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.

A selection of data from the large data set relating to the temperature and rainfall in Beijing for the first 10 days in October in both 1987 and 2015 is given above.

The large data set records rainfall data for 184 consecutive days in both 1987 and 2015.

(i) State why the rainfall data shown above should not be used to compare the rainfall in Beijing for these two years.

(ii) Describe how a systematic sample of 10 days could be taken to compare the rainfall data.

Climate activists are using temperature data to argue that temperatures are becoming less consistent due to climate change.

Using the data from the first 10 days of October given above, find the range of the daily mean air temperature for both 1987 and 2015 and state whether the data above supports the activists’ claims.

The Office for National Statistics runs a compulsory census every ten years to gather information about all individuals and households in England and Wales.  The information gathered helps organisations make decisions on planning and funding for public services in each area, including transport, education and healthcare.

Suggest one advantage and one disadvantage of the Census only being carried out every ten years.

A local council wants to gather opinions from residents about opening a new care home.  They decide to conduct their own survey and need to pick between using a systematic or a stratified sample. 

Give two reasons why the council may be better off conducting their own survey rather than attempting to use census data to obtain the desired information.

Explain the main differences between a systematic sample and a stratified sample.

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.

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

A group of 20 sloth sanctuaries across Central and South America record data on all the sloths in their care.  The sanctuaries have a central database where data for each sloth is collated.  A large variety of data on each individual sloth is collected and used to help decide when sloths are ready for releasing into the wild. 

(i) Explain why a single central database may be helpful for sanctuary owners to use when comparing data on the sloths in their care.

(ii) Explain the difference between qualitative and quantitative data and give an example of each in the context of the question.

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.

In the database there are currently 240 adult sloths, 60% of whom are male, and 64 juvenile sloths.  Explain how a stratified sample of size 35 could be taken.

Sanctuary owners want to look at a separate sample of sloths to get an idea of how many may be suitable for release.  Sloths can be released into the wild as long as they reach a heathy weight and are over the age of 3.  Male sloths when fully matured are generally heavier than females, although for juvenile sloths this weight difference is negligible.

Given that a quarter of the 64 juvenile sloths in the database are over the age of 3, explain how a stratified sample of size 35 could be taken to study suitability for release.

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 two advantages and one disadvantage of this 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 calculator or a random number generator to take a simple random sample from the 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 from the female students aged 13 to 18.

Freda 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.

(i) Define the word ‘population’ in the context of Freda’s survey.

(ii) State the sampling technique Freda has used.

Having been unsuccessful in obtaining enough data from her previous attempt, Freda decides to look at the electoral register for her town and select a new sample of people to contact.  She needs a sample of at least 50 people, so she decides to choose a person at random from the register and then use that person and every 5th person on the register after that (wrapping back around to the start of the register if necessary) to build her sample.

(i) State the sampling technique Freda has used.

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

Suggest an alternative method for Freda to use and explain your reasons.

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) Give two reasons 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 two problems with sending out the questionnaire in this way.

Jamie decides to separate users by exam board to gather more detailed opinions.  A member of the Maths Content Team suggests the use a table of random numbers to select a random sample of 100 users from the 4581 IB mailing list subscribers.  The first five random numbers from the table are as follows.

                               02743      45290      19024      24337      90044

Explain how Jamie could use these random numbers to select the first few members in the sample.

A researcher measured heights of a random sample of giraffes.  The heights in metres are summarised in the table below.

(i) State the class boundaries, midpoint and class width for the group containing the greatest number of giraffes.

(ii) Given that all the heights had been rounded to the nearest centimetre in the data set on which the table is based, what is the minimum possible range of heights for the giraffes as represented in the data set? 

All giraffes are allocated a unique four-digit ID number.  The researcher wants to randomly select five of the giraffes to test a new tracking device.  The researcher selects the first five giraffes with three zeros in their ID number.

(i) Explain why this may not be a good method for selecting the giraffes.

(ii) Describe an improved method of selecting the giraffes.

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.  The loads required for the handles to break are shown below:

         2.035 kg       2.845 kg         2.528 kg        1.998 kg        2.212 kg        2.378 kg

The factory claims that the fruit baskets can carry 2 kg of fruit without breaking.Use the sample data to comment on this claim.

(i) Describe any limitations to the sample the farm has used.

(ii) 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. 

Using the large data set, Charlie selects data from the 1st and 15th of each month to compare the weather in Hurn in 1987 and 2015. 

(i) Charlie says he has done a systematic sample to select the data. Explain why Charlie is wrong.

(ii) Describe how Charlie could take a systematic sample of 12 days for each year from the data for Hurn for 1987 and 2015.

Charlie wants to use numerical analysis to compare the daily total rainfall from his samples.  Using your knowledge of the large data set, explain why Charlie’s sample may not necessarily give him 12 usable data points to compare for each year.