STATISTICS Foundation Tier Paper 2

STATISTICS Foundation 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 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 22F01* IB/G/Jun23/E11 8382/2F Answer all questions in the spaces provided. box 1 Ted has these 10 letter cards. V O L L E Y B A L L He selects one card at random. What is the probability that Ted selects the letter L? Circle your answer. [1 mark] 1 2 4 10 6 10 4 6 2 Here is a line graph. Circle the letter that best describes the relationship shown by the graph. [1 mark] A As the size increases, the price increases. B The size and price are not related. C As the size decreases, the price decreases. D As the size increases, the price decreases. 3 Here are seven numbers. 2 4 9 11 14 14 14 3 (a) What is the value of the median? Circle your answer. 4 11 12.5 14 3 (b) What is the value of the lower quartile of the seven numbers? Circle your answer. 2 3 4 11 Turn over for the next question [1 mark] [1 mark] box Turn over ► 4 Seb asks a sample of 24 people how many films they have watched at the cinema in the last month. Here are his results. box 1 3 0 1 1 2 4 1 2 2 5 0 1 1 1 2 3 3 5 0 1 3 2 2 4 (a) Seb’s data can be described as raw data. What are raw data? [1 mark] 4 (b) Complete the tally chart to show Seb’s results. [3 marks] Number of films watched Tally Frequency 0 1 2 3 4 5 Turn over for the next question box Turn over ► 5 The table shows the number of single-use plastic bags issued by two supermarkets in different years. box Year Plastic bags issued by supermarket A (thousands) Plastic bags issued by supermarket B (thousands) 2015 750 314 2016 420 235 2017 309 168 2018 184 73 2019 96 44 2020 75 28 2021 No data 24 5 (a) Work out the total number of single-use plastic bags issued by supermarket A and supermarket B in 2016. [2 marks] Answer thousand 5 (b) Describe the trend in the number of single-use plastic bags issued by supermarket B. [1 mark] 5 (c) Between which two consecutive years was the biggest change in the number of single-use plastic bags issued by supermarket B? [2 marks] Answer and 5 (d) The manager of supermarket A claims that the number of plastic bags issued by this supermarket dropped by more than a third between 2017 and 2018. Do the data in the table support this claim? Tick () a box. Yes No You must show your working. [3 marks] 5 (e) There are no data for supermarket A in 2021. Give one possible reason why no data are available. [1 mark] Turn over for the next question *07* Turn over ► 6 Anna owns a shop. She wants to find out what her past customers think about the quality of the headphones they bought. 6 (a) Write down two advantages of asking a sample of customers rather than taking a census. [2 marks] 1 2 6 (b) Anna considers asking all the contacts listed on her mobile phone. Give two reasons why this is not a good sample. [2 marks] 1 2 *0* Turn over for the next question DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED box Turn over ► box 7 (a) Show that Peter grows 31 sunflowers from packet A. [1 mark] 7 (b) Tick () the correct statement about the maximum height of a sunflower that Peter grows from packet A. [1 mark] The maximum height must be less than 175 cm. The maximum height could be less than 175 cm. The maximum height must be greater than 200 cm. The maximum height could be greater than 200 cm. The table shows information about the heights of sunflowers he grows from packet B. Height, h (cm) Frequency 0 ⩽ h 50 2 50 ⩽ h 100 3 100 ⩽ h 150 9 150 ⩽ h 200 13 200 ⩽ h 250 4 Turn over for the next question box Turn over ► 8 Bob has a fair spinner and a fair, six-sided dice. In an experiment, Bob spins the spinner and rolls the dice. 8 (a) Complete the sample space diagram below to show all the possible outcomes. [2 marks] Dice Spinner 8 (b) (i) Write down the probability of getting a yellow and a 5 [1 mark] Answer 8 (b) (ii) Work out the probability of getting a blue and a number less than 3 [2 marks] Answer 8 (c) Bob says, “If I repeat my experiment a total of 60 times, I would expect to get more than 25 results that are a green or a 4 or both.” Show that he is not correct. [3 marks] Turn over for the next question Turn over ► 9 The table, from the Driver and Vehicle Standards Agency, shows information about driving tests taken by 17- to 25-year-olds in two different centres in England. Age (years) Centre A Centre B Number of tests taken Percentage of tests passed Number of tests taken Percentage of tests passed 17 1566 43.0 972 59.1 18 1160 36.9 553 57.9 19 671 34.4 414 52.2 20 506 33.0 326 46.9 21 444 38.3 290 50.3 22 407 37.8 247 49.0 23 386 40.9 262 49.6 24 269 37.5 228 52.2 25 270 39.6 219 47.5 Total 5679 38.5 3511 53.6 Source: box 9 (a) (i) What type of data are shown in the table? Tick () a box. Primary data Secondary data Give a reason for your answer. [1 mark] Question 9 continues on the next page box Turn over ► Here is the table again. box Age (years) Centre A Centre B Number of tests taken Percentage of tests passed Number of tests taken Percentage of tests passed 17 1566 43.0 972 59.1 18 1160 36.9 553 57.9 19 671 34.4 414 52.2 20 506 33.0 326 46.9 21 444 38.3 290 50.3 22 407 37.8 247 49.0 23 386 40.9 262 49.6 24 269 37.5 228 52.2 25 270 39.6 219 47.5 Total 5679 38.5 3511 53.6 Source: 9 (d) How does the number of tests change at both centres as age increases? [1 mark] 9 (e) Kim is 20 years old. She can book her driving test at Centre A or Centre B. Kim says, “The number of 20-year-olds passing their driving test is greater at Centre A than at Centre B, so I shall book my test at Centre A.” Comment on her statement and her decision to book her test at Centre A. Use calculations to support your answer. [4 marks] The number of 20-year-olds passing at Centre A is greater Kim’s decision to book at Centre A Turn over for the next question *17*