Types of data

Louise wants to find out what local residents think about changes to car parking in the local town centre.

Louise is going to use a questionnaire.

Here is one of the questions she puts on the questionnaire.

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

quantitative discrete continuous qualitative

Here is a different question on her questionnaire.

Discuss whether or not this is a suitable question for the questionnaire.

Here is another question that Louise wants to put on the questionnaire.

This is not a suitable question. Explain why.

Tsena is researching the ages of Oscar winners.

She has collected data from the internet about the ages of the winners of the Best Actor and Best Actress categories from 2000 to 2022

Data from the internet is an example of secondary data.

Explain what is meant by secondary data.

Here are the ages of the winners of the Best Actor category from 2000 to 2022

40 36 47 29 43 37 38 45 50 48 60 50

39 55 44 32 41 41 59 37 83 53 54 (Source: www.openintro.org and www.oscars.org)

The stem and leaf diagram gives the ages of the winners of the Best Actress category from 2000 to 2022

Complete the stem and leaf diagram with the ages of the winners of the Best Actor category. You should also complete the key.

(Source: www.openintro.org and www.oscars.org)

Work out the median age for the winners of the Best Actress category from 2000 to 2022

Michelle thinks it is more appropriate to use the interquartile range than the range as a measure of spread for these sets of data.

Give a reason why Michelle may think this.

Work out the interquartile range for the winners of the Best Actress category from 2000 to 2022

The table gives information about the ages of the winners of the Best Actor and Best Actress categories before 2000 It also gives information about the ages of the winners of the Best Actor category from 2000 to 2022

Compare the distribution of ages for the winners of the Best Actor category with the distribution of ages for the winners of the Best Actress category. You may use the blank column in the table to record your answers to parts (c) and (e) to help you. You should interpret your comparisons in context.

Tsena is researching the ages of Oscar winners.

She has collected data from the internet about the ages of the winners of the Best Actor and Best Actress categories from 2000 to 2022

Data from the internet is an example of secondary data.

Explain what is meant by secondary data.

Here are the ages of the winners of the Best Actor category from 2000 to 2022

40 36 47 29 43 37 38 45 50 48 60 50

39 55 44 32 41 41 59 37 83 53 54 (Source: www.openintro.org and www.oscars.org)

The stem and leaf diagram gives the ages of the winners of the Best Actress category from 2000 to 2022

Complete the stem and leaf diagram with the ages of the winners of the Best Actor category. You should also complete the key.

(Source: www.openintro.org and www.oscars.org)

Work out the median age for the winners of the Best Actress category from 2000 to 2022

Michelle thinks it is more appropriate to use the interquartile range than the range as a measure of spread for these sets of data.

Give a reason why Michelle may think this.

Work out the interquartile range for the winners of the Best Actress category from 2000 to 2022

The table gives information about the ages of the winners of the Best Actor and Best Actress categories before 2000 It also gives information about the ages of the winners of the Best Actor category from 2000 to 2022

Compare the distribution of ages for the winners of the Best Actor category with the distribution of ages for the winners of the Best Actress category. You may use the blank column in the table to record your answers to parts (c) and (e) to help you. You should interpret your comparisons in context.

Agatha is investigating the times taken in the 2022 Olympic Women’s Skiathlon race.

There are two parts to the Skiathlon race. There is a 7.5 km classic stage and a 7.5 km free stage.

Agatha thinks there may be a relationship between the time taken by each skier to complete the classic stage and the time taken by each skier to complete the free stage. She suggests calculating a correlation coefficient to check.

Discuss the appropriateness of this suggestion. You should consider the type of data in your answer.

Agatha found the times taken for the event by all the skiers.

The incomplete histogram and incomplete grouped frequency table give information about the times taken, in minutes, to complete the 7.5 km classic stage of the race.

Use the information in the histogram to complete the table.

Use the information in the table to complete the histogram.

Agatha also drew this histogram for the overall times for the race.

Agatha concludes that the median is in the 50 t ≤ 52 minute time interval.

Does the histogram support Agatha’s conclusion? Show calculations to support your answer.

A ski manufacturer produces wax used on skis.

It has made a new type of wax and wants to find out if using this wax improves the skiers’ times.

Agatha thinks a matched pairs approach should be used to find out if the wax improves the time taken to complete the race.

Agatha suggests matching skiers based on the type of ski that they use and their times in the race. One skier in each pair would use their original wax and the other skier would use the new wax.

Comment on the appropriateness of this suggestion. Give a reason for your answer.

Leya has collected data about 15 butterflies.

The table gives information about the length of time, in days, each butterfly lived.

Length of time lived (d days)	Frequency
0 d 3	7
3 d 6	4
6 d 9	3
9 d 12	0
12 d 15	0
15 d 18	1

Leya uses the table to calculate an estimate for the mean length of time these butterflies lived. Her estimate for the mean is 4.5 days.

Without performing a calculation, explain why Leya’s value for the mean is an estimate.

Explain why using the mean to represent the average length of time these butterflies lived may not be appropriate.

Mandeep visited Marple Wood Farm and tallied the types of animals he saw.

Circle the word in the list below that best describes the type of data for the types of animals.

Quantitative Discrete Continuous Categorical

The incomplete tally chart and incomplete bar chart give some information about Mandeep’s results.

Complete the tally chart and the bar chart.

This is a sign at the entrance to the farm.

Mandeep tallied 55 animals during his visit. Using his results, Mandeep claims that the most common animal in the farm is a chicken.

Give two reasons why Mandeep’s claim may be incorrect.

A professor of sports science wanted to test if listening to music improved running performance.

She tested a sample of 20 adult males. All the males were similar in age and in fitness level.

The professor completed the study as a laboratory experiment. She asked all the males to run as far as they could in six minutes.

Each male ran twice. The first time he ran he listened to music. The second time he ran he did not listen to music.

Give two advantages of the professor completing this study as a laboratory experiment.

The professor believes the explanatory variable in this experiment is if the runners are listening to music or not.

State the response variable in this experiment.

One extraneous variable in this experiment is the type of music that the runners listen to.

How could the professor control this extraneous variable?

Explain why it is important to control extraneous variables in experiments.

Divyesh is investigating the number of games won by two Los Angeles basketball teams, the Clippers and the Lakers. He collects some data from the NBA website.

Complete the sentence with an appropriate statistical word.

Divyesh has collected data from the internet and so this is_........ data.

Using the information in the bar chart to compare the number of games won by each team over the four years,

write down one comparison between the two teams,

describe the trend in the number of games won by the Lakers over the four seasons.

The table contains information about the number of games won by the Clippers in the 2022–23 season.

Complete the table. Give your answers correct to the nearest whole number.

The line graph shows the cumulative games played and the cumulative percentage of games won by the Lakers in the same season.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Each team played 82 games in the 2022–23 season.

Which team won the most games by the end of the 2022–23 season? You should justify your answer.

Divyesh is investigating the number of games won by two Los Angeles basketball teams, the Clippers and the Lakers. He collects some data from the NBA website.

Complete the sentence with an appropriate statistical word.

Divyesh has collected data from the internet and so this is_........ data.

Using the information in the bar chart to compare the number of games won by each team over the four years,

write down one comparison between the two teams,

describe the trend in the number of games won by the Lakers over the four seasons.

The table contains information about the number of games won by the Clippers in the 2022–23 season.

Complete the table. Give your answers correct to the nearest whole number.

The line graph shows the cumulative games played and the cumulative percentage of games won by the Lakers in the same season.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Each team played 82 games in the 2022–23 season.

Which team won the most games by the end of the 2022–23 season? You should justify your answer.

The population pyramid shows the age distribution of the world population in the year 1960

Each percentage is given correct to one decimal place.

10% 8% 6% 4% 2% 0% 2% 4% 6% 8% 10%

Work out the percentage of males aged 65 or over in 1960

Kiran is carrying out research into how the population of Finland is changing. She uses the data for Finland in 2023

	Finland 2023
Age (y years)	Percentage of the population (%)
0 y 15	14.91
15 y 30	17.13
30 y 45	19.52
45 y 60	18.39
60 y 75	18.88
75 y	11.17

Use linear interpolation to work out an estimate of the median age in Finland in 2023

In 1960, the median age in Finland was 27 years correct to the nearest year. Kiran claims that Finland’s population is getting older.

Explain whether or not Kiran’s claim is correct. You should justify your answer.

On a website, Kiran reads that the median age in Finland in 2023 was 42.8 years. (Source: www.worldometers.info)

Suggest a reason why the median of 42.8 from the website and a median found using linear interpolation would be different.

In world athletics, an athlete’s personal best results in different track and field events are recorded.

Zara wants to compare a sample of athletes’ longest recorded long jump against their height. She is going to present this information on a scatter diagram.

Explain why it is appropriate to use a scatter diagram.

Zara plotted the athletes’ heights on the x‑axis.

Give a reason why plotting the heights on the x‑axis is appropriate.

Zara selects 12 athletes ranked as some of the world’s best long jumpers. She calculates the Pearson Product Moment Correlation Coefficient (PMCC) for their personal best long jump distances against their heights.

The PMCC value is 0.02 (Source: www.worldathletics.org)

Describe the correlation shown by the PMCC.

Using data for the same 12 athletes, Zara compares their personal best long jump distances (m metres) to their fastest times in a 100 metre race (t seconds).

She calculates the PMCC to be –0.5

Describe and interpret the relationship between the athletes’ personal best long jump distances and their personal best 100 metre race times in context.

The data for the 12 athletes is shown in the table below.

World rank April 2023	Long jump athlete	Personal best long jump distance (m metres)	Personal best 100 m race time (t seconds)
1	M Tentoglou	8.60	10.70
3	M Dendy	8.42	10.31
4	S Ehammer	8.45	10.46
5	T Montler	8.38	10.49
8	E Cáceres	8.37	10.37
10	T Gayle	8.69	10.13
11	E Lasa	8.28	11.03
15	H Frayne	8.34	10.96
16	Y Hashioka	8.36	10.53
17	R Ju ka	8.31	11.07
26	C Mitrevski	8.21	10.27
30	H Santos	8.19	11.77

(Source: www.worldathletics.org)

The linear regression line for these data is t = 25 – 1.7m

In April 2023, M Massó was ranked number 2 in the world for the long jump. His personal best long jump distance was 8.39 m.

Zara uses this regression line to predict that M Massó could run the 100 m race in 10.7 seconds.

Comment on the reliability of this prediction in context.

A fjord is a deep and narrow part of a sea with steep land on three sides.

Emily is investigating the length of fjords in Norway. She collects some data from the internet and puts the data into a grouped frequency table.

The grouped frequency table below shows information about the results she collected.

Length of fjord (lkm)	Frequency
0 l 50	199
50 l 100	17
100 l 150	12
150 l 200	3
200 l 250	1

(Source: https://en.wikipedia.org/wiki/List_of_Norwegian_fjords)

Work out the number of fjords that have a length of at least 100 km.

Calculate an estimate of the mean length of these fjords. Give your answer to 1 decimal place.

Explain why your answer to part (b)(i) is only an estimate.

How could Emily have improved the accuracy of her answer to part (b)(i)?

Emily plans to use a frequency polygon to represent the lengths of the fjords.

Discuss whether or not a frequency polygon would be an appropriate diagram to use.

Timur is investigating the heights and weights of rugby players. He collected data from the internet about the heights and weights of players from the Wales rugby squad.

The players from the Wales rugby squad are classed as Forwards or Backs. Timur draws a scatter diagram for the heights and weights of some of the Backs from the Wales rugby squad.

Explain why a scatter diagram is appropriate for the type of data Timur collected.

The data for three of the players was not plotted on the scatter diagram. The height and weight of each of these players is given in the table below.

Complete the scatter diagram by plotting the points for players A, B and C.

Describe and interpret the type of correlation shown by the scatter diagram.

The double mean point for the heights and weights of all of the Backs is (184, 92).

Draw a line of best fit through the double mean point.

Timur also collected the heights and weights of players from the England rugby squad. He found the Spearman’s rank correlation coefficient for the heights and weights of the Forwards from the England rugby squad.

The correlation coefficient was 0.00

Interpret this correlation coefficient in context.

Timur used statistical software to find the following information about the heights (x cm) and weights (y kg) of the Backs from the Wales rugby squad and the Backs from the England rugby squad.

Compare the Spearman’s rank correlation coefficients and interpret this comparison in the context of the question.

Timur uses the information in the table to conclude that the weight of the England rugby squad Backs increases faster than the weight of the Wales rugby squad Backs as their height increases.

Assess the validity of Timur’s conclusion with reference to the statistical results.

Matthew is investigating average household income for different states in the USA.

Give a reason why it is appropriate to use secondary data for this.

Matthew creates a choropleth map giving information about the mean household income by state for the USA in 2023

Mean annual household income in $ thousands.

2.

5.

Which three states have the lowest mean household income?

Matthew concludes that the mean household incomes are highest on the West coast and the East coast.

Does the choropleth map support this conclusion? Give a reason for your answer.

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.

Matthew is investigating average household income for different states in the USA.

Give a reason why it is appropriate to use secondary data for this.

Matthew creates a choropleth map giving information about the mean household income by state for the USA in 2023 Mean annual household income in $ thousands.

2.

5.

10.

Which three states have the lowest mean household income?

Matthew concludes that the mean household incomes are highest on the West coast and the East coast.

Does the choropleth map support this conclusion? Give a reason for your answer.

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.

David asked 15 of his friends about the number of pets they each have. Here is the data he collected.

0 0 0 0 0 1 1 2 2 2 4 4 4 4 8

Circle the word in the list below that describes this type of data.

continuous qualitative discrete grouped

Write down the modal number of pets.

Find the median number of pets.

State which average, the mode or the median, best represents these data. Give a reason for your answer.

Find the interquartile range of the number of pets.

Wanda asked some of her friends about the number of pets they each have. The table below is a summary of the data she collected.

Compare the distribution of the numbers of pets for David with the distribution of the numbers of pets for Wanda. Give two comparisons and interpret each of your comparisons.

Wanda recorded the highest number of pets as 15 She says that this must be an outlier and concludes that it should be removed from her data.

Give one reason why Wanda’s conclusion may be appropriate.

Give one reason why Wanda’s conclusion may not be appropriate.

Kyle is investigating the heights and the weights of professional basketball players.

He found the weight, in kilograms, of some professional basketball players from 1950 to 1959

Circle the word in the list below that describes weight, in kilograms, as a type of data.

discrete continuous ordinal categorical

The incomplete histogram and incomplete grouped frequency table give information about the weights, in kilograms, of the professional basketball players from 1950 to 1959

Weight (w kilograms)
Frequency

65 w 70	5
70 w 75	15
75 w 80	61
80 w 85	81
85 w 90
90 w 95
95 w 100	35
100 w 105	14
105 w 110	9
110 w 115	1

Use the information in the histogram to complete the table.

Use the information in the table to complete the histogram.

Kyle also drew a histogram for the weights of professional basketball players from 2000 to 2009 This histogram was negatively skewed.

Interpret the negative skew of the weights of professional basketball players from 2000 to 2009

Kyle also collected data about the heights of professional basketball players from 1950 to 1959 and the heights of professional basketball players from 2000 to 2009

The grouped frequency table below gives information about the heights of professional

The estimate of the mean height for professional basketball players from 1950 to 1959 is calculated to be 190.9 cm to one decimal place.

Calculate an estimate of the mean height of basketball players from 2000 to 2009

Comment on how the mean height of professional basketball players has changed between the two sets of data.

The incomplete comparative bar chart shows the total number of medals won by three of the countries that took part in the 2014 and 2018 Winter Olympics.

Number of medals won in 2014 and 2018 Winter

The total number of medals won by Sweden in the 2018 Winter Olympics was 14

Complete the comparative bar chart for Sweden.

Work out how many more medals were won by Sweden than Great Britain in the 2014 Winter Olympics.

Compare the total number of medals won by Sweden, Great Britain and Switzerland in the 2014 Winter Olympics.

Thomas says that the data displayed in the comparative bar chart is quantitative data.

Explain what is meant by quantitative data.

Sam used the internet to collect the times, in minutes, it took for 50 cyclists to compete in a hill climb competition. He used a group frequency table to record the results he collected.

Give one advantage of using grouped data rather than raw data.

Give one disadvantage of using grouped data rather than raw data.

Sam used this grouped frequency table to show the results for the hill climb.

Before Sam collected the data he did not know what the longest time would be. The longest time in the hill climb was 28.3 minutes.

Explain why this table cannot be used to show the data for all 50 riders.

Sam drew this frequency polygon for the hill climb results.

Sam decided not to include the value of 28.3 minutes on his frequency polygon.

Suggest a reason why Sam’s decision might be appropriate.

Describe the skew of the distribution.

Interpret the skew of the distribution in context.

Alexa needs to know the population of California.

Using the internet, Alexa found that an estimate for the population of California in 2019 is 39.5 million people. (Source: www.worldpopulationreview.com)

Explain why this statistic is an example of secondary data.

Give one advantage and one disadvantage of using secondary data.

Dylan investigates the ages of 150 people at a music festival. The youngest person at the festival is 21 years old and the oldest person is 68 years old.

Dylan decides to use a grouped frequency table to show his results.

Give two advantages of using grouped data rather than raw data.

Give one disadvantage of using grouped data rather than raw data.

Dylan is considering using one of the two possible frequency tables, Table A or Table B, shown below.

Dylan claims that Table B gives more detail than Table A about his results.

Assess whether or not Dylan’s claim is appropriate.

Dylan wants to work out the average age of the 150 people at the music festival. He decides to use Table B.

Calculate an estimate for the mean age of the 150 people at the music festival. Give your answer to one decimal place.

120 adults were each asked if they enjoy watching any of the sports Football, Cricket or Rugby.

The Venn diagram gives information about the numbers of these adults who enjoy watching these sports.

How many of these adults enjoy watching all three sports?

One of these adults is chosen at random.

Find the probability that this adult enjoys watching Cricket.

Find the probability that this adult enjoys watching Rugby or Football.

One of the adults who enjoys watching Football is chosen at random.

Find the probability that this adult also enjoys watching Cricket.

Here are five words that can be used to describe different types of data.

qualitative quantitative bivariate discrete continuous

Use one of the words in the list to describe the type of data needed for names of sports.

Use two of the words in the list to describe the type of data needed for numbers of adults.

Viktoria collects information about the times taken, in seconds, by 50 boys to run 400 metres. She records her results in the grouped frequency table, shown below, and gives the grouped frequency table to her friend Emeka.

Time taken (t seconds)	Frequency (f)
50 t 60	1
60 t 65	5
65 t 70	15
70 t 75	17
75 t 80	12

Viktoria asks Emeka to use only the information in the grouped frequency table to work out an estimate of the standard deviation of the times taken.

Using Emeka’s estimates of the summary statistics, calculate an estimate of the skew of the distribution of the times taken by the 50 boys. Give your answer to 2 decimal places.

Interpret your answer to part (b) in the context of the data in the table.

Irina is investigating whether the percentage of the population of a country living in urban areas has an effect on the life expectancy in that country.

Suggest a hypothesis Irina could use for her investigation.

Irina collected the following information about 10 countries.

The Urban population (%) refers to the percentage of the population of the country who live in urban areas.

Irina used statistical software to draw a scatter diagram for the information in the table.

Give a reason why a scatter diagram is an appropriate diagram to use.

For this investigation, which variable is the explanatory variable? Give a reason for your answer.

The scatter diagram from the statistical software is shown below.

Explain, giving a statistical reason, whether or not this scatter diagram supports your hypothesis in part (a).

For these 10 countries, the double mean point of the data is (63.9, 77.8).

Using this information, draw a line of best fit on the scatter diagram.

Using statistical software, Irina finds that the gradient of the line of best fit should be 0.19

Interpret the gradient of the line of best fit.

Irina now finds that South Africa has Urban population 65% and Life expectancy 63 years.

Determine how this information for South Africa fits with the relationship shown in the scatter diagram for the other countries.

Irina is investigating whether the percentage of the population of a country living in urban areas has an effect on the life expectancy in that country.

Suggest a hypothesis Irina could use for her investigation.

Irina collected the following information about 10 countries.

The Urban population (%) refers to the percentage of the population of the country who live in urban areas.

Irina used statistical software to draw a scatter diagram for the information in the table.

Give a reason why a scatter diagram is an appropriate diagram to use.

For this investigation, which variable is the explanatory variable? Give a reason for your answer.

The scatter diagram from the statistical software is shown below.

Explain, giving a statistical reason, whether or not this scatter diagram supports your hypothesis in part (a).

For these 10 countries, the double mean point of the data is (63.9, 77.8).

Using this information, draw a line of best fit on the scatter diagram.

Using statistical software, Irina finds that the gradient of the line of best fit should be 0.19

Interpret the gradient of the line of best fit.

Irina now finds that South Africa has Urban population 65% and Life expectancy 63 years.

Determine how this information for South Africa fits with the relationship shown in the scatter diagram for the other countries.

Andy is investigating the lateness of the trains that arrive at Manchester Piccadilly.

Explain why it is sensible for Andy to collect secondary data for his investigation.

Andy found out data on the lateness of each of 238 trains arriving at Manchester Piccadilly from London on Monday to Friday for one week.

The histogram below was drawn using Andy’s data.

A negative time for a train means that the train arrived early at Manchester Piccadilly.

In the week, 14 trains arrived early.

Find how many of the 238 trains did not arrive more than 10 minutes late at Manchester Piccadilly.

For a long distance journey, such as London to Manchester Piccadilly, a train is only considered to be late when it arrives more than 10 minutes late.

Andy says that more than 1 in 3 trains from London arrive late at Manchester Piccadilly.

Determine whether or not Andy is correct.

You should comment on the reliability of your conclusion.

Julie asked 20 of her friends how many days last week they each played a sport.

Here are her results.

3 4 5 3 2 2 3 3 2 5 1 0 1 0 2 3 3 2 5 3

Which word from the list below best describes Julie’s data before it is processed?

Julie draws the following tally chart for her results.

Write down two things that could be misleading or are wrong with Julie’s tally chart.

The median for Julie’s results is 3

Interpret this value in context.

Julie says the mode of her results is 7

Is Julie correct? Give a reason for your answer.

Albert groups Julie’s results and then draws the following bar chart.

Assess whether or not Albert’s way of presenting Julie’s results is appropriate. Give two reasons for your answer.

The manager of an art shop wants to find out about the shopping habits of customers in his shop. He wants to find out how many customers leave the shop without buying anything.

For the next four weeks he plans to record how many customers leave the shop without buying anything each Monday.

Give one problem with the manager’s plan for data collection.

The manager asks his staff to record the number of people served at the till each hour.

‘Number of people served’ is an example of which type of data?

The staff record the number of people served per hour. Here is the completed table.

Identify two problems with this completed table.

The manager also collected data on the type of art that his customers produce.

The incomplete bar chart shows information about the type of art produced by some of his customers.

Photography is the type of art produced by 11 customers.

Complete the bar chart.

Which type of art is produced by half as many customers as those who produce paintings?

Shona and Luke are investigating housing.

Shona wants to find out about the types of house in which people live. She plans to collect data by asking people to tell her in which type of house they each live.

Complete the sentence with an appropriate statistical word.

Shona is collecting the data herself and so this is_........ data.

Design a data collection sheet for Shona to use.

Luke has collected data about the number of people living in each of the 12 houses in his street.

Here is his data.

2 2 3 3 3 4 4 4 4 5 5 11

Luke wants to work out the average of the number of people living in each house in his street.

Which average, mean or median, would it be more appropriate for Luke to use? Give a reason for your answer.

There is one outlier in the data.

Excluding the outlier, work out the range of the number of people living in the houses in the street.

Shona has collected data about the number of people living in each of the houses in her street. She has collected data for 2014 and for 2019

The table gives the range of the number of people living in the houses in Shona’s street

Compare the range for 2014 with the range for 2019 and interpret your comparison in context.

Diana is investigating the numbers of wolf pups in wolf dens and the numbers of fox pups in fox dens.

She collected data from the internet.

Data collected from the internet is an example of secondary data.

Explain why data collected from the internet is an example of secondary data.

Diana finds data on the number of wolf pups observed in a random sample of 16 wolf dens.

Here is the data.

3 3 4 4 5 5 5 5

5 6 6 7 7 8 8 9

(Source: college.cengage.com)

Diana also collects data on the number of fox pups in each den of a random sample of fox dens.

Here is information about the numbers of fox pups in the fox dens.

(Source: foxsurvey.ucdavis.edu)

Compare the distribution of the numbers of wolf pups in the wolf dens and the distribution of the numbers of fox pups in the fox dens. Justify your comparisons and interpret one of them in the context of the numbers of pups.

Explain how the use of secondary data affects the reliability of your conclusions in part (b)(i).

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.

The bar line graph gives information about the total rainfall, in mm, in the UK for each

In which month was there the greatest total rainfall?

Here are some words to describe data.

discrete bivariate categorical continuous

Select the word from the list to complete correctly the sentence.

Total rainfall, in mm, is an example of_........ data.

A wet month is a month in which the total rainfall for the month is greater than 100 mm.

Determine whether or not more than half of the months in 2017 were wet months. You must show how you reach your conclusion.

Richard finds information from the internet about the most popular colours for cars in the UK in 2017

Table 1 gives this information.

Explain why the information in Table 1 is secondary data.

Richard drew this pictogram to represent his information about the most popular car colours.

Complete this key for the pictogram.

Jill says that a pictogram is not the most appropriate way to display Richard’s information.

Is Jill correct? Give a reason for your answer.

Richard decides to collect some data about car colours by recording the colour of each of the 60 cars in a car park.

Table 2 gives information about his results.

The modal car colour from Table 2 is blue.

Explain whether or not blue is the expected modal car colour based on the information in Table 1

Explain why, for the information in Table 2, the mode is the most appropriate average to use.

Using the information in Table 1 and Table 2, compare the number of silver cars in the car park with the expected number of silver cars in a car park with 60 cars.

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.

Mike is investigating whether or not there is a relationship between the distance from the nearest car park to a restaurant and the annual profit made by the restaurant.

He finds out the distance, in metres, from the nearest car park to a restaurant and the annual profit, in £, made by the restaurant. He does this for twenty restaurants in a city.

Mike then draws a scatter diagram for this information.

Explain why annual profit is the response variable for this scatter diagram.

Mike’s hypothesis is that, for these restaurants, the further the restaurant is from its nearest car park the less is its annual profit.

Explain, giving a statistical reason, whether or not the scatter diagram supports Mike’s hypothesis.

Mike wants to draw a line of best fit on the scatter diagram. Using statistical software he obtains the following information about these restaurants.

Using this information, draw a line of best fit on the scatter diagram.

Interpret the value of the intercept of the line of best fit on the Annual profit axis.

Restaurant A and restaurant B are two other restaurants in the city. Restaurant A is 250 m from its nearest car park. Restaurant B is 700 m from its nearest car park. Mike uses the scatter diagram to find an estimate for the annual profit of each of these restaurants.

Explain which of these two estimates will be the more reliable estimate.

Mike finds a positive correlation between the number of tables at a restaurant and its annual profit. He concludes that as the number of tables increases this causes the annual profit to increase.

Explain whether or not this conclusion is valid.

Mike reads an article in a newspaper that says that restaurant profits for the top 100 restaurants had fallen from £345 million to £125 million in the past year. (Source: telegraph.co.uk)

Using the data in the newspaper article, calculate the percentage decrease in restaurant profits for the top 100 restaurants in the past year.

Mike is investigating whether or not there is a relationship between the distance from the nearest car park to a restaurant and the annual profit made by the restaurant.

He finds out the distance, in metres, from the nearest car park to a restaurant and the annual profit, in £, made by the restaurant. He does this for twenty restaurants in a city.

Mike then draws a scatter diagram for this information.

Explain why annual profit is the response variable for this scatter diagram.

Mike’s hypothesis is that, for these restaurants, the further the restaurant is from its nearest car park the less is its annual profit.

Explain, giving a statistical reason, whether or not the scatter diagram supports Mike’s hypothesis.

Mike wants to draw a line of best fit on the scatter diagram. Using statistical software he obtains the following information about these restaurants.

Using this information, draw a line of best fit on the scatter diagram.

Interpret the value of the intercept of the line of best fit on the Annual profit axis.

Restaurant A and restaurant B are two other restaurants in the city. Restaurant A is 250 m from its nearest car park. Restaurant B is 700 m from its nearest car park. Mike uses the scatter diagram to find an estimate for the annual profit of each of these restaurants.

Explain which of these two estimates will be the more reliable estimate.

Mike finds a positive correlation between the number of tables at a restaurant and its annual profit. He concludes that as the number of tables increases this causes the annual profit to increase.

Explain whether or not this conclusion is valid.

Mike reads an article in a newspaper that says that restaurant profits for the top 100 restaurants had fallen from £345 million to £125 million in the past year. (Source: telegraph.co.uk)

Using the data in the newspaper article, calculate the percentage decrease in restaurant profits for the top 100 restaurants in the past year.

Kate is investigating the lengths of earthworms. She wants to find out if the lengths of common earthworms can be modelled by a normal distribution. She has found out that the greatest length of the common earthworm is 36 cm. (Source: www.nationalgeographic.com)

Kate plans to group the data that she will collect in the table shown below.

Comment on whether Kate’s choice of class intervals in the grouped frequency table is appropriate.

Bien is researching the lengths of time, in days, lived by flies. He wants to know if the lengths of time lived by flies can be modelled by a normal distribution.

He has collected data for 80 flies.

The table gives information about the length of time lived by each fly.

Here is Bien’s plan to test whether the lengths of time lived by flies can be modelled by a normal distribution.

Comment on whether Bien’s plan is appropriate.

Lena is researching information about the numbers of British Oscar winners.

Here are her results, giving the number of British Oscar winners for each of the years 1981 to 2010

(Source: www.theguardian.com)

Lena found the data in a newspaper.

Correctly complete the following sentence.

Because Lena found the data in a newspaper, the data is_........ data.

Fill in the tally chart for Lena’s results and complete the frequency column.

Write down the modal group.

Work out the total number of years between 1981 and 2010 for which there were fewer than 7 British Oscar winners.

Suggest a suitable diagram that could be used for Lena’s results.

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.

Chris is carrying out an experiment to see if left handed people have a better memory than right handed people. He has two groups of people with the same number of people in each group.

Group A contains left handed people only and group B contains right handed people only.

Each person is given 15 objects to memorise and then they are tested to see how many objects they remember.

The variables for the experiment are shown in the table.

For each variable, put a tick () in the correct column of the table to show the type of variable.

Chris is not sure whether to work out the mean or the median number of objects each group remembered.

Describe a situation for which it would be more appropriate to work out the median than the mean.

Chris worked out these summary statistics for the number of objects people in group A remembered.

Lower quartile = 5 Median = 7 Upper quartile = 8

Sanjit is a member of group A.

He remembered 14 objects.

Determine whether or not the number of objects Sanjit remembered is an outlier.