10.04 Sampling
Hannah has chosen to collect information using a sample instead of a census.
State the advantages of a sample.
Peter has chosen to collect information using a census instead of a sample.
State the advantages of a census.
Determine whether the following is a census or sample:
Lucy has asked everyone in her office what snacks should be provided in the office.
James asks a few of his friends how they did in the test to see if he is above average in his class.
Joanne finds the height of the entire class to try to find the average height of 15 year old students in Australia.
Justin has determined the age of 10\% of houses from each suburb in Sydney.
Valentina tests every engine that the factory produces.
Oprah checks every dog brought to her vet to assess the treatment of dogs in the city.
A random selection of some people at a mall.
A stock take of all the goods in store.
A crash test of new cars just manufactured by a factory.
Asking all the teachers at your school whether they approve of a new class timetable.
An election to decide the premier of Queensland.
Asking a random selection of students in your class whether they approve of the teacher.
A taste test of a large batch of cookies you have just baked.
A body scan of randomly selected passengers at Melbourne International Airport.
Determine whether a census or sample would be better for the following examples, and explain your choice.
A school teacher wants to find out what grade level his students are reading at.
A university student wants to find the average reaction times for humans.
A hospital wants to find out which heart rate machines are faulty.
A store manager wants to know the exact number of stolen items from the store.
A farmer wants to find the average height of the stalks of wheat in his field.
State whether a sample or a census would be more suitable for determining:
The number of ambulances in Australia.
The number of people watching Lost.
The average number of letters in the surnames of teachers at your school.
The number of smokers in Queensland.
The average weight of students in your class.
The average dress size of girls in Germany.
The number of students with brown eyes in a library.
The most listened to radio station in Sydney.
The average handwriting speed of students in Victoria.
The average time it takes students in your grade to run a lap around the school.
The number of train stations in Sydney.
The amount of petrol used up by the family car in December.
Students' favourite colour in your class.
The average time it takes students in your class to sprint 100 metres.
The number of post offices in Western Australia.
The number of dogs in Queensland.
The local mayor wants to determine how people in her town feel about the new construction project. State the type of sampling that each of the following scenarios use:
Selecting every 50th name from an alphabetical list of residents.
Giving each resident a random number between 1 and 10 and then selecting everyone with the number 3.
Selecting 10\% of the residents from each suburb.
For each item, detemine the type of sampling method used for these following events
Drawing out the winning ticket number in a lottery.
Choosing every 50th person on the class roll to take part in a survey.
Choosing 5\% of the of the students in each year for Years 7-12.
In a group of 360 students, 90 are primary students and 270 are secondary students. A stratified sample of 120 is to be selected from the group based on year level.
How many primary students should be selected?
How many secondary students should be selected?
A factory produces 1980 laptops every day. How many laptops are tested daily if the factory tests a systematic sample of 1 out of every:
11 laptops.
90 laptops.
A factory produces 3432 iPhones every day. One in every how many iPhones needs to be tested, if the factory is to test a systematic sample of:
13 iPhones per day.
88 iPhones per day.
In a group of 2160 students, 960 are male and 1200 are female. A stratified sample of 18 is to be selected from the group based on gender.
How many males should be selected?
How many females should be selected?
Users of a particular streaming service can be in one of four categories - Standard, Family, Premium or Business. The table shows the number of people in each category:
How many customers are there across all the categories?
If a stratified sample of 400 is to be taken from the group, state the proportion of people who will be chosen.
For the sample to be stratified, give the number of customers that should be chosen in each category:
Standard
Family
Premium
Business
| Team | Number of People |
|---|---|
| \text{Standard} | 3500 |
| \text{Family} | 1500 |
| \text{Premium} | 2000 |
| \text{Business} | 3000 |
A group of people is divided into four teams - Blue, Red, Green and Yellow. The table shows the number of people in each team:
How many people are there combined in all of the teams?
If a stratified sample of 1 in 30 is to be taken from the group, state the number of people who will be chosen.
For the sample to be stratified, give the number of people should be chosen from the following:
Blue team
Red team
Green team
Yellow team
| Team | Number of People |
|---|---|
| Blue | 150 |
| Red | 390 |
| Green | 270 |
| Yellow | 300 |
At a music concert there is expected to be a crowd of 3240 people. The band is giving away some shirts for some people that attend based on what order they enter the venue.
If the band are to give away 18 shirts, find the proportion in simplified fraction of people that will get shirts.
If the band are to give away 60 shirts, find the proportion in simplified fraction of people that will get shirts.
A factory produces 1820 TVs every day. How many TVs are tested daily if the factory tests a systematic sample of:
Every 13th TV.
Every 70th TV.
The owner of a cinema wants to use stratified sampling in their survey of people who come to their cinema.
Determine whether the methods below would be considered as stratified sampling:
Interview 10\% of the people who used the candy bar and 10\% of people who didn't.
Interview every person that sees a romantic movie.
Interview 10\% of the people from each movie.
Interview every 10th person that purchases a ticket.
The principal wants to use systematic sampling in their survey on how students in their school feel about the new auditorium.
Determine whether they can use the following systematic sampling methods:
Interview every 7th person on the school student list for that year grade.
Interview every 7th person that walks past their office.
Interview one random person from each class in that year.
Organise every student in the year by their height and then select every 7th person in the line.
Interview 110 random people from the year.
Beth is interested in which students from her school catch public transport.
Determine whether the following sampling methods are likely to be biased or not:
Selecting every 10th person on the bus she catches.
Selecting every 10th person on the student list.
Selecting the first 50 students that arrive in the morning.
Selecting by having a computer randomly choose student numbers.
Georgia wants to know how the people in Australia are going to vote in an upcoming referendum. She selects 50 random people from her city to interview.
Determine whether the following are the reasons why this sampling might give poor results:
The sample doesn't include anyone from New Zealand.
Random sampling always leads to a very bias sample.
The people of this suburb are not a good representation of Australia.
The sample size is too small for such a big population.
Justin wants to know how the students at his school might vote for the next school captain. He leaves three flyers in each class to complete by whatever students want to complete them.
Determine whether the following are the reasons why this sampling might give poor results:
Sampling within each class is self selected.
Stratified sampling always leads to a very biased sample.
The sample includes people from outside the population.
The students are under 18 so can't legally vote.