Sampling & Data Collection (Edexcel A Level Maths: Statistics): Exam Questions

Helen is studying one of the qualitative variables from the large data set for Heathrow from 2015.

She started with the data from 3rd May and then took every 10th reading.

There were only 3 different outcomes with the following frequencies

State the sampling technique Helen used.

From your knowledge of the large data set

(i) suggest which variable was being studied,

(ii) state the name of outcome .

George is also studying the same variable from the large data set for Heathrow from 2015.

He started with the data from 5th May and then took every 10th reading and obtained the following

Helen and George decided they should examine all of the data for this variable for Heathrow from 2015 and obtained the following

State what inference Helen and George could reliably make from their original samples about the outcomes of this variable at Heathrow, for the period covered by the large data set in 2015.

Charlie is studying the time it takes members of his company to travel to the office.

He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.

State the sampling method Charlie used.

State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.

Taruni decided to ask every member of the company the time, minutes, it takes them to travel to the office.

State the data selection process Taruni used.

Every week, an orangutan sanctuary measures the weight of each of its orangutans.

The weights, to the nearest kg, of ALL their 18 adult are listed below:

52, 57, 63, 80, 56, 66, 101, 68, 55, 96, 70, 62, 66, 64, 99, 91, 55, 92

The order represents the order in which the orangutans were weighed.

(i) State the data collection process used to collect the above data.

(ii) Describe the type of data collected.

Tom uses opportunity sampling and selects the first six orangutans that were weighed.

Calculate the mean weight of the orangutans included in Tom's sample. Round your answer to 1 decimal place.

Tina also takes a random sample of six orangutans. Tina uses systematic sampling based on the order in which they get weighed. The first orangutan in her sample is the second one to get weighed.

Calculate the mean weight of the orangutans included in Tina's sample. Round your answer to 1 decimal place.

A supermarket wants to gather data from its shoppers on how far they have travelled to shop there. One lunchtime an employee is stationed at the door of the shop for half an hour and instructed to ask every customer how far they have travelled.

(i) State the sampling method the employee is using.

(ii) Give one advantage and one disadvantage of using this method.

It is known that 400 people visit the supermarket during a lunchtime. 250 of these people use a basket for their shopping and the rest use a trolley.

Briefly describe how the employee could use quota sampling to obtain the required data for a sample of 30 customers.

A company wants to survey 60 members of its staff to find out gather opinions about working from home.  The company’s 580 members of staff are grouped by job as follows:

• 295 engineers,

• 11 managers,

• 154 office staff

• and 120 apprentices.

Explain how the company can use stratified sampling to obtain its sample.

A toy shop, ‘Toys 4 U’, tests the battery life for a new toy by leaving a sample of the toys switched on until their batteries run out.

Give one reason why the shop decided to use a sample rather than a census.

Five random toys out of a shipment of 5000 were tested and the battery life (in minutes) of each toy was recorded:

172    252    248     155    161

(i) Calculate the mean.

(ii) Explain why the mean is unlikely to be representative of the average battery life of all the toys.

Freya needs to conduct a survey to investigate the type of ice cream people prefer.  She wants a random sample of people who eat ice cream.  She decides to stand in a busy high street on a Sunday afternoon and attempt to get shoppers to answer her questions.

State the sampling technique Freya has used.

Having been unsuccessful in obtaining enough data from her previous attempt, Freya decides to look at the electoral register for her town and select a new sample of people to contact. 

There are 5000 people in the town. Freya creates a sample by randomly picking one of the first 100 people listed on the electoral register, and then every 100^th person after that. Freya then sends a survey out to those 50 people.

(i) State the sampling technique Freya has used.

(ii) Give two reasons why Freya may again be unsuccessful getting the data required using this sampling technique.

Freya suspects that the age of a person influences their favourite type of ice cream. The ages of the people in the town are not given on the electoral register.

Suggest a sampling method that Freya should use

An online magazine which offers both free and paid for content has a large number of readers.  Readers can view additional content by paying a monthly subscription fee.  Based on reviews on the magazine’s website, the editor of the magazine believes that an additional type of content could be introduced.  Before making any changes, the editor decides to carry out a sample survey to obtain the opinions of the readers. 

Define the population that would be associated with the magazine.

Give one advantage and one disadvantage that would have resulted from the editor using a census rather than a sample survey.

The editor decides to gather opinions from only those readers who subscribe to the additional content.  A random sample of 25 subscribers is selected for the sample survey.

State two sources of uncertainty that may arise based on the chosen sampling method and sample size.

Stephan is researching the effects a new energy drink has on the glucose levels of students aged 13 to 18.  He decides to measure the blood glucose levels of 50 female students and 50 male students.

(i) State, with a reason, whether Stephan is using a census or a sample to conduct his study.

(ii) Give one advantage and one disadvantage of this sampling method.

Stephan is provided with an alphabetical list of 350 male students aged 13 to 18, each of whom has agreed to supply a blood sample if asked.

Explain how Stephen could use a list of random numbers or a random number generator to take a simple random sample of 50 male students aged 13 to 18.

Stephen has an equivalent list of 350 female students aged 13 to 18.

Explain how Stephen could take a systematic sample of 50 female students aged 13 to 18.

A factory produces paper fruit baskets used for fruit pickers at ‘pick your own’ farms.  The breaking load of a paper fruit basket is the maximum load that it can carry before the basket handles break.  One ‘pick your own’ farm purchased 15 000 paper fruit baskets but wishes to test a sample of these to establish the breaking load of the baskets.

Suggest two reasons why a census would be unsuitable for this purpose.

The farm tests a random sample of six paper fruit baskets.

Suggest one way the farm could improve the reliability of its results.

The large data set provides weather data for 184 consecutive days in each of the years 1987 and 2015. 

Describe how Charlie could take a systematic sample of 12 days from the data for Hurn for 1987 so that each date has a chance of being selected.

Charlie also takes a sample of 12 dates from the data for Hurn for 2015.

Using your knowledge of the large data set, explain why Charlie’s sample may not necessarily give him 12 numerical values to compare for each year.

The CEO of Save My Exams, Jamie, wants to find out what users would like to see on the revision website in future.  He notices that around 15% of those who access the site have signed up to the mailing list to get content updates.

An employee suggests that they send out an email to all those who have signed up to the mailing list with a questionnaire for them to complete and return. 

(i) Explain why the users who return the questionnaire would not form a random sample of users of the website.

(ii) Given the site has over 650 000 users, state a problem with sending out the questionnaire in this way.

Jamie decides to separate users by qualification to gather more detailed opinions.  There are 4581 A Level users on the mailing list and want to include 100 of them in a sample.

Jamie assigns each of them a unique number from 1 to 4581. Jamie uses his calculator to generate three-digit numbers from 0.000 to 0.999 inclusive. Jamie multiplies each number by 4581 , adds 1 and then rounds to the nearest integer. He then selects the user who has been assigned with that number.

The first four random numbers from his calculator are as follows:

0.314      0.315      0.316      0.317

Determine the numbers of the users who would be picked using these numbers.

Explain why this method is biased.

Sanctuary owners want to look at a sample of sloths as part of a general health and well-being survey.  Sloths are said to have matured into adults when they reach the age of 5. Before this, they are classed as juveniles.  While juveniles may be treated as a single group for this survey, it is important that adult females and adult males be considered separately.

There are currently 240 adult sloths and 64 juvenile sloths.  The ratio of adult male sloths to adult female sloths is 3:2. A sample of 35 sloths is taken using stratified sampling.

Find the number of adult male sloths included in the sample.

There will be 7 juvenile sloths in the sample.

Explain how the sanctuary owners can select these sloths for the stratified sample.