Sampling methods

Priya is the manager of a company that makes toys.

The company wants to extend the working hours of the employees to increase production. Priya plans to ask a sample of the employees what they think about the proposed changes.

Each employee works in the department of administration, customer service, manufacturing or delivery.

The table shows the number of employees working in each of the departments.

Priya suggests using a stratified sample that is stratified by department.

Explain why this is appropriate.

Priya plans to sample 50 of the employees.

Work out the number of employees in the manufacturing department she should include in this sample.

Benjamin collected data on the results for the male competitors in the Ironman Canada competition in 2022

The incomplete histogram and incomplete grouped frequency table give information about the times taken, in hours, for these competitors to complete the competition.

Time (t hours)	Frequency
8 t 9	2
9 t 10	23
10 t 11	58
11 t 12	134
12 t 13	188
13 t 14	183
14 t 15	..................
15 t 16	..................
16 t 17	102

Use the information in the histogram to complete the table.

Use the information in the table to complete the histogram.

Benjamin also collected data about the results of the male competitors in the Ironman UK competition in 2022

The histogram below gives information about the times taken, in hours, for these competitors to complete the Ironman UK competition.

Identify and interpret the type of skew shown in this histogram of the times for these competitors in the Ironman UK competition.

The time taken, in hours, for each competitor to complete the competition was recorded when the digital tag worn by the competitor passed the finish line.

Discuss the reliability of any conclusions made based on this method of data collection. Give a reason for your answer.

Benjamin wants to find out how competitors prepare for Ironman competitions. He plans to give a questionnaire to the finishers of his local competition. There are 1200 people in the competition. Benjamin intends to use systematic sampling and ask every 10th competitor who crosses the finish line.

Comment on the appropriateness of this plan for data collection.

A council wants to encourage people to use the council leisure centres. The council has put advertisements in the town centres to tell people about the opening times and the available facilities in the leisure centres.

Nico has been asked to find out if the advertising has been successful. He plans to use cluster sampling where the clusters are customers at each leisure centre. For the selected clusters he will ask the customers to complete a questionnaire about the advertisements.

Comment on the suitability of Nico’s plan for sampling in this context.

Keti suggests that they should do a pilot study before they give out the questionnaire.

Give a reason why it is appropriate to do a pilot study.

The council also gave a voucher for one free admission to every child in the county.

The council thinks that some people have collected and used more than one of the free admission vouchers per child. Nico is going to include a question about this on the questionnaire. He thinks that he should use the random response technique.

Explain why it is appropriate to use the random response technique in this context.

Design a random response question that Nico could use on the questionnaire in order to collect this information.

Nico wants to find out if the number of people using the leisure centres increased after the advertisements and vouchers started a month ago.

He would also like to predict the number of people likely to use the leisure centres in the future.

Here is the plan for his investigation.

Discuss whether Nico’s plans for collecting, processing and presenting data are appropriate.

The cumulative frequency diagram gives information about the lengths, in mm, of a sample of 80 pike, caught in the Yukon River in Alaska. The pike were put back into the river.

Estimate how many of these pike had a length of 440 mm or more.

These data were collected using opportunity sampling.

State an advantage of using opportunity sampling.

The box plot below shows information about the lengths of the pike sampled from the Yukon River.

Here are the summary statistics, in mm, for a sample of pike caught in the Chena River in Alaska.

On the grid above, draw a box plot for the lengths of the pike caught in the Chena River.

Give three comparisons between the distribution of the lengths of pike from the Yukon River and the distribution of the lengths of pike from the Chena River. Interpret one of these comparisons in context.

The cumulative frequency diagram gives information about the lengths, in mm, of a sample of 80 pike, caught in the Yukon River in Alaska. The pike were put back into the river.

Estimate how many of these pike had a length of 440 mm or more.

These data were collected using opportunity sampling.

State an advantage of using opportunity sampling.

The box plot below shows information about the lengths of the pike sampled from the Yukon River.

Here are the summary statistics, in mm, for a sample of pike caught in the Chena River in Alaska.

On the grid above, draw a box plot for the lengths of the pike caught in the Chena River.

Give three comparisons between the distribution of the lengths of pike from the Yukon River and the distribution of the lengths of pike from the Chena River. Interpret one of these comparisons in context.

The management of a factory is considering changing the working hours of their employees. Muhammad and Rose want to get the views of the employees in the factory.

Employees in the factory work on the production line or in the warehouse or in the office.

20 employees work on the production line. 15 employees work in the warehouse. 25 employees work in the office.

Muhammad plans to use a questionnaire. He plans to take a sample of the employees and ask them the questions on his questionnaire. For his sample, he decides to ask all of the employees who work on the production line.

Name this sampling technique.

Give two reasons why using this sampling technique may not be appropriate.

Muhammad wants to find out how many extra hours each employee would be willing to work each week.

Design a closed question that Muhammad could use in his questionnaire.

Muhammad collects the completed questionnaires. He finds that some of the employees on the production line have not responded.

Suggest two ways in which Muhammad could have reduced the number of non‑responses.

Rose decides to take a 10% systematic sample of all the 60 employees in the factory.

Describe in detail how this sample could be selected.

Rose plans to use a face-to-face interview.

How would using a face-to-face interview rather than a questionnaire improve the quality of the responses?

Chris is a manager at a theme park.

He wants to find out what food options visitors would like to be able to buy in the theme park.

State the population for this investigation.

Chris decides that he will take a convenience sample of visitors in the section of the park selling food.

Explain what is meant by a convenience sample.

Give one disadvantage of using a convenience sample.

Chris plans to use the data collection sheet below.

Discuss whether this data collection sheet is appropriate.

You should consider how Chris might use the data and describe any problems he might have when he uses the data collection sheet.

Chris suggests using a stem and leaf diagram to represent the data that he collects.

Discuss whether or not this would be a suitable diagram to represent his data.

Some researchers investigated the hand span, in centimetres, of adult pianists by their level – international, national and amateur.

The box plots below give information about the hand spans for national level and amateur level pianists.

Circle the word in the list below that describes hand span, in centimetres, as a type of data.

qualitative ordinal continuous bivariate

The table gives information about the hand spans of the international level pianists.

Using the information in the table, draw on the grid above a box plot for the hand spans of the international level pianists.

Compare the three distributions of hand spans. Give three comparisons and interpret two of your comparisons.

Pavel owns a music shop. He wants to investigate the keyboard sizes used by pianists with different hand spans. He collects data about the hand spans of the pianists who use his shop.

The table gives information about the number of these pianists with hand spans in each of four size categories.

Hand span (cm)	A B C D (less than 19) (19 span 22) (22 span 24) (24 or more)
Number of pianists	24 65 57 14

Pavel plans to sample 20 of these pianists stratified by hand span size.

Explain how Pavel can obtain his stratified sample. You should include details of any calculations he should use.

Some researchers investigated the hand span, in centimetres, of adult pianists by their level – international, national and amateur.

The box plots below give information about the hand spans for national level and amateur level pianists.

Circle the word in the list below that describes hand span, in centimetres, as a type of data.

qualitative ordinal continuous bivariate

The table gives information about the hand spans of the international level pianists.

Using the information in the table, draw on the grid above a box plot for the hand spans of the international level pianists.

Compare the three distributions of hand spans. Give three comparisons and interpret two of your comparisons.

Pavel owns a music shop. He wants to investigate the keyboard sizes used by pianists with different hand spans. He collects data about the hand spans of the pianists who use his shop.

The table gives information about the number of these pianists with hand spans in each of four size categories.

Hand span (cm)	A B C D (less than 19) (19 span 22) (22 span 24) (24 or more)
Number of pianists	24 65 57 14

Pavel plans to sample 20 of these pianists stratified by hand span size.

Explain how Pavel can obtain his stratified sample. You should include details of any calculations he should use.

A town council is proposing to build a new leisure centre. Michelle is going to carry out a survey to find out what all the people in the town think of the proposal.

Michelle thinks that she should take a sample rather than a census.

Give two reasons why Michelle might think this.

Michelle plans to use the electoral register as the sampling frame.

Explain what you understand by the term sampling frame.

Give one problem Michelle may have using the electoral register as the sampling frame.

Michelle intends to conduct a pilot study.

Give two reasons why it is a good idea to conduct a pilot study.

Michelle is writing a plan for her investigation into people’s views on the leisure centre proposal.

Write down what Michelle should include in her plan. You should include each of the following

• a sampling method

• a question she could ask in her questionnaire

• a statistical diagram she could use to show the results of the survey.

Explain why each of the things you have written down is appropriate.

The table gives information about the ages of people on the electoral register in the West Midlands in December 2018

(Source: Office for National Statistics)

A researcher wanted to find out information about voting intentions in the West Midlands.

He sent a questionnaire to a sample of 10 000 people on the electoral register in the West Midlands stratified by age of voter.

Describe how the researcher would have carried out this stratified sampling.

You should show any calculations that you use.

Discuss the appropriateness of this stratified sample.

The following is an extract from part of a row of a random number list.

68236 35335 71329

Use the random number list to complete the table for the first 5 random 2-digit numbers.

The most common blood type in the United Kingdom is O+

The percentage of people in the United Kingdom with O+ blood type is 38%

Asha uses a simulation method to estimate how many donors would be needed to find exactly 3 donors with O+ blood type.

Asha is going to use the following 2-digit numbers for her simulation.

Explain why this is an appropriate way to allocate the random numbers.

Asha runs trials using her simulation method. The result of each trial is the number of random numbers used until Asha gets exactly 3 donors with O+ blood type. The table below shows the results of her first 4 trials.

The set of random numbers used by Asha to complete the fifth trial are shown below.

60 13 12 86 73 10 98 95 43 46

Using this set of random numbers, find the result for the fifth trial. You must make it clear how you obtain your answer.

Asha finds the mean of her 5 results and decides that the results of her simulation are sufficient to predict the number of donors needed to find at least 3 with O+ blood type in the next blood donation session.

Explain whether the method that Asha uses to predict the number of donors required is appropriate.

Rose is investigating the number of brothers and sisters that students in her secondary school have.

To investigate this she asks 10 students in Year 8 and 10 students in Year 11 how many brothers and sisters they each have.

Assess Rose’s method for her data collection.

The vertical line graph shows the data that she collected.

How many students have 2 or more brothers and sisters?

Write down the mode.

Rose uses her vertical line graph to conclude that no student in her school has 5 or more brothers or sisters.

Assess whether or not Rose’s conclusion is appropriate.

A theme park in Staffordshire has around 30 000 visitors per day. (Source: www.statista.com)

Navine is a manager at the theme park. Navine is investigating what visitors think about the theme park. He is going to do a survey of visitors at the theme park.

Navine decides to question 30 people aged under 18 and 30 people aged 18 and over as they leave the theme park one day.

He plans to ask them face to face what their favourite ride was.

Name this sampling method.

Describe the population for this survey.

Assess Navine’s plan to get the opinions of the people who have visited the theme park.

Mrs Singh is the Headteacher of a school with 1200 students.

She wants to find out about the ways the students at her school use the internet to complete their homework.

She is going to write a plan for her enquiry.

Write down one thing Mrs Singh should include in her plan for each of

• data collection

• choice of sampling method

• a diagram to represent the data collected.

Explain why each of the things you have written down is appropriate.

Sheffield City Council has more than 8000 employees. These employees work at different locations in Sheffield. (Source: Wikipedia.org)

A researcher wants to find out about the different methods of transport that these employees use to get to work.

She plans to ask the 9 employees, who work in one library, how they got to work that morning.

Give two reasons why this is not a good plan.

A supermarket chain has 93 stores in the United Kingdom with a total of 4502 employees. Each store is either a large store or a small store.

The directors of the supermarket chain are proposing to make changes to the employees’ working hours. The directors want to survey a sample of 450 employees from the total workforce in order to ask them for their views on the proposed changes.

Three possible sampling methods in order to select the employees to be in the survey are suggested.

Method A The directors will choose two employees from each small store and six employees from each large store.

Method B All 4502 employees are allocated a number from 0001 to 4502 Start with number 0010 and take every 10th employee so that the sample consists of employees with the numbers 0010, 0020, 0030, … and 4500

Method C Each employee in each store will be given a raffle ticket and 10% of the number of employees in each store will be chosen at random by taking raffle tickets out of boxes, one box for each store.

For each of the three methods, identify the sampling method and discuss whether the sampling method is an appropriate way to select the employees to be in the survey.

As part of your discussion you should also state, with reasons, which of the three sampling methods is the most appropriate method for the directors to use.

Nikola asks 50 male and 50 female drivers arriving at a car park if the type of car they are driving is petrol, diesel or electric.

The two-way table shows some information about her results.

Complete the two-way table.

Nikola wants to compare her results for male drivers with her results for female drivers. To do this she uses the information she collected to draw the two pie charts shown below.

Work out the angle for electric cars in the pie chart for male drivers. You must show the calculation.

Nikola told Seb how she collected her data. She then gave Seb a copy of each of her two pie charts and asked him to tell her what they showed. Seb used the pie charts to reach the following conclusions.

The most common type of car is diesel.

Males are more likely than females to be drivers of electric cars.

Use the information in the pie charts to assess Seb’s two conclusions. You should also consider how Nikola’s data collection method affects the reliability of Seb’s conclusions.

Explain what is meant by a simple random sample.

The manager of a health centre is reviewing the amount of time allowed for each patient to be seen by a doctor.

The manager wants to get the opinions of the people registered at the health centre.

She plans to give a questionnaire to each patient who has an appointment with a doctor next Monday. She wants each patient to complete the questionnaire at home and return the completed questionnaire to the health centre.

Assess the manager’s plan to get the opinions of the people registered at the health centre.

Here is an open question that the manager is considering for her questionnaire.

What do you think about the 5 minutes currently allowed for appointments?

This is not a good question.

Give one reason why.

Design a suitable closed question for the manager to use on her questionnaire so that she can decide how long should be allowed for each patient to be seen by a doctor.

When the manager has designed her questionnaire, she decides to pre-test it by using a pilot survey with a small sample of patients.

From the five options below, tick (✓) the three that are the best reasons for the manager to pre-test her questionnaire in this way.

A garden centre has a register of 400 loyalty card members. The owner of the garden centre wants to find out information about the distribution of the amount of money spent by each loyalty card member on each visit to the garden centre.

The owner decides on the following plan.

• Record the amount of money spent by each of the first 50 customers to the garden centre on Monday morning.

• Draw a bar chart for the amounts of money spent.

• Find the mean of the amounts of money spent.

Discuss whether the manager’s plan is likely to be effective.

You should comment on both the collection of data and on the analysis of results.

Where appropriate you should suggest improvements to the plan.

Bethany is the union representative at the large company where she works. She is investigating the salaries of the employees at the company.

Bethany takes a simple random sample of 8 employees at the company and asks each of them to tell her their salary.

Describe what you understand by the term ‘simple random sample’.

The salaries of the 8 employees are listed below.

£16 000 £3 000 £23 000 £31 000

£21 000 £24 000 £17 000 £25 000

Work out the mean.

Show that the range is £28 000

Bethany believes that one of the salaries is an outlier.

Write down the salary that is most likely to be an outlier.

Explain why you think this value is an outlier.

Bethany removes the outlier and calculates the mean of the remaining seven salaries.

Without carrying out any further calculations, state whether the mean of the remaining seven salaries is greater than, is equal to or is less than the mean of all eight salaries. Give a reason for your answer.

Bethany uses the mean of the remaining seven salaries to draw conclusions about the salaries of all of the employees at her company.

Describe two things that could affect the reliability of her conclusions.

John and Susan are investigating films.

John wants to find out the favourite type of film of the students at his school.

Susan wants to find out which type of film made the most money in UK cinemas last year.

State the population for

John’s investigation,

Susan’s investigation.

Susan plans to collect the information for her investigation from the internet.

Give advice to Susan so that she can ensure that the information she collects is reliable.

John is deciding between two different sampling methods for his investigation.

Method A: Quota sampling by sampling 20 students from each year group.

Method B: Opportunity sampling by selecting the first 50 students he sees one day.

For each method, give one reason why the method is not random.

Explain which of the two methods John should use in order to minimise bias. Give a reason for your answer.

A firm produces pottery. The firm produces 1000 plates each week.

The manager of the firm wants to take a systematic sample of 5% of the plates to check for faults.

Describe how the manager should take this sample.

Give one disadvantage of using systematic sampling.

The manager also collects information about the orders that the firm has received.

The grouped frequency table gives a summary of the costs of the 80 orders received last week.

Cost (£c)	Frequency
0 c 50	15
50 c 100	18
100 c 150	20
150 c 200	19
200 c 250	3
250 c 300	5

Write down the class interval which contains the median cost.

Use linear interpolation to work out an estimate of the median cost.

Emily and Jess work in the head office of a chain of restaurants.

The menu in all of the restaurants has recently been changed. Emily and Jess have been asked to find out the effect of these changes.

They are going to start by finding out what the kitchen staff think of the new menu.

Emily thinks that they should use a cluster sample of kitchen staff in the restaurants. The restaurants would be the clusters.

Jess thinks that they should use judgement sampling. The head chef of the company would be asked to select suitably experienced kitchen staff for the judgement sample.

Discuss whether these two sampling methods are suitable for Emily and Jess to use.

A website gives diners the opportunity to rate their dining experience at restaurants. Here is one of the questions that diners are asked to answer.

Poor Excellent

1 2 3 4 5 Mark with a cross (X) on the scale, one of the numbers 1 (poor), 2, 3, 4, 5 (excellent) to show how you rate your meal at the restaurant.

Emily recorded the mean ratings, correct to one decimal place, for meals at each of the 28 restaurants in the chain.

The stem and leaf diagram gives information about Emily’s recorded mean ratings.

Emily picks at random one of the restaurants.

Find the probability that the mean rating recorded by Emily for meals at this restaurant is less than 2.5

Jess separates the ratings into those that were made for meals from the previous menu and those that were made for meals from the new menu.

Jess uses her data to draw a percentage composite bar chart in order to compare the ratings for the previous menu and the ratings for the new menu.

The table below gives the percentages for each rating for the new menu.

Use the information in the table to complete the percentage composite bar chart for the new menu.

Use information from the composite percentage bar charts to describe what conclusions can be made about the effects of the changes to the menu.

A construction company employs three types of employee: builders, carpenters and electricians.

The table gives the number of each type of employee.

The owner of the construction company wants to find out what the employees feel about their jobs.

She plans to take a sample of 30 employees, stratified by type of employee.

Calculate the number of carpenters that should be in her sample.

The owner wants to know whether the employees in her sample believe that they work hard consistently. She knows that she will have to ask a sensitive question so she plans to use a random response question in order to find out this information.

Design a random response question that the owner could use on a questionnaire in order to collect this information.

Sam works in a bank.

He wants to survey the people who work at the bank in order to investigate whether there is a relationship between a person’s height and the person’s salary.

Suggest a hypothesis for Sam’s investigation.

Sam plans to collect the data himself.

Complete correctly the sentence below.

Data collected by the person who is going to use the data is called_........ data.

Explain why Sam may have difficulty in collecting data about people’s salaries.

The list below contains some variables that Sam is planning to collect.

salary height age

The variables that Sam is planning to collect are all examples of which type of data?

Sam decides to take a sample of employees by putting the name of everyone who works at the bank in a list in alphabetical order and selecting every 5th name on the list.

Write down the name of this sampling method.

Part of a spreadsheet of data that has been collected by Sam is given below.

Sam tries to use his spreadsheet to calculate automatically the mean salary, the mean height and the mean age of the employees in his sample.

Sam’s computer gives him an error message for two of these calculations.

Write down the calculation for which there is not an error message. Give a reason why there is an error message for the other two variables.

A presenter wants to get feedback on a lecture that she gave.

There were 467 students at the lecture.

The presenter plans to give a questionnaire to a sample of 50 of these students.

One of the questions on the questionnaire is

Circle the word from the list that best describes the type of data that this question collects.

ordinal bivariate continuous grouped

Describe how the presenter can use a list of random numbers to select a simple random sample of 50 students.

A presenter wants to get feedback on a lecture that she gave.

There were 467 students at the lecture.

The presenter plans to give a questionnaire to a sample of 50 of these students.

One of the questions on the questionnaire is

Circle the word from the list that best describes the type of data that this question collects.

ordinal bivariate continuous grouped

Describe how the presenter can use a list of random numbers to select a simple random sample of 50 students.

Reeta read a report that said that these days more 18 to 24 year olds find out what is happening in the news from social media than find out by watching TV. She decided to investigate how the 12 000 students at her university find out what is happening in the news. Reeta wrote the following as a hypothesis: Do more students get their news from social media than from other sources?

Comment on whether it is appropriate to use this as a hypothesis.

Reeta planned to use a sample of the students at her university stratified by gender and by age.

Explain why this method of sampling would be appropriate.

Reeta found that she could not get a list of all the students at her university to use for her stratified sample. Instead she decided she would question students in the university cafeteria. Here is the data collection sheet Reeta plans to use.

Discuss whether Reeta’s data collection sheet is appropriate for her to use. You should consider how Reeta might use the responses and describe any problems she may have when she uses the data collection sheet.

Reeta’s friend George is at a different university with 18 000 students.

George carried out a similar investigation at his university so that he and Reeta could compare their results.

They each questioned the same percentage of students at the university they each attend.

They decided to compare their results by using comparative pie charts.

Explain why comparative pie charts would be appropriate.

Reeta used a circle with diameter 10 cm for her pie chart.

Calculate the diameter of the circle that George used for his pie chart.

Discuss two things that Reeta and George should have considered in planning their investigations to help improve the reliability and validity of their comparisons.

Mehmet wants to conduct an investigation about school meals at his school. He wants to take a sample of students from his school.

Write down a sampling frame he could use.

Mehmet has two hypotheses:

● Younger students have school meals, rather than packed lunches, more often than older students do. ● More female students than male students are vegetarian.

Here are sections A, B and C of his plan for his investigation.

Name the sampling method that Mehmet plans to use.

Discuss whether or not Mehmet’s plans are appropriate. You must comment on each of the three sections A, B and C.

Mehmet also collects information about the amounts that the students pay for their school meals.

He sorts the costs of the meals into classes with equal widths of 5p.

The table gives some of his results.

Mehmet decides to use classes with equal widths of 10p instead of 5p.

Write down one advantage and one disadvantage of doing this.

Matthew is collecting information about road safety in his town.

He wants to collect information from drivers who live in his town.

Matthew plans to ask drivers at his local car park about their views on road safety. He plans to collect a quota sample of 20 drivers from each of three age groups.

Matthew’s three age groups of drivers are

39 years old or younger 40 years old to 59 years old 60 years old or older

Comment on whether Matthew’s plans are appropriate.

Matthew wants to know how many drivers, who live in his town, drive faster than the speed limit on the motorway. Matthew knows that he will have to ask a sensitive question so he plans to use the random response technique to find out this information.

Design a random response question that Matthew could use on a questionnaire in order to collect this information.

A supermarket manager is planning the design of a new petrol station.

He wants to use the results of spinning a coin to simulate on which side of a car the fuel filler cap is. He assumes that the fuel filler cap is equally likely to be on the left of the car as it is to be on the right of the car. He wants to use the simulation in order to predict how many cars will arrive at the petrol station before there are four consecutive cars with filler caps on the same side.

Explain how he could use a coin to carry out the simulation.

A new cafe is also opening at the supermarket. Three different types of hot drink – tea, coffee and hot chocolate – will be sold in the cafe.

The table gives, for each type of hot drink, the fraction of the total number of hot drinks sold in other cafes of this supermarket chain.

The manager wants to predict how many of each type of hot drink the cafe will sell in an hour the first Saturday the cafe is open.

The manager expects that there will be 40 customers in the cafe that hour.

He assigns the numbers shown in the table below to each type of hot drink.

He will then use a calculator to generate 40 random numbers between 0 and 9 to simulate 40 customers.

Comment on the suitability of the manager’s plan.

Mike owns a shop.

He wants to collect information about the types of games liked by people in his town.

The following list gives the information he is going to collect about people’s favourite board games. type of game average playing time minimum number of players

From this list, write down the information that is

categorical data,

discrete data.

Mike is planning to send a questionnaire to some of his customers. He wants to select the customers by using systematic sampling. Mike has a list of all of his 200 customers.

Explain how Mike can select a systematic sample of 20 people from his list of customers.

The table gives information about the numbers of students from different types of schools who applied to Cambridge University in 2016

(Source: www.cam.ac.uk)

Richard is going to take a sample of 200 of these students stratified by gender.

Work out how many female students there should be in this sample.

Describe a situation when it would not be appropriate to take a sample stratified by gender.

Richard could have used a different category for his stratified sample.

What is this different category?

A student is to be chosen at random from the 9963 students.

F is the event that the student chosen is female.

I is the event that the student chosen is from an independent school.

M is the event that the student chosen is from a maintained school.

Explain why the event F and the event I are not mutually exclusive.

Find P(I or M).

The table gives information about the numbers of students from different types of schools who applied to Cambridge University in 2016

(Source: www.cam.ac.uk)

Richard is going to take a sample of 200 of these students stratified by gender.

Work out how many female students there should be in this sample.

Describe a situation when it would not be appropriate to take a sample stratified by gender.

Richard could have used a different category for his stratified sample.

What is this different category?

A student is to be chosen at random from the 9963 students.

F is the event that the student chosen is female.

I is the event that the student chosen is from an independent school.

M is the event that the student chosen is from a maintained school.

Explain why the event F and the event I are not mutually exclusive.

Find P(I or M).