tō tuhinga.

http://nzbirdsonline.org.nz/species/banded-dotterel

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MĀ TE KAIMĀKA

ANAKE

(b) Matapakitia ngā ia, ngā tauira auau me ngā āhuatanga rerekē e kite ana koe i roto i te kauwhata raraunga o te maha o ngā tūturiwhatu i tēnei tauwāhi.

Tukuna mai ngā whakaaturanga mai i te kauwhata hei tautoko i ō tauākī.

Parahautia tō tuhinga ki ngā pūtake tauanga.

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QUESTION ONE

The tūturiwhatu (also known as the banded dotterel) is a small New Zealand bird. It is typically found along seashores, estuaries, and riverbeds. The population of these birds changes during certain times of the year as they move within New Zealand and as far away as Australia.

The graph below shows the population of tūturiwhatu at one location in New Zealand between January 2015 and October 2020.

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Population of tūturiwhatu (banded dotterel)

(a) When was the lowest number of tūturiwhatu recorded?

Justify your answer.

http://nzbirdsonline.org.nz/species/banded-dotterel

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Mathematics and Statistics 91037, 2020

ASSESSOR’S USE ONLY

(b) Discuss any trends, regular patterns, and unusual features that you notice in the graph of the data of the number of tūturiwhatu at this location.

Provide evidence from the graph to back up your statements.

Justify your answer using statistical reasons.

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MĀ TE KAIMĀKA

ANAKE

(c) Kāore ētahi o ngā tūturiwhatu e neke atu ki ētahi atu wāhi i te mea kua tino māuiui, kua pakeke rānei ki te rere.

E whakaatu ana te papatau i raro i tētahi tīpakonga matapōkere o ngā tūturiwhatu 1350 i Rakiura i te tau 2019 i wehe atu, i noho mai rānei.

I hopukia tēnei tīpakonga mā te ira manu.

I wehe atu I noho mai Tapeke

Uwha 690 165 855

Toa 410 85 495

Tapeke 1100 250 1350

(i) I tīpakohia tētahi tūturiwhatu mai i tēnei tīpakonga.

He aha te tūponotanga i noho mai he uwha?

(ii) I noho mai tētahi tūturiwhatu i tīpakohia. He aha te tūponotanga he toa?

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MĀ TE KAIMĀKA

ANAKE


(iii) Ko te tikanga ka wehe atu he uwha, he toa rānei?

Parahautia tō tuhinga ki ngā raraunga kei te papatau o te whārangi 6.

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(c) Some of the tūturiwhatu will not move to other areas because they are too sick or too old to travel far.

The table below shows a random sample of 1350 tūturiwhatu on Stewart Island during 2019 that either moved away or stayed.

This sample was recorded by gender.

Moved away Stayed Totals

Female 690 165 855

Male 410 85 495

Totals 1100 250 1350

(i) One tūturiwhatu was selected from this sample.

What is the probability that it is a female that stayed?

(ii) One of the tūturiwhatu that stayed was selected. What is the probability that it is male?

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(iii) Is a female or male tūturiwhatu more likely to move away?

Justify your answer using the data provided in the table on page 8.

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MĀ TE KAIMĀKA

ANAKE

TŪMAHI TUARUA

(a) Kitea ai ngā tohorā tuapuku i ngā moana nui, iti hoki puta noa i te ao.

E whakaatu ana te kauwhata i raro i ngā taumaha o tētahi tīpakonga matapōkere o ngā tohorā tuapuku toa me te uwha, e inea ana ki te kirokaramu.

He mea kohikohi ngā raraunga mai i ngā tohorā tuapuku i te tai hauāuru o Aotearoa i te koanga o te tau 2019.

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Toamōkito: 29001lq: 29399wawaenga: 29446tau toharite: 29481uq: 29600mōrahi: 29999tau: 30

Uwhamōkito: 29131lq: 29371.5wawaenga: 29673tau toharite: 29620uq: 29766.5mōrahi: 29999tau: 40

Taumaha o ngā tohorā tuapuku mā te ira tohorā

Uwha

Toa

(i) I kī tētahi ākonga he whānui ake te pouaka o ngā tohorā tuapuku uwha i te pouaka o ngā tohorā tuapuku toa.

Whakamāramatia mai he aha te tikanga o tēnei ina whiriwhiri ana i tēnei tīpakonga tohorā tuapuku.

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MĀ TE KAIMĀKA

ANAKE

(ii) Āta whakaahuatia kia rua ngā āhuatanga hira rerekē i te iti rawa ki te tuaritanga o te tīpakonga o ngā taumaha mō ngā tohorā tuapuku toa me te uwha.

Me kōrero mō ngā ōritetanga me ngā rerekētanga.

(iii) Ka puta tētahi whakapae i te koanga 2019, i te nuinga o te wā he taumaha ake ngā tohorā tuapuku uwha i ngā tohorā tuapuku toa i ngā takutai katoa o Aotearoa.

Homai he kōrero mō tēnei whakapae, e ai ki te tīpakonga o ngā tohorā kua tukuna.


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QUESTION TWO

(a) Humpback whales are found in oceans and seas all around the world.

The graph below compares the weights of a random sample of male and female humpback whales, measured in kilograms.

The data has been collected from humpback whales found along the west coast of New Zealand during spring in 2019.

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Malemin: 29001lq: 29399med: 29446mean: 29481uq: 29600max: 29999num: 30

Femalemin: 29131lq: 29371.5med: 29673mean: 29620uq: 29766.5max: 29999num: 40

Weight of humpback whales by gender

Female

Male

(i) A student comments that the box of the female humpback whales is wider than the box of the male humpback whales.

Interpret what this means when considering this sample of humpback whales.

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(ii) Clearly describe at least two different key features in the sample distribution of the weights for both male and female humpback whales.

Note any similarities and differences.

(iii) A claim is made that in the spring of 2019, female humpback whales tended to weigh more than male humpback whales around all of the coasts of New Zealand.

Comment on this claim, based on the sample of whales provided.


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MĀ TE KAIMĀKA

ANAKE

(b) He rā tuwhera nui tā te Society for the Prevention of Cruelty to Animals (SPCA) i Aotearoa i ia tau, e whakatenatenatia ana te tangata kia haere ake ki te SPCA o tō rātou rohe ki te tiki mōkai mā rātou.

E whakataurite ana te kauwhata i raro i tētahi tīpakonga matapōkere o ngā kararehe e 820 i whakahokia ki te kāinga mai i tētahi SPCA o te rohe i te rā tuwhera kua hipa.

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(i) He aha te tūponotanga ko te kararehe ka whakahokia ki te kāinga mai i tēnei SPCA he kinipoaka?

(ii) He aha te tūponotanga mēnā he kurī te kararehe ka whakahokia ki te kāinga mai i tēnei SPCA he uwha?

(iii) E kī ana tētahi tuhipānui o te ipurangi he nui ake te tūponotanga he uwha ngā kararehe ka whakahokia ki te kāinga i ēnei rā tuwhera, i te toa.

Arotakehia tēnei whakapae mā ngā pūtake tauanga, ka homai kia toru ngā kōrero i te iti rawa.

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MĀ TE KAIMĀKA

ANAKE


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(b) The Society for the Prevention of Cruelty to Animals (SPCA) in New Zealand has a special open day every year, when people are encouraged to visit their local centre and take home a pet.

The graph below compares a random sample of 820 animals that were taken home from one local SPCA centre on its last open day.

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(i) What is the probability that an animal taken home from this SPCA centre was a guinea pig?

(ii) What is the probability that if a dog was taken home from this SPCA centre, it was female?

(iii) An article on the internet claims that female animals have more chance than male animals of being taken home on one of these open days.

Evaluate this claim using statistical reasoning, providing at least three comments.

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MĀ TE KAIMĀKA

ANAKE

TŪMAHI TUATORU

(a) Ko ngā arewhana o Awherika tētahi o ngā momo maha o te arewhana. Ka tīpakohia tētahi tīpakonga matapōkere o ngā arewhana o Awherika 55 mai i ngā rohe kararehe, mai i te koraha hoki.

E whakaatu ana te kauwhata marara i raro i te pānga i waenga i te nui o te wae me te hope o ngā arewhana. Ka inea te nui o te wae me te hope ki te cm.

Ko ngā tapawhā pango he inenga pango ērā he mea tango i ngā arewhana toa o Awherika. Ko ngā ira kiwikiwi nō ngā arewhana uwha o Awherika.

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(i) Homai he kōrero mō te tūponotanga ka nui ake i te 450 cm te nui o te hope o tētahi arewhana o Awherika.


(ii) Ki te kauwhata marara i runga ake, tātuhia he rārangi e tino hāngai ana ki te pānga i waenga i te “nui o te wae” me te “nui o te hope” o ngā arewhana o Awherika.

Me kōrero mō te kaha o te pānga.


Ki te hiahia koe ki te tuhi anō i tēnei

kauwhata, whakamahia te tukutuku kei te

whārangi 26.

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MĀ TE KAIMĀKA

ANAKE

(iii) Whakaahuatia mai me te whakamāori kia rua i te iti rawa ngā āhuatanga rerekē ka kitea i roto i te kauwhata o te “nui o te hope” ki te “nui o te wae” i roto i tēnei tīpakonga o ngā arewhana o Awherika.


(iv) E whakapono ana a Difyr ka tino whaitake tēnei kauwhata marara hei matapae i te nui o te hope o ngā arewhana katoa e ai ki te nui o te wae.

Aromātaihia te whakapae a Difyr mā te whakamahi i te pūtake tauanga, ā, ka homai kia toru ngā tauākī kua parahautia i te iti rawa.

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QUESTION THREE

(a) African elephants are one of several species of elephant. A random sample of 55 African elephants from zoos and from the wild are selected.

The scatter graph below shows the relationship between the foot size of elephants and their waist size. Foot size and waist size are both measured in cm.

The black squares are measurements taken from male African elephants. The grey dots are from female African elephants.

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African elephant waist size v foot size

(i) Comment on the chance of an African elephant having a waist size greater than 450 cm.


(ii) On the scatter graph above, draw a line that best fits the relationship between the “foot size” and “waist size” of African elephants.

Comment on the strength of the relationship.


If you need to redraw this graph,

use the grid on page 27.

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(iii) Describe and interpret at least two different features visible in the graph of the data of “waist size” versus “foot size” in this sample of African elephants.


(iv) Difyr believes that this scatter graph would be very useful to predict the waist size of all elephants based on their foot size.

Evaluate Difyr’s claim using statistical reasoning, giving at least three different justified statements.

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MĀ TE KAIMĀKA

ANAKE

(b) I te rohe kararehe, ka tākaro a Māia, Teina rātou ko Nīkau i tētahi kēmu e taea ai te whiwhi tētahi tohu kararehe mēnā ka tāhurihuritia e rātou tētahi pikitia o taua kararehe.

E toru ngā momo tāhurihuri rerekē, arā, ko ngā pikitia o ngā arewhana, ngā raiona me ngā kumi ihuroa kei runga.

Ki te Tāhurihuri X, e ono ngā pikitia – e rua ngā arewhana, e rua ngā raiona, e rua ngā kumi ihuroa.

Ki te Tāhurihuri Y, e ono ngā pikitia – e toru ngā arewhana, e rua ngā raiona, kotahi te kumi ihuroa.

E toru anake ngā mata o te Tāhurihuri Z, ā, kotahi anake te pikitia kei ia mata – kotahi he arewhana, kotahi he raiona, kotahi he kumi ihuroa.

Tāhurihuri X Tāhurihuri Y Tāhurihuri Z

(i) Ko te whakaaro o Māia ka nui ake te tūponotanga ka wikitōria ia i tētahi tohu kumi ihuroa (mā te tāhurihuri i tētahi kumi ihuroa) mēnā ka whakamahia e ia te Tāhurihuri X. E whakaae ana koe?


(ii) Ka tāhurihuritia e Teina te Tāhurihuri Z kia rima ngā wā, e manako ana ia kia wikitōria i tētahi tohu arewhana.

Anei ana otinga i muri i ngā tāhurihuringa e rima: raiona kumi ihuroa kumi ihuroa raiona kumi ihuroa

E whakapono ana a Teina kei te tītaha pea te āhua o te Tāhurihuri Z i te mea kāore i puta ake te pikitia o te arewhana i roto i ana tāhurihuringa e rima. Kei te whakaae koe?


Ngā ata: www.flaticon.com

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ANAKE


(iii) Ka tāhurihuritia e Nīkau ana huringa katoa e toru i te wā kotahi. He aha te tūponotanga ka wikitōria ngā tāhurihuri katoa e toru i tētahi tohu arewhana?


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(b) At the zoo, Maia, Teina, and Nikau play a game that will allow them to win an animal badge if they spin a picture of that animal.

There are three different spinners, with pictures of elephants, lions, and crocodiles on them.

On Spinner X, there are six pictures – two of elephants, two of lions, two of crocodiles.

On Spinner Y, there are also six pictures – three of elephants, two of lions, one of a crocodile.

Spinner Z has only three faces with a single picture on each face – one of an elephant, one of a lion, one of a crocodile.

Spinner X Spinner Y Spinner Z

(i) Maia thinks that she has more chance of winning a crocodile badge (by spinning a picture of a crocodile) if she uses Spinner X. Do you agree?


(ii) Teina spins Spinner Z five times, hoping to win an elephant badge.

His results after five spins were: lion crocodile crocodile lion crocodile

Teina believes that Spinner Z must be biased in some way because the elephant picture did not appear at all after his five spins. Do you agree?


Icons: www.flaticon.com

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(iii) Nikau spins all three spinners once each. What is the chance that all three spinners will win an elephant badge?


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MĀ TE KAIMĀKA

ANAKE

NGĀ TUKUTUKU TĀPIRI

Ki te hiahia koe ki te tātuhi anō i tō urupare ki te Tūmahi Toru (a)(ii), whakamahia te kauwhata i raro nei. Kia mārama tonu tō tohu ko tēhea te tuhinga ka hiahia koe kia mākahia.

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SPARE GRIDS

If you need to redo Question Three (a)(ii), use the graph below. Make sure you make it clear which answer you want marked.

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MĀ TE KAIMĀKA

ANAKETAU TŪMAHI

He whārangi anō ki te hiahiatia.Tuhia te (ngā) tau tūmahi mēnā e tika ana.


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QUESTION NUMBER

Extra space if required.Write the question number(s) if applicable.

MĀ TE KAIMĀKA

ANAKETAU TŪMAHI

He whārangi anō ki te hiahiatia.Tuhia te (ngā) tau tūmahi mēnā e tika ana.


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31



QUESTION NUMBER

Extra space if required.Write the question number(s) if applicable.

Level 1 Mathematics and Statistics 202091037 Demonstrate understanding of chance and data

9.30 a.m. Friday 20 November 2020 Credits: Four

Achievement Achievement with Merit Achievement with ExcellenceDemonstrate understanding of chance and data.

Demonstrate understanding of chance and data, justifying statements and findings.

Demonstrate understanding of chance and data, showing statistical insight.

Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page.

You should attempt ALL the questions in this booklet.

Show ALL working.

If you need more room for any answer, use the extra space provided at the back of this booklet.

Check that this booklet has pages 2–31 in the correct order and that none of these pages is blank.

YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION.

9103

7M

English translation of the wording on the front cover

Te Pāngarau me te Tauanga, Kaupae 1, 2020

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