Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials General Certificate of Secondary Education Foundation Tier June 2013 Pages 3 4 5 Mark Statistics Written Paper 43101F 6 7 8 9 10 11 Monday 24 June 2013 For this paper you must have: l a calculator l mathematical instruments. 1.30 pm to 3.00 pm F 12 13 14 15 16 17 18 19 Time allowed l 1 hour 30 minutes 20 21 TOTAL Instructions l Use black ink or black ball-point pen. Draw diagrams in pencil. l Fill in the es at the top of this page. l Answer all questions. l You must answer the questions in the space provided. around each page or on blank pages. l Do all rough work in this book. Cross through any work that you do not want to be marked. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 80. l You may ask for more answer paper, graph paper and tracing paper. These must be tagged securely to this answer booklet. l You are expected to use a calculator where appropriate. Advice l In all calculations, show clearly how you work out your answer. (JUN1343101F01) 43101F
2 You may need to use the following formulae: fx Mean of a frequency distribution = f fx Mean of a grouped frequency distribution =, f where x is the mid-interval value. (02)
3 Answer all questions in the spaces provided. 1 In a game at a fair you always win one of four prizes. The table shows the probability of winning each type of prize. Prize Probability Toy 0.65 Sweets 0.20 Pen 0.10 Pack of stickers 0.05 1 (a) Which prize are you most likely to win? Answer... 1 (b) Work out the probability that you win a Toy or Sweets. Answer... 1 (c) Work out the probability that you do not win a Pen. Answer... 1 (d) In 100 games, estimate the number of Packs of stickers that you would win. Answer... Turn over 7 (03)
4 2 Ahmed has 20 coins as shown. 10p 10p 05p 10p 10p 10p 02p 20p 10p 01p 02p 10p 10p 20p 10p 10p 05p 05p 10p 10p 2 (a) Fill in the tally column and the frequency column for the coins. Value of Coin Tally Frequency 1p 2p 5p 10 p 20 p (3 marks) 2 (b) Draw a pictogram for the coins. Value of Coin Key: = 2 coins 1p 2p 5p 10 p 20 p (3 marks) (04)
5 2 (c) Write down the modal value of the coins. Answer... p 2 (d) Sally also has some coins. This table shows a summary. Value of Coin Frequency Total Value (pence) 1p 3 3 2p 6 12 5p 4 20 10 p 7 20 p 5 Complete the table and work out the total value of all her coins. Answer... (3 marks) 10 Turn over (05)
6 3 The multiple bar chart shows some minimum and maximum temperatures for Derby. Minimum temperature Maximum temperature 20 18 16 14 Temperature C 12 10 8 6 4 2 0 Mon Tue Wed Thu Fri Day 3 (a) What is the minimum temperature on Monday? Answer... ºC 3 (b) What is the maximum temperature on Tuesday? Answer... ºC (06)
7 3 (c) Here is the information for Thursday and Friday. Day Minimum temperature (ºC) Maximum temperature (ºC) Thursday 10 16 Friday 9 17 Complete the multiple bar chart. (4 marks) 3 (d) On which of the five days is the biggest difference between minimum and maximum temperatures? Answer... 3 (e) One of these five days is chosen at random. 3 (e) (i) Write down the probability that the maximum temperature is 18 ºC. Answer... 3 (e) (ii) Work out the probability that the minimum temperature is less than 8 ºC. Answer... 10 Turn over (07)
8 4 Niles is investigating how much sport people play. He will use a questionnaire. First he will do a pilot study. 4 (a) What is a pilot study? 4 (b) Why should Niles carry out a pilot study? 4 (c) Niles looks at some of the pilot study data about the number of hours each person plays sport per week. 5 4 0 2 6 0 120 4 2 3 4 (c) (i) How many of these people claim to play no sport? Answer... 4 (c) (ii) One of the values has been misrecorded. Which one is it? Misrecorded value... How do you know? (08)
9 4 (d) Niles research question is Do men play more hours of sport than women? Apart from hours of sport, what other variable must Niles record? 5 A school has 1000 pupils. Pat wants to take a sample of these pupils. 5 (a) Give one reason why Pat might want to take a sample rather than a census. 5 (b) Briefly describe how Pat could obtain a random sample of the 1000 pupils. Turn over for the next question 9 Turn over (09)
10 6 Sam and Tom have both taken the same five tests. Each test is out of 50 marks. These are the results. Sam 30 24 48 13 25 Tom 36 20 25 39 20 Compare how Sam and Tom did overall. You must support your answer with calculations. You may use the table to help you. Mean Median Range Sam Tom (5 marks) (10)
11 7 Josh is investigating how long people spend playing games on their phones. Here are some of the tasks he does to investigate this. They are in the wrong order. A B C D E Josh writes his conclusion Josh suggests a hypothesis Josh calculates some averages Josh collects the data Josh selects his sample Put these tasks in the correct order so that Josh has a suitable strategy for his investigation. First task First task First task First task Last task Turn over for the next question 7 Turn over (11)
12 8 Here is some sample information from a survey about pets in England. Question: Do you own a cat or dog? Cat 28.5% Dog 24.8% Neither 53.7% Source: Ipsos Mori 8 (a) These percentages add up to 107% rather than 100%. Why is this? 8 (b) The proportion of people in the survey who own a dog is 0.248 Estimate the proportion of the population who own a dog. Answer... (12)
13 8 (c) People with cats or dogs were asked how many they owned. CATS Number Owned by 1 55.9% 2 29.5% 3 8.3% 4 or more 6.3% DOGS Number Owned by 1 74.8% 2 20.2% 3 3.3% 4 or more 1.7% Source: Ipsos Mori What percentage of dog owners own three or more dogs? Answer... % 8 (d) Using all three tables in this question, explain why there are probably more cats than dogs in England. 6 Turn over (13)
14 9 Freshly cut wood is full of moisture and needs to dry out. George cuts some silver birch logs and weighs one over a period of drying. 9 (a) The table gives the mass of the log whilst drying in the garage. Number of days since being cut 0 3 7 10 14 17 21 Mass (g) 1925 1775 1710 1640 1570 1525 1480 Source: George 9 (a) (i) What was the mass of the log on the day it was cut? Answer... g 9 (a) (ii) What type of data has George collected? Circle the two correct answers. Primary Secondary Discrete Continuous Categorical 9 (a) (iii) Which of these words are appropriate to this data collection method? Circle the two correct answers. Measurement Observation Interview Experiment (14)
15 9 (b) George then moves the log into his dining room. The table gives the mass of the log during this time. Number of days in dining room 0 3 7 10 14 17 Mass (g) 1480 1450 1430 1410 1390 1380 Source: George Draw a time series graph for the data in this table using the grid below. 1480 1460 1440 Mass (g) 1420 1400 1380 1360 1340 0 2 4 6 8 10 12 14 16 18 20 22 Number of days in dining room (3 marks) 8 Turn over (15)
16 10 The age to which 100 pet ducks live is shown on the frequency polygon. 45 40 35 30 Frequency 25 20 Pet ducks 15 10 5 0 0 5 10 15 20 Age, x (years) 25 (16)
17 The age to which 100 wild ducks live is shown in the table. Age, x (years) 0 x 5 5 x 10 10 x 15 15 x 20 Frequency 18 40 38 4 Midpoint 2.5 7.5 10 (a) (i) The midpoint of the group 0 x 5 is 2.5 years. Complete the table by writing in the two missing midpoints. 10 (a) (ii) Use the midpoints to draw the frequency polygon for wild ducks on the same grid as for pet ducks. (3 marks) 10 (b) Compare the age to which these pet ducks and wild ducks live. Comparison 1... Comparison 2... 6 Turn over (17)
18 11 (a) At the beginning of 2012 the town of Brigg had a population of 6000. In 2012 there were 63 births in the town. Calculate the crude birth rate for Brigg in 2012. Answer... per thousand 11 (b) In 2012 the crude death rate for Brigg was 8 per thousand. Were there more births or deaths in Brigg in 2012? Circle your answer. Births Deaths Give a reason for your answer. (18)
19 12 This is an output gap chart for the USA. 3 2 1 0 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 1 year 2 3 4 12 (a) The label for the vertical axis is missing What should it be? Answer... 12 (b) In 2010 the USA was in recession. How can you see this from the graph? 12 (c) In a recession, what is likely to happen to unemployment? Circle your answer. Decreases Stays the same Increases 6 Turn over (19)
20 13 The table shows the number of miles travelled (thousands) and depth of tread (mm) on eight tyres of the same type. Number of miles (thousands) Depth of tread (mm) 5 10 15 25 31 36 40 46 7.2 6.6 6.2 4.9 4.8 3.8 3.3 2.4 13 (a) Complete the scatter diagram for the data. The first four points have been plotted for you. Depth of tread (mm) 8 7 6 5 4 3 2 1 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Number of miles (thousands) 13 (b) For the data, the mean number of miles is 26 thousand. 13 (b) (i) Work out the mean depth of tread. Answer... mm (20)
21 13 (b) (ii) Use these mean values to help you draw a line of best fit on the scatter diagram. 13 (c) Use your line of best fit to estimate the depth of tread for a tyre which has travelled 20 thousand miles. Answer... mm 13 (d) It is illegal to have less than 1.6 mm of tread on a tyre. Use your line to estimate the number of miles travelled before a tyre becomes illegal. Answer... thousand miles 13 (e) Which of your answers, 13(c) or 13(d), do you think is more reliable? Tick a. 13(c) 13(d) Give a reason for your choice. 13 (f) Is there likely to be a causal relationship between the number of miles travelled and the depth of tread? Tick a. Yes No Give a reason for your answer. END OF QUESTIONS 11 (21)
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