STATISTICS Higher Tier Paper 2

STATISTICS Higher Tier Paper 2 Monday 19 June 2023 Afternoon Time allowed: 1 hour 45 minutes Materials For this paper you must have: • a calculator • mathematical instruments. Instructions • Use black ink or black ball-point pen. Draw diagrams in pencil. • Fill in the boxes at the top of this page. • Answer all questions. • You must answer the questions in the spaces provided. Do not write outside the box around each page or on blank pages. • If you need extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s). • Do all rough work in this book. Cross out any work you do not want to be marked. Information • The marks for the questions are shown in brackets. • The maximum mark for this paper is 80. • You may ask for more answer paper and graph paper. These must be tagged securely to this answer booklet. *JUN23 3 22H01* IB/G/Jun23/E10 8382/2H Answer all questions in the spaces provided. 1 Tirunesh asks 50 people which of the following instruments they play, • piano (P) • violin (V) • trombone (T). The results are shown in the diagram. Tirunesh chooses one person at random. 1 (a) Circle the probability that this person plays the piano. 10 50 22 50 23 50 14 50 1 (b) Circle the value of P(V | T). [1 mark] [1 mark] box box Circle the number of customers who bought 3 tickets. [1 mark] 5 7 8 15 3 Tony is investigating students’ scores in statistics exams. He says that it depends on the following factors, • time spent studying • score in maths exams. Circle the term that best describes the type of data Tony uses. [1 mark] Turn over ► 4 The table shows information about births in the UK in 2010 and 2019. box Year 2010 2019 Number of births 807 300 712 700 Total population Birth rate 10.7 Source: ONS 4 (a) Complete the table by finding the birth rate in 2010. Use the formula number of births birth rate = total population × 1000 [2 marks] 4 (b) The birth rate in Iceland in 2019 was 12.5 Jack concludes, “Iceland had a higher number of births than the UK in 2019 because it had a higher birth rate.” Comment on Jack’s conclusion. [1 mark] 5 (a) Name one other consideration for Mr Roper when grouping the students. [1 mark] 5 (b) The test scores for the app group are shown in the stem-and-leaf diagram. 5 (b) (i) Work out the median score. [1 mark] Answer % 5 (b) (ii) Show that the interquartile range is 20% [2 marks] Turn over ► box 5 (c) The percentage scores of the 15 students who were in the book group are, box 71 46 57 37 50 44 69 40 58 83 42 56 39 55 79 Use these results to complete the back-to-back stem-and-leaf diagram that shows both sets of results on the same diagram. Remember to complete the key and the labels for the diagram. [4 marks] Turn over for the next question box *07* Turn over ► 6 Frieda, Piran and Elliot are investigating the most popular type of ice cream or ice lolly of the 1200 students at their school. They want to take a sample of 60 students. They each suggest a sampling method to collect the data. Frieda’s method Ask the first 60 students who arrive at school. Piran’s method Number each student on the register from 1 to 1200 Use a random number generator to find a starting point between 1 and 20 Choose to ask every 20th student after the starting point. Elliot’s method For each year group, put all the names of the students in a hat. Pick 5% of the names out for each year group. Ask each of these students. *0* box box 6 (c) (i) Write down the name of the sampling technique Elliot suggests. [1 mark] Answer 6 (c) (ii) The table shows the number of students in each year group at their school. Year Number of students 7 260 8 200 9 178 10 280 11 282 Calculate the number of students Elliot should sample from Year 7 [2 marks] Answer Question 6 continues on the next page Turn over ► 6 (d) The table shows the most popular types of ice cream or ice lolly and the percentage of people of different ages and gender who chose them in the UK. Gender (%) Age category (%) Ice cream or ice lolly All Male Female 18–24 25–49 50–64 65+ Magnum 28 27 28 12 22 39 42 Fab 8 9 8 11 11 6 1 Solero 8 6 9 7 8 8 7 Twister 7 6 7 11 10 2 2 Feast 6 5 7 6 9 6 1 Calippo 5 6 4 7 6 3 2 Orange 3 3 2 1 1 3 10 Cornetto 3 2 3 2 3 2 1 Other 32 36 32 43 30 31 34 Source: adapted from YouGov box Compare the preferences of different age groups. [2 marks] Comparison 1 Comparison 2 Turn over for the next question DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box Turn over ► 7 Leanne wants to buy a ticket to fly from Manchester to Greece next year. Tickets are released by the airline exactly six months in advance of departure. She investigates how the price of tickets changes over these six months. She draws this scatter graph showing the ticket price, £P, plotted against the time in months, t, since the tickets were released. Leanne calculates that the equation of the regression line for her data is, P = 32t − 16 7 (a) Interpret the value of 32 in Leanne’s equation. Give your answer in context. [1 mark] 7 (b) Leanne does not want to pay more than £100 for her ticket next year. Use the equation of the regression line to predict the latest time after tickets are released that Leanne could buy a ticket. [2 marks] Answer months 7 (c) Give a reason, in context, why the regression equation is not appropriate when the tickets are initially released. [1 mark] 7 (d) The product moment correlation coefficient for Leanne’s data is 0.91 Leanne says, “This shows there is a strong linear relationship.” Looking at the scatter graph, is Leanne’s conclusion appropriate? Tick () a box. Yes No Give a reason for your answer. [1 mark] Turn over for the next question Turn over ► 8 The table shows average house prices in the UK. box Year Average price (£) 2016 283 000 2017 280 000 Source: ONS 8 (a) Comment on the reliability of the source of the data. [1 mark] 8 (b) Using 2016 as the base year, show that the index number for 2017, to 1 decimal place, is 98.9 [1 mark] 8 (c) Using 2016 as the base year, the index number for 2020 is 107.0 8 (c) (i) A house purchased in 2016 cost £430 000 Calculate an estimate for the value of this house in 2020. [2 marks] Answer £ 8 (c) (ii) Carla bought a house for £215 000 in 2016 and sold it for £233 000 in 2020. Did Carla’s house increase by a greater proportion than the index number for 2020 suggests? Tick () a box. Yes No You must show your working. [2 marks] 8 (d) The table shows some index numbers relating to average house prices for a town. Year Index number 2017 100 2019 96.2 2021 104.2 Andy says, “Average house prices in the town increased by 8% from 2019 to 2021.” Is Andy’s conclusion valid? Tick () a box. Give a reason for your answer. [1 mark] Turn over ► 9 An airline records the length of delay, in minutes, whenever a flight is delayed. The histogram represents this information for flights in May. Flights in May 9 (a) Calculate an estimate for the number of flights in May that were delayed by more than 20 minutes. [3 marks] Answer 9 (b) (i) Give a reason why it is not possible to calculate the exact value of the mean length of a delay from the histogram. [1 mark] 9 (b) (ii) Give a reason why the mean may not be representative for the length of a delay in May. [1 mark] 9 (c) The histogram represents the length of delay, in minutes, for flights in June. Flights in June The director of the airline says, “The range for the length of a delay was smaller in June than in May.” Complete these sentences to comment on this statement. [2 marks] The director may be correct because The director may not be correct because *17*