New QMaths 11B CD-ROM
Additional exercise 2.1
Collecting statistical data
1 In each case below, identify the variable and classify it as nominal, discrete or continuous. a Hung has 2 sisters.
b Sarah shot 11 baskets in the game. c Roberto jumped 1.85 m in the high jump.
d Terri put 38 L of petrol in the fuel tank of her car. e Tam received 12 marks for his assignment.
f Last year, Australia’s wheat production was 13.95 million tonnes. g The second-hand desk was in fair condition.
h After the race, Sam’s pulse rate was 95 beats per minute. i It took the horse 2 minutes 3 seconds to complete the race. j Juan has 3 264 321 hairs on his head.
k The most popular colour for new cars bought in 2002 was white.
New QMaths 11B CD-ROM
Additional exercise 2.1 Collecting statistical data continued
3 Anna plans to set up a video games arcade in a suburban shopping centre. What variables will she need information about before she goes ahead with the venture?
4 Max is a keen gardener and has decided to quit his job and open a plant nursery. What should Max find out about prospective locations before he takes the big step?
5 Identify the population, parameters and statistics for each of the following situations.
a Thirty people leaving a supermarket were asked how much they had spent. The smallest amount was $8.30, the average $127.64 and the largest amount $288.75.
b Fifty people with telephone numbers starting with (07) 3275 were rung at 8 pm one night to ask what TV channel they were watching: 20 said Channel 9, 15 said Channel 7, 8 said Channel 10 and 7 said Channel 2.
c The cars crossing a bridge were noted by a traffic surveyor. In one 15-minute period there were 18 white cars, 9 yellow cars, 5 blue cars, 7 red cars and 8 cars of other colours.
d A fast-food shop sold 75 hamburgers, 30 fish’n’chips, 15 salad rolls, 42 mini pizzas, 52 sausage rolls and 27 pies between 5 pm and 6 pm.
e The bicycles in a rack inside the entrance of a school were checked. From 30 bicycles, 20 had chromolly frames. There were more mountain bikes than other types.
6 Use systematic sampling to select a sample of 4 pies from a batch of 50, starting at number 17.
7 Start at row 3, column 21 of the 2-digit random number table on page 43 and select 10 different numbers that are:
a 2-digit numbers between 1 and 50 b 4-digit numbers between 1000 and 2000 c 3-digit numbers between 200 and 700 d 5-digit numbers between 50 000 and 99 999.
8 Use stratified random sampling to state how many of each group should be chosen from the following to obtain the specified sample.
a Sample of 10 from 120 Year 8s, 150 Year 9s, 130 Year 10s, 80 Year 11s and 90 Year 12s b Sample of 15 from 28 sales reps, 8 managers, 35 clerical staff and 15 stores staff c Sample of 8 from 40 surfers, 55 boogie boarders and 30 sailboarders
9 Explain some of the difficulties that may occur when an attempt is made to take a census of a population.
10 A TV channel recently ran a ‘telephone poll’ on the issue of capital punishment. The poll was conducted because of a particularly callous and brutal murder. Do you think that this poll could have been biased? How/why?
11 Each year, the students of Griffith University are surveyed to estimate how many have part-time jobs. a What is the population? b What is the parameter?
12 A manager wishes to select 10 items from a group of 150 on an inventory. Use the table of random numbers on page 43 to select 10 items for the manager. (Start at row 2, column 5.)
13 Many research companies use the telephone book to select samples to be surveyed. a Discuss various methods of selecting a random sample of:
i 10 pages from the telephone book
ii 10 names from a particular page of the telephone book iii 10 names from the telephone book
New QMaths 11B CD-ROM
Additional exercise 2.1 Collecting statistical data continued
14 A medical research team wishes to randomly select 6 people to test possible side effects of an experimental drug. It has 40 volunteers seated in 5 rows with 8 chairs in each row.
a In order to select the sample, the team numbers 5 cards 1 to 5 and places the letters A to H on another 8 cards. The cards are shuffled separately, then one from each ‘deck’ is selected. In this way a selection of 2,C would indicate the person in the 2nd row sitting on the 3rd chair. The cards are then returned to the respective decks, which are reshuffled, and selections continue in this way until the required sample is chosen. Comment on the suitability of this selection method.
b If there were 28 people seated on the 40 chairs, comment on the suitability or otherwise of the method described in part a.
15 Design suitable survey questions to determine: a the most popular radio station in your suburb b how often Maths B students do maths homework
c where students at your school are going in the next school holiday period d the popularity of various fast-food outlets in your local area
e why Brisbane people watch a particular TV network’s evening news presentation f the most popular ‘soaps’ on TV
g the career aspirations of students in your year level at school h the ages of people entering a movie theatre
i the occupations of people who eat breakfast at a certain fast-food chain
j the highest standard of education completed by the workers on a construction project at an inner-city development site.
16 For each of the situations listed in question 15: i state the population concerned
ii explain how you would select a survey sample iii explain how you would administer the questionnaire.
17 Discuss the relative advantages and disadvantages of the following methods for distributing questionnaire forms.
a Forms personally handed to interviewees b Forms sent to interviewees in the mail c Forms printed in a local newspaper
d Forms left outside a central location with a sign reading ‘Please take a form’
e Forms left at participating stores with a prize drawn for forms completed by 15 May
18 The following questionnaire was designed to obtain information about people’s preferences with regard to housing. Critically examine the questionnaire.
1 What is your age?
2 What is your sex?
3 Do you own your own home?
4 Would you like to have high-density housing in your street?
5 Would you like to have medium-density housing in your street?
6 What is the most suitable location for high-density housing?
New QMaths 11B CD-ROM
Additional exercise 2.1
Answers
1 a Number of sisters, discrete b Number of baskets, discrete
c Height, continuous d Litres of petrol, continuous
e Number of marks, discrete f Mass of wheat, continuous g Condition of desk, nominal h Pulse rate, continuous
i Time, continuous j Number of hairs, discrete
k Colour of cars, nominal
2 Answers will vary.
3 Population growth, numbers of young people, proximity of other recreational/amusement facilities and schools
4 Population growth, number of new housing starts, proximity of other nurseries and outlets that sell plants and their levels of sales
5 a The shoppers at the supermarket; smallest, average and largest amounts spent; smallest = $8.30, average = $127.64 and largest = $288.75
b People who watch TV; audience of each channel; Channel 9 = 40%, Channel 7 = 30%, Channel 10 = 16%, Channel 2 = 14%
c Cars; colour of cars; white = 38%, yellow = 19%, blue = 11%, red = 15%, others = 17%
d Tea-time sales of fast-foods at the shop; number of each type; hamburgers = 31%, fish’n’chips = 12%, salad rolls = 6%, mini pizzas = 17%, sausage rolls = 22%, pies = 11%
e The bikes ridden to the school; type of frame, type of bike; chromolly frames = 67%, mountain bikes the most popular
6 Pies 17, 29, 41, 3
7 a 14, 48, 43, 18, 26, 41, 37, 49, 22, 35
b 1545, 1808, 1040, 1393, 1148, 1340, 1068, 1602, 1729, 1535 c 417, 301, 251, 490, 668, 314, 349, 561, 632, 286
d 62 739, 99 482, 55 380, 51 038, 55 694, 88 904, 98 147, 99 823, 57 536, 65 237
8 a 2 Year 8s, 3 Year 9s, 2 Year 10s, 1 Year 11, 2 Year 12s b 5 sales reps, 1 manager, 6 clerical staff, 3 stores staff c 2 surfers, 4 boogie boarders, 2 sailboarders
9 Difficult to contact all members of a population, costly, time-consuming, some will refuse.
10 Biased—only those with telephones involved; poll conducted after emotive story; people able to ‘vote’ more than once; only those watching that TV channel aware of poll; people with strong feelings are more likely to phone in.
11 a Student body at Griffith University in a particular year b Number of students who have part-time jobs
12 Items 127, 135, 90, 149, 94, 105, 122, 97, 142, 87
13 a Examples include:
i Use a random number table to select 10 page numbers.
ii Determine the number of names on a page and use a random number table to select 10 numbers up to that number of names; start at the top left comer of the page and work down the column.
iii Select 10 pages as in i, then select one name on each selected page as in ii.
New QMaths 11B CD-ROM
Additional exercise 2.1 Answers continued
14 a Fair and unbiased, but it would be possible to select people more than once
b Fair and unbiased but quite inefficient, as some selections would probably have no person seated in that position
15 Sample answers are provided for only the first three parts of this question, to act as a guide. a
b
c
16 i a The radio listeners in your suburb
b The Maths B students c The students at your school
d The people who use fast-food outlets in your area e The Brisbane people who watch evening news on TV
f People in Australia who watch soap operas on TV g The students in your year level at your school h The people entering the theatre
i People who eat breakfast at the fast-food chain j The workers on the construction project
ii a Randomly select 20 to 50 streets in your suburb and then every 3rd or 4th household in the selected streets.
b Get class lists of Maths B students and select every 3rd or 4th student. c Get class lists and distribute forms to every 5th student on the lists. d Similar to a.
e Select every 1000th name from the Brisbane electoral roll.
f Select every (say) 10 000th household in Australia using the electoral rolls. g Obtain a list of names of students in your year level and select every 5th student. h Select every 3rd or 4th person entering the theatre.
i Randomly select table numbers and ask all people at these tables. j Obtain a list of workers and select every 3rd or 4th name.
iii a Visit houses and ask people the questions—record responses.
b Enlist the help of Maths B teachers to distribute/collect questionnaires. c Enlist the help of form teachers to distribute/collect questionnaires. d See a.
e Send questionnaire form and pre-paid reply envelope to selected persons.
Which radio station do you listen to most often?
X Y Z Other:
How often do you do Maths B homework?
Every day 6 times a week
5 times a week 4 times a week
3 times a week 2 times a week
Once a week Never
Are you going away on holiday in the next school holiday period?
Yes No
If yes, where are you going?
New QMaths 11B CD-ROM
Additional exercise 2.1 Answers continued
f Mail questionnaires to selected households. g See c.
h Wait outside the theatre and ask selected patrons their age.
i Distribute questionnaires to selected tables and provide a box for completed forms at the exit. j Visit the site and question selected workers.
17 a For: You know that interviewees receive forms; you can ensure that questionnaires are completed and collected.
Against: Time-consuming; costly to administer. b For: Easy to administer; reasonably inexpensive.
Against: Possibly low response; you don’t know who has completed the questionnaires. c For: Wide coverage; inexpensive to administer.
Against: Probably low response; only get responses from those with extreme views; can’t guard against multiple returns from individuals.
d For: Inexpensive to administer.
Against: Low response; extreme views; possible multiple returns; limited audience. e For: Reasonably inexpensive.
Against: Responses only from shoppers at these stores; can’t guard against multiple responses.
18 Age should be in categories. Housing densities are not explained. Locations for high-density housing are not explained.
