Statistical enquiry

A survey was carried out to find how many books children read during the holidays.

The following two questions were asked in a questionnaire.

Q1. Most children read lots of books.

Do you read lots of books?........

Q2. How many books do you read during the holidays?

None 1–10 books 10–20 books More than 20 books

Give one reason why Q1 was not a suitable question.

Give one reason why Q2 was not a suitable question.

The survey was carried out by asking children as they left the library on a Saturday morning.

Give one criticism of how the survey was carried out.

A survey was carried out to find how many books children read during the holidays.

The following two questions were asked in a questionnaire.

Q1. Most children read lots of books.

Do you read lots of books?........

Q2. How many books do you read during the holidays?

None 1–10 books 10–20 books More than 20 books

Give one reason why Q1 was not a suitable question.

Give one reason why Q2 was not a suitable question.

The survey was carried out by asking children as they left the library on a Saturday morning.

Give one criticism of how the survey was carried out.

100 people took part in a fundraising event last Saturday and Sunday. They raised money for charity by working towards some fitness targets.

The target for Saturday was to achieve a mean of 6500 steps per person.

The results for Saturday are shown in the table below.

Calculate an estimate of the mean number of steps per person on Saturday to

show that this target was met.

On Sunday, the 100 people were divided into three groups, A, B and C, based upon their results from the Saturday. Each group was given a target of a mean number of steps per person.

The targets for groups A, B and C were 8000, 9000 and 10 000 steps, respectively.

The table below shows the mean number of steps per person that each group achieved

The ratio of the number of people in the different groups was A: B: C = 18: 4: 3.

Calculate the overall mean of the number of steps taken per person by these

100 people on Sunday.

The organiser says,

“A fabulous result on Sunday! Two of the three groups met their target. This means that two-thirds of the targets given were met.”

Give a reason why this could be seen as a misrepresentation of the outcome of

Sunday’s fundraising event.

Sharon has a new job in Margam Park.

On a Saturday afternoon, Sharon carried out a survey. She asked visitors who were leaving Margam Park to choose their favourite activity. Sharon shows the activities and some of her results in the tally

Sharon then realises she did not record the replies of the last 9 visitors. Of these: • 3 visitors chose the tree-top adventure • 3 visitors chose the castle tour • 3 visitors chose mountain biking.

Sharon says:

“The modal favourite activity in the park is the Playground.”

Complete the tallies and frequencies in the tally chart above to decide if Sharon is correct.

Is Sharon correct?

Give a reason for your answer.

Yes No

How many visitors took part in the survey in total?

Sharon displays her findings in a vertical line diagram. She shows this to other staff at a monthly meeting.

Draw Sharon’s vertical line diagram.

Complete the statement below:

‘The number of visitors who chose the Playground was_{……………........ ………} times the number who chose the Park train ride.’

At the monthly meeting, Sharon looks at the results from her Saturday afternoon survey and says:

“This month, the Park train ride is not doing very well when compared with the Playground.”

Give one reason why this may not be true.

Sharon has checked the weather forecast for next week and it shows that it will rain on 5 out of the 7 days. One day from next week is chosen at random.

Which of the following best describes the chance that it will rain on that day?

Circle your answer.

impossible unlikely even chance likely certain

Eleri is investigating whether people working in offices are happy with the processing speed of their office computer.

She considers the data she needs to collect.

Eleri includes the following two questions in her questionnaire. For each question, write down one set of possible groups she could use as answer options.

Question 1: How many days per month do you work in your office?

Possible groups for answer:

Question 2: How happy are you with the processing speed of your office computer?

Possible groups for answer:

A survey was carried out in the U.S.A.

743 teenagers were interviewed. They were asked what type of information they posted on social media. The results were displayed on the internet, as shown below.

Posts on social media Percentage of American teenagers who say they have posted about the following:

Type of information:

Emotions and feelings 34%

How many times bigger is the percentage of the teenagers who posted about their

family than the percentage who posted about their religious beliefs?

What fraction of these teenagers posted about their emotions and feelings?

Give your answer in its simplest form.

Dewi looks at the type of information posted by these teenagers.

What is the modal type of information?

The modal type of information is_........

What information would have been needed in the original data so that the following

hypothesis could be tested?

In the U.S.A., teenage girls post about family more often than teenage boys.

How many of these 743 teenagers posted about their religious beliefs?

You must show all your working.

Lottie is confused by the data in the diagram.

She says,

The diagram is correct.

Explain why the bars do not add up to 100%.

A survey was carried out to find how often primary school children play board games.

A questionnaire was designed for primary school children to answer. The following two questions were asked.

Q1. Do you live within 5 minutes’ walking distance of school?

Q2. How often do you play board games?

Never 1–5 times 5–10 times More than 10 times

For each question, give one reason why it is not suitable.

The survey was carried out by leaving copies of the questionnaire in the local supermarket.

Give one criticism of how the survey was carried out.

A survey was carried out to find how often primary school children play board games.

A questionnaire was designed for primary school children to answer. The following two questions were asked.

Q1. Do you live within 5 minutes’ walking distance of school?

Q2. How often do you play board games?

Never 1–5 times 5–10 times More than 10 times

For each question, give one reason why it is not suitable.

The survey was carried out by leaving copies of the questionnaire in the local supermarket.

Give one criticism of how the survey was carried out.

Catrin considers the data she needs to collect to find out if people are happy with their bank.

Catrin includes the following questions in her questionnaire.

Write down one set of possible groups that could be used as answer options for each of these

questions.

Question 1: How old are you?

Groups:

Question 2: If you have a bank account, how happy are you with your bank?

Groups:

Danielle is studying the growth of the population of Wales.

She used the 2001 and 2011 Census data to draw these histograms.

Use Danielle’s histograms to answer the following questions:

Circle the earliest decade in which anyone included in the histograms could have

been born.

1890–1899 1900–1909 1910–1919 1920–1929 1930–1939

From Danielle’s histogram, the population of under-50s in Wales was 1 870 000 in 2001. Calculate the increase in the population of under-50s in Wales from 2001 to 2011.

The 60 to 69-year-olds saw the biggest increase in population from 2001 to 2011. Calculate the percentage increase in the number of 60 to 69-year-olds from 2001 to 2011.

Give your answer to the nearest whole number.

The data in this table was also available to Danielle.

Explain why Danielle did not include this data in her histograms.

The number of 40 to 49-year-olds in 2011 was different to the number of 30 to 39-year- olds in 2001.

Give a full explanation for what could have caused this.

Lekan’s parents have complained that they are paying too much towards his mobile phone bill each month.

Lekan decides to ask a number of students in school how much their parents or carers pay towards their mobile phone bills each month. He displays the results in a scatter diagram. These include his own results.

Lekan’s parents want to know the names of some of these students.

The two 15-year-old students are Harriet and Eleri. Eleri is older than Harriet.

Gwilym and Aled’s parents each pay £27.50 per month. Aled is younger than Gwilym.

21 21

Complete each of the following statements.

‘Eleri’s parents or carers pay £_{………........ ……….} each month towards her mobile phone bill.’

‘Harriet’s parents or carers pay £_{………........ ……….} each month towards her mobile phone bill.’

Complete each of the following statements.

‘Gwilym is_{………........ ….} years_{………........ ….} months old.’

‘Aled is_{………........ ….} years_{………........ ….} months old.’

Lekan’s parents pay £32.50 per month towards his mobile phone bill. He is the youngest of the 3 students who receive £32.50 per month towards their mobile phone bill.

How old is Lekan?

Do you think Lekan’s parents are right to complain that they are paying too much towards his mobile phone bill each month?

You must use the scatter diagram to give a reason for your answer.

Yes No

The tables below show all of the international football results for Wales in 1984 and 1985.

1984

22 May 1984
Wales 1 – 1 Northern Ireland

1985

Geraint says, ‘On average, the Wales international football team scored more goals per match in 1985 than in 1984.’

In checking the truth of Geraint’s statement, why would it not be helpful to consider the

range of the number of goals scored per match in each year?

By considering the mean number of goals scored per match by Wales each year, is Geraint’s statement true?

You must show calculations for each year to support your answer.

Give one reason why this method does not necessarily show that the Wales

international football team results were better in 1985 than in 1984.

Lekan’s parents have complained that they are paying too much towards his mobile phone bill each month.

Lekan decides to ask a number of students in school how much their parents or carers pay towards their mobile phone bills each month. He displays the results in a scatter diagram. These include his own results.

Lekan’s parents want to know the names of some of these students.

The two 15-year-old students are Harriet and Eleri. Eleri is older than Harriet.

Gwilym and Aled’s parents each pay £27.50 per month. Aled is younger than Gwilym.

Complete each of the following statements.

‘Eleri’s parents or carers pay £_{………........ ……….} each month towards her mobile phone bill.’

‘Harriet’s parents or carers pay £_{………........ ……….} each month towards her mobile phone bill.’

Complete each of the following statements.

‘Gwilym is_{………........ ….} years_{………........ ….} months old.’

‘Aled is_{………........ ….} years_{………........ ….} months old.’

Lekan’s parents pay £32.50 per month towards his mobile phone bill. He is the youngest of the 3 students who receive £32.50 per month towards their mobile phone bill.

How old is Lekan?

Do you think Lekan’s parents are right to complain that they are paying too much towards his mobile phone bill each month?

You must use the scatter diagram to give a reason for your answer.

Yes No

Ffion thinks that the taller you are, the greater your waist measurement will be.

She recorded the height and waist measurements, in centimetres, for 6 people.

Give one reason why using this scatter graph to estimate the waist measurement of other

people is unlikely to give reliable results.

Lloyd has carried out a survey in his school.

He surveyed 300 pupils. Below is a section from his questionnaire.

1. Which year group are you in?_{……........ ……}

2. Do you like the colours of the school uniform?_{……........ ……}

3. What is your favourite colour?_{……........ ……}

Afterwards, Lloyd thinks he should have given option boxes in questions 1 and 2.

What could these option boxes be?

Question 1:

Question 2:

A pie chart displaying the results from question 3 of the questionnaire is shown below.

Which colour was chosen by 75 pupils as their favourite colour?

Circle your answer.

Black Red Blue Yellow Other

What fraction of the pupils said that blue was their favourite colour?

Give your answer in its simplest form.

Which school and year group has an approximately equal split between the 3 categories: • pupils who cycle to school, • pupils who would like to cycle to school, and

• other pupils?

School:_........ Year Group:_........

Circle either TRUE or FALSE for each of the following statements.

In January 2011, there were 1200 miles of National Cycle Network (NCN) routes in Wales. In January 2016, there were 1400 miles of NCN routes in Wales.

If the number of miles of NCN routes in Wales were to continue to increase by the same number of miles per year, how many miles of cycle routes would there be in

January 2018?

Why is your answer in (i) unlikely to be an accurate estimate of the number of miles

of NCN routes in Wales in January 2018?

Lloyd has carried out a survey in his school.

He surveyed 300 pupils. Below is a section from his questionnaire.

1. Which year group are you in?_{……........ ……}

2. Do you like the colours of the school uniform?_{……........ ……}

3. What is your favourite colour?_{……........ ……}

Afterwards, Lloyd thinks he should have given option boxes in questions 1 and 2.

What could these option boxes be?

Question 1:

Question 2:

A pie chart displaying the results from question 3 of the questionnaire is shown below.

Which colour was chosen by 75 pupils as their favourite colour?

Circle your answer.

Black Red Blue Yellow Other

What fraction of the pupils said that blue was their favourite colour?

Give your answer in its simplest form.

Which school and year group has an approximately equal split between the 3 categories: • pupils who cycle to school, • pupils who would like to cycle to school, and

• other pupils?

School:_........ Year Group:_........

Circle either TRUE or FALSE for each of the following statements.

In January 2011, there were 1200 miles of National Cycle Network (NCN) routes in Wales. In January 2016, there were 1400 miles of NCN routes in Wales.

If the number of miles of NCN routes in Wales were to continue to increase by the same number of miles per year, how many miles of cycle routes would there be in

January 2018?

Why is your answer in (i) unlikely to be an accurate estimate of the number of miles

of NCN routes in Wales in January 2018?

A survey was carried out to find how often teenagers buy DVDs.

The following two questions were asked in a questionnaire.

Q1. Where do you live?

Q2. How often do you buy DVDs?

Never 1-10 times 10-15 times More than 15 times

For each question give one reason why it is not suitable.

The survey was carried out by leaving copies of the questionnaire on the DVD shelves in a supermarket.

Give one criticism of how the survey was carried out.

Students are taking tests in English and Welsh. The English test is marked out of 80. The Welsh test is marked out of 70.

Dyfed scores 35 in his English test. Estimate Dyfed’s score as a percentage.

Circle your answer.

4% 20% 23% 44% 51%

Liam scores 22 in his Welsh test. Estimate Liam’s score as a percentage.

Circle your answer.

Rowena states a hypothesis, ‘Boys do better than girls in their English tests.’

She displays the test marks for 5 girls and 5 boys in scatter diagrams.

Boys’ test results Mark in Welsh

Does the data support Rowena’s hypothesis?

You must give a reason for your answer.

How could Rowena improve the testing of her hypothesis?

For each question give one reason why it is not suitable.

The survey was carried out by leaving copies of the questionnaire on the DVD shelves in a supermarket.

Give one criticism of how the survey was carried out.

Students are taking tests in English and Welsh. The English test is marked out of 80. The Welsh test is marked out of 70.

Dyfed scores 35 in his English test. Estimate Dyfed’s score as a percentage.

Circle your answer.

4% 20% 23% 44% 51%

Liam scores 22 in his Welsh test. Estimate Liam’s score as a percentage.

Circle your answer.

Rowena states a hypothesis, ‘Boys do better than girls in their English tests.’

She displays the test marks for 5 girls and 5 boys in scatter diagrams.

Boys’ test results Mark in Welsh

Does the data support Rowena’s hypothesis?

You must give a reason for your answer.

How could Rowena improve the testing of her hypothesis?