91037M 910375 1SUPERVISOR'S USE ONLY Te Pāngarau me te Tauanga, Kaupae 1, 2015 91037M Te whakaatu māramatanga ki te tūponotanga, raraunga hoki 9.30 i te ata Rāhina 9 Whiringa-ā-rangi 2015 Whiwhinga: Whā Te whakaatu māramatanga ki te tūponotanga, raraunga hoki. Paetae Kaiaka Kairangi 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. TAPEKE MĀ TE KAIMĀKA ANAKE 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.
2 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). MĀ TE KAIMĀKA ANAKE Te Maha o ngā Tāngata e Wehe ana i Aotearoa ki te Hararei 45 000 40 000 Te maha o ngā tāngata e haere ana ki te whenua (ia hauwhā) 35 000 30 000 25 000 20 000 15 000 10 000 Ahitereiria 5 000 Haina 0 2000Q1 2010Q1 2009Q4 2009Q3 2009Q2 2009Q1 2008Q4 2008Q3 2008Q2 2008Q1 2007Q4 2007Q3 2007Q2 2007Q1 2006Q4 2006Q3 2006Q2 2006Q1 2005Q4 2005Q3 2005Q2 2005Q1 2004Q4 2004Q3 2004Q2 2004Q1 2003Q4 2003Q3 2003Q2 2003Q1 2002Q4 2002Q3 2002Q2 2002Q1 2001Q4 2001Q3 2001Q2 2001Q1 2000Q4 2000Q3 2000Q2 Tau me te hauwhā Te Pāngarau me te Tauanga, 91037M, 2015
3 (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. MĀ TE KAIMĀKA ANAKE (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. Te Pāngarau me te Tauanga, 91037M, 2015
4 QUESTION ONE ASSESSOR S USE ONLY 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). 45 000 Number of People Leaving New Zealand for Holidays 40 000 Number of people going to the country (per quarter) 35 000 30 000 25 000 20 000 15 000 10 000 Australia 5 000 China 0 2000Q1 2010Q1 2009Q4 2009Q3 2009Q2 2009Q1 2008Q4 2008Q3 2008Q2 2008Q1 2007Q4 2007Q3 2007Q2 2007Q1 2006Q4 2006Q3 2006Q2 2006Q1 2005Q4 2005Q3 2005Q2 2005Q1 2004Q4 2004Q3 2004Q2 2004Q1 2003Q4 2003Q3 2003Q2 2003Q1 2002Q4 2002Q3 2002Q2 2002Q1 2001Q4 2001Q3 2001Q2 2001Q1 2000Q4 2000Q3 2000Q2 Year and quarter Mathematics and Statistics 91037, 2015
(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. 5 ASSESSOR S USE ONLY (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. Mathematics and Statistics 91037, 2015
6 (c) E whakaatu ana tēnei kauwhata i te ōrau o ngā tāngata haere i haere ki Haina i ia hauwhā o te tau 2014. MĀ TE KAIMĀKA ANAKE Ngā tāngata haere ki Haina 2014 Hauwhā 4 29% Hauwhā 1 28% Hauwhā 3 21% Hauwhā 2 22% (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. Te Pāngarau me te Tauanga, 91037M, 2015
7 (c) This graph shows the percentage of travellers who travelled to China in each quarter of 2014. ASSESSOR S USE ONLY Travellers to China in 2014 4th Quarter 29% 1st Quarter 28% 3rd Quarter 21% 2nd Quarter 22% (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. Mathematics and Statistics 91037, 2015
8 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. MĀ TE KAIMĀKA ANAKE Auautanga Frequency 100 90 80 70 60 50 40 30 20 10 0 0 4 5 9 Ngā Tatau Memory Whakamātautau Test Scores Pūmahara 10 14 15 19 20 24 25 29 30 34 35 39 40 44 45 49 50 54 55 59 60 64 65 69 70 74 75 79 80 84 85 89 90 94 95 99 Ngā Memory rōpū tatau score pūmahara groups Females Wāhine Males Tāne (a) Whakatauritehia te tuaritanga o ngā tatau whakamātautau pūmahara mō ngā tāne me ngā wāhine. Te Pāngarau me te Tauanga, 91037M, 2015
9 QUESTION TWO ASSESSOR S USE ONLY 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. Frequency 100 90 80 70 60 50 40 30 20 10 0 Memory Test Scores 0 4 5 9 10 14 15 19 20 24 25 29 30 34 35 39 40 44 45 49 50 54 55 59 60 64 65 69 70 74 75 79 80 84 85 89 90 94 95 99 Memory score groups Females Males (a) Compare the distribution of memory test scores for males and for females. Mathematics and Statistics 91037, 2015
10 Ka tuaruatia i raro nei te kauwhata pou a Rei kei te whārangi o mua ake. MĀ TE KAIMĀKA ANAKE Auautanga Frequency 100 90 80 70 60 50 40 30 20 10 0 0 4 5 9 Ngā Tatau Memory Whakamātautau Test Scores Pūmahara 10 14 15 19 20 24 25 29 30 34 35 39 40 44 45 49 50 54 55 59 60 64 65 69 70 74 75 79 80 84 85 89 90 94 95 99 Ngā Memory rōpū tatau score pūmahara groups Females Wāhine Males Tāne (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. Te Pāngarau me te Tauanga, 91037M, 2015
11 (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. MĀ TE KAIMĀKA ANAKE (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? Te Pāngarau me te Tauanga, 91037M, 2015
12 Rei s bar graph on the previous page is repeated below. ASSESSOR S USE ONLY Frequency 100 90 80 70 60 50 40 30 20 10 0 Memory Test Scores 0 4 5 9 10 14 15 19 20 24 25 29 30 34 35 39 40 44 45 49 50 54 55 59 60 64 65 69 70 74 75 79 80 84 85 89 90 94 95 99 Memory score groups Females Males (b) Looking at the graph above, are females better at this memory test than males? Explain your answer. Mathematics and Statistics 91037, 2015
(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. 13 ASSESSOR S USE ONLY (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? Mathematics and Statistics 91037, 2015
14 TŪMAHI TUATORU Kei te tūtohi i raro nei ngā tauanga mō ngā raraunga a Rei: MĀ TE KAIMĀKA ANAKE Mōkito Hauwhā Raro Tau Waenga Toharite Hauwhā Runga Mōrahi Rahi o te Tīpako wahine 21 36 42 44.88 50 94 284 tāne 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. Te Pāngarau me te Tauanga, 91037M, 2015
15 (c) (i) Ki te kōwhirihia matapōkeretia tētahi ākonga mai i tēnei tīpako, he aha te tūponotanga he tāne te ākonga? MĀ TE KAIMĀKA ANAKE (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. Te Pāngarau me te Tauanga, 91037M, 2015
16 QUESTION THREE ASSESSOR S USE ONLY 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 94 284 male 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. Mathematics and Statistics 91037, 2015
17 (c) (i) If a student from this sample was chosen at random, what is the probability that the student is male? ASSESSOR S USE ONLY (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. Mathematics and Statistics 91037, 2015
18 (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. MĀ TE KAIMĀKA ANAKE 100 Pūmahara Memory ki vs te Age Tau Tatau whakamātautau Memory test score pūmahara 80 60 40 20 6 8 10 12 14 16 18 Age 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. Te Pāngarau me te Tauanga, 91037M, 2015
19 (e) Rei wondered if the ages of the students doing the memory test affected how well they scored. He drew the scattergraph below. ASSESSOR S USE ONLY 100 Memory vs Age 80 Memory test score 60 40 20 6 8 10 12 14 16 18 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. Mathematics and Statistics 91037, 2015
20 TAU TŪMAHI He whārangi anō ki te hiahiatia. Tuhia te (ngā) tau tūmahi mēnā e tika ana. MĀ TE KAIMĀKA ANAKE Te Pāngarau me te Tauanga, 91037M, 2015
21 QUESTION NUMBER Extra paper if required. Write the question number(s) if applicable. ASSESSOR S USE ONLY Mathematics and Statistics 91037, 2015
English translation of the wording on the front cover Level 1 Mathematics and Statistics, 2015 91037 Demonstrate understanding of chance and data 9.30 a.m. Monday 9 November 2015 Credits: Four 91037M Achievement Achievement with Merit Achievement with Excellence Demonstrate 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.