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© Mana Tohu Mātauranga o Aotearoa, 2015. Pūmau te mana. Kia kaua rawa he wāhi o tēnei tuhinga e whakahuatia ki te kore te whakaaetanga tuatahi a te Mana Tohu Mātauranga o Aotearoa.

MĀ TE KAIMĀKA ANAKE

TAPEKE

Te Pāngarau me te Tauanga, Kaupae 1, 201591037M Te whakaatu māramatanga ki te tūponotanga,

raraunga hoki

9.30 i te ata Rāhina 9 Whiringa-ā-rangi 2015 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 whakamātau koe i ngā tūmahi KATOA kei roto i tēnei pukapuka.

Whakaaturia ngā mahinga KATOA.

Mēna ka hiahia whārangi atu anō mō ō tuhinga, whakamahia ngā whārangi wātea kei muri o tēnei pukapuka, ka āta tohu ai i ngā tau tūmahi.

Tirohia mēnā e tika ana te raupapatanga o ngā whārangi 2 – 21 kei roto i tēnei pukapuka, ā, 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.

Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKE

TŪMAHI TUATAHI

E whakaatu ana te kauwhata e whai ake nei i te maha o ngā tāngata e wehe ana i Aotearoa ki te hararei i Ahitereiria, i Haina rānei.

E whakaatu ana te kauwhata i te maha o ngā tāngata e haere ana i ia hauwhā, mai i te tau 2000 ki te tau 2009.

He 3 marama ia hauwhā (Q1 = Kohitātea ki te Poutūterangi, Q2 = Paengawhāwhā ki te Pipiri, Q3 = Hōngongoi ki te Mahuru, Q4 = Whiringa-ā-nuku ki te Hakihea).

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Ahitereiria

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Te Maha o ngā Tāngata e Wehe ana i Aotearoa ki te Hararei

Tau me te hauwhā

Te m

aha

o ng

ā tā

ngat

a e

haer

e an

a ki

te w

henu

a (ia

hau

whā

)

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Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKE

(a) Kōrero mō te kauwhata e pā ana ki te maha o ngā tāngata e haere ana ki Ahitereiria mō ngā hararei.

Me matapaki koe i ngā ia, ngā pānga ā-wāhanga tau, ngā āhuatanga rerekē rānei ka kite koe.

(b) He pēhea te taurite o te kauwhata o ngā tāngata e haere ana ki Haina ki te kauwhata o ngā tāngata e haere ana ki Ahitereiria i roto i ēnei tau?

Me matapaki koe i ngā rerekētanga, ōritetanga rānei i roto i ngā kauwhata.

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QUESTION ONE

The following graph shows how many people leave New Zealand for holidays to Australia or to China.

The graph shows the number of people travelling per quarter, from 2000 to 2009.

Each quarter is a group of 3 months (Q1 = January to March, Q2 = April to June, Q3 = July to September, Q4 = October to December).

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Australia

China

Number of People Leaving New Zealand for Holidays

Year and quarter

Num

ber o

f peo

ple

goin

g to

the

coun

try (p

er q

uarte

r)

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Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

(a) Comment on the graph of the number of people going to Australia for holidays.

You should discuss any trends, seasonal effects, or unusual features that you notice.

(b) How does the graph of people going to China compare with the graph of people going to Australia over these years?

You should discuss any differences or similarities in the graphs.

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Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKE

(c) E whakaatu ana tēnei kauwhata i te ōrau o ngā tāngata haere i haere ki Haina i ia hauwhā o te tau 2014.

Ngā tāngata haere ki Haina 2014

Hauwhā 128%

Hauwhā 429%

Hauwhā 222%

Hauwhā 321%

(i) Ka kōwhirihia matapōkeretia tētahi tangata haere ki Haina mai i te tau 2014.

He aha te tūponotanga kāore ia i haere i te hauwhā 4 (Q4)?

(ii) Ka kōwhirihia matapōkerehia tētahi tangata haere ki Haina mai i te tau 2015.

Whakatau tatahia te tūponotanga kāore ia i haere i te hauwhā 4 (Q4) o te tau 2015.

Whakamāramahia ō whakaaro whaitake.

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(c) This graph shows the percentage of travellers who travelled to China in each quarter of 2014.

Travellers to China in 2014

1st Quarter28%

4th Quarter29%

2nd Quarter22%

3rd Quarter21%

(i) A traveller to China in 2014 is chosen at random.

What is the probability that they did not travel in the 4th quarter (Q4)?

(ii) A traveller to China in 2015 is chosen at random.

Estimate the probability that they did not travel in the 4th quarter (Q4) of 2015.

Explain your reasoning.

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Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKE

TŪMAHI TUARUA

E kī ana te whaea o Rei “he pai ake te pūmahara o ngā wāhine i ngā tāne”. Ka whakaaro a Rei mēnā he pono tēnei. Ka whakamahia e ia ētahi raraunga mai i Te Tatauranga i ngā Kura hei whakautu i tana pātai. He mea kohi ngā raraunga mai i ngā ākonga i whakauru ki tētahi whakamātautau pūmahara tuihono e whakamāramahia ana e ēnei kupu:

Whakamātauhia tō pūmahara. He pēhea tō tere ki te tūhono i ngā pikitia takirua katoa? • Pāwhirihia te Tīmata ka pāwhiri i ngā tapawhā e rua hei hura i ana pikitia. • Ka noho hura ngā tapawhā ōrite. • Me pāwhiri tonu kia kitea e hia ngā takirua ka huraina e koe i roto i te 3 meneti.

Koinei tō tatau pūmahara.

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Memory Test ScoresNgā Tatau Whakamātautau Pūmahara

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Wāhine

Tāne

(a) Whakatauritehia te tuaritanga o ngā tatau whakamātautau pūmahara mō ngā tāne me ngā wāhine.

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QUESTION TWO

Rei’s mother says that “females have better memories than males”. Rei wonders if this is true. He uses some data from Census at Schools to try to answer his question. The data was collected from students who took part in an online memory test described by these words:

Test your memory. How quickly can you match all the pairs of pictures? • Click on “Start” and then click on two squares to uncover their pictures. • Matching squares will remain uncovered. • Keep clicking to see how many pairs you can uncover in 3 minutes.

This is your memory score.

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Memory score groups

Females

Males

Memory Test Scores

(a) Compare the distribution of memory test scores for males and for females.

9

Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKE

Ka tuaruatia i raro nei te kauwhata pou a Rei kei te whārangi o mua ake.

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Memory Test ScoresNgā Tatau Whakamātautau PūmaharaA

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(b) Mā te tirotiro i te kauwhata i runga ake, he pai ake ngā wāhine i ngā tāne mō te whakamātautau pūmahara?

Whakamāramahia tō tuhinga.

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Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKE

(c) He pai anō ngā raraunga o tēnei whakamātautau hei whakamātau mā Rei i te tauākī a tōna whaea “he pai ake ngā pūmahara o ngā wāhine i ngā tāne”?

Parahautia tō tuhinga.

(d) Ka āta tirotiro a Rei ki te kauwhata pou me tana kite anō he nui ake ngā raraunga mai i ngā wāhine tēnā i ngā tāne.

He aha ngā mea ka taea e ia ināianei me ana raraunga, me tana kauwhata rānei kia pai ake te whakaatu a tana kauwhata pou i ngā raraunga?

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Rei’s bar graph on the previous page is repeated below.

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Memory Test Scores

(b) Looking at the graph above, are females better at this memory test than males?

Explain your answer.

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Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

(c) Is the data from this experiment a good way for Rei to test his mother’s statement that “females have better memories than males”?

Justify your answer.

(d) Rei looks closely at his bar graph and realises that there was more data from females than from males.

What could he now do with his data or his graph to make his bar graph display the data better?

13

Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKE

TŪMAHI TUATORU

Kei te tūtohi i raro nei ngā tauanga mō ngā raraunga a Rei:

Mōkito Hauwhā Raro

Tau Waenga

Toharite Hauwhā Runga

Mōrahi Rahi o te Tīpako

wahine 21 36 42 44.88 50 94 284tāne 23 39 48 50.7 59 98 203

(a) Mā te whakamahi i ngā raraunga i roto i tēnei tūtohi, he aha te inenga whānui i waenga hauwhā mō ngā wāhine?

(b) He nui ake ngā wāhine i ngā tāne i roto i tēnei tīpako. E kī ana te hoa o Rei a Waiari kāore i te tika ngā otinga me ngā kauwhata nā tēnei take.

Kei te whakaae koe, kāore rānei?

Whakamahia te whakaaro whaitake o te tauanga hei parahau i tō tuhinga.

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Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKE

(c) (i) Ki te kōwhirihia matapōkeretia tētahi ākonga mai i tēnei tīpako, he aha te tūponotanga he tāne te ākonga?

(ii) Ki te kōwhirihia matapōkeretia tētahi tāne mai i tēnei tīpako, he aha te tūponotanga he 59, iti ake rānei tana tatau whakamātautau pūmahara?

(d) I tāpirihia te tatau a Brianna ki te tīpako mō ngā wāhine. I piki te tatau toharite mō ngā wāhine, ā, i noho ōrite tonu te tatau waenga.

He aha ō mōhio mō te tatau whakamātautau a Brianna?

Whakamāramahia ō whakaaro whaitake.

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QUESTION THREE

The statistics for Rei’s data are given in the table below:

Min. Lower Quartile

Median Mean Upper Quartile

Max. Sample Size

female 21 36 42 44.88 50 94 284male 23 39 48 50.7 59 98 203

(a) Using the data in this table, what is the interquartile range for the females?

(b) There are more females than males in this sample. Rei’s friend Waiari said that the results and the graphs are not fair because of this.

Do you agree or disagree?

Use statistical reasons to justify your answer.

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Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

(c) (i) If a student from this sample was chosen at random, what is the probability that the student is male?

(ii) If a male from this sample was chosen at random, what is the probability that his memory test score is 59 or less?

(d) Brianna’s score was added to the sample of females used here. The mean score for the females then went up, while the median score stayed the same.

What can you deduce about Brianna’s test score?

Explain your reasoning.

17

Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKE

(e) I te whakaaroaro a Rei mēnā he pānga o ngā tau o ngā ākonga ki te pai o ā rātau tatau. I tuhia e ia te kauwhata marara i raro nei.

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Memory vs AgePūmahara ki te Tau

Tata

u w

haka

māt

auta

u pū

mah

ara

Tau

He aha te whakatau a Rei mō te pānga i waenga i ngā tau o ngā ākonga me ā rātau tatau whakamātautau pūmahara e whakaaturia ana e tēnei kauwhata?

Whakamāramatia tō tuhinga.

18

(e) Rei wondered if the ages of the students doing the memory test affected how well they scored. He drew the scattergraph below.

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Memory vs Age

What should Rei conclude about the relationship between the age of the students and their memory test score revealed from this graph?

Explain your answer.

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Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

Te Pāngarau me te Tauanga, 91037M, 2015

MĀ TE KAIMĀKA

ANAKETAU TŪMAHI

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

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Mathematics and Statistics 91037, 2015

ASSESSOR’S USE ONLY

QUESTION NUMBER

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

91

03

7M

Level 1 Mathematics and Statistics, 201591037 Demonstrate understanding of chance and data

9.30 a.m. Monday 9 November 2015 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 space for any answer, use the page(s) provided at the back of this booklet and clearly number the question.

Check that this booklet has pages 2 – 21 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.

English translation of the wording on the front cover