Measures of dispersion

There is an award for board and card games.

Matthew collected a list of the 9 games that were recommended by the awards panel in the critics prize category for 2022

Here is a list of the ratings given to these games by players. A higher rating represents a better game.

8.0 7.79 7.52 7.0 6.6 7.2 6.9 7.59 6.9

(Source: www.spiel‑des‑jahres.de and boardgamegeek.com)

Work out the mean of the ratings.

Work out the range of the ratings.

Matthew also collected the ratings awarded to the games that were recommended in 2021

The table gives information about these ratings.

Matthew concludes that the players liked the games recommended by the panel in 2022 more than they liked the games recommended by the panel in 2021

Do the statistics support this conclusion? Give a reason for your answer.

Give another conclusion based on these statistics.

Passengers for airline flights have their suitcases weighed when they check in.

LocalHop offers flights to and from islands in a small plane.

Here is a list of the weights, in kilograms, of each of the suitcases for a flight to one of the islands on Monday.

16.8 8.9 15.7 16.7 15.4 4.1 19.2 17.4 16.4 15.3 14.9

Mikolaj thinks that it is more appropriate to use the median rather than the mean as an average for these weights.

Explain why Mikolaj may be correct.

Calculate the interquartile range for these weights.

For the return flight on Sunday the interquartile range for the weights of the suitcases is 1.6 kilograms.

Compare these interquartile ranges 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.

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.

David collected data on the times, in hours, taken for men to complete the Ironman Canada 2022 race and the Ironman UK 2022 race.

These graphs and summary statistics were produced for this data using statistical software.

Mean
13.53 Median
13.49 Number of male competitors 992

Standard deviation 1.839 Skewness 0.0653

Mean
13.98 Median
14.12 Number of male competitors 1128

Standard deviation 1.489 Skewness –0.282

(Source: www.coachcox.co.uk)

Show that there are no outliers in the times for the Ironman Canada 2022 men’s results.

Compare, in context, the distribution of the Ironman Canada 2022 men’s results with the distribution of the Ironman UK 2022 men’s results.

Dan competed in the Ironman Canada 2022 race.

Here is information about the performance of all male competitors in the swim, bike and run stages of the race, and some of Dan’s standardised scores.

Dan took 5.64 hours to complete the run.

Use standardised scores to compare Dan’s performances relative to the other competitors in each stage of the race. Give reasons for your comparisons.

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 table shows some of the percentile eye lengths (mm) in children between the ages

Compare the 5th to the 75th interpercentile range for 6 year old boys with the 5th to the 75th interpercentile range for 6 year old girls. You must show your working.

Give an interpretation of your comparison in part (a).

During a sports day competition students take part in two races. Each student runs a 100 m race and a 400 m race. The table shows the mean and the standard deviation of the times taken by the students in the 100 m race and in the 400 m race.

Dominic and Kai take part in the two races. The incomplete table below gives their times and standardised scores.

Dominic and Kai make the following conclusions.

• Dominic concludes that he performed better in the 400 m race compared to the 100 m race.

• Kai concludes that he finished over one second slower than Dominic in the 400 m race.

Complete the table and assess Dominic’s and Kai’s conclusions. Give a reason for each of your decisions.

Tachi collects data on the heights, in metres, of a sample of Egyptian pyramids.

Here is her data.

136.4 101.1 104 62.6 138.8 65.5 93.5 (Source: www.rankred.com)

Tachi picks one of these pyramids at random.

Find the probability that this pyramid will have a height of more than 100 m.

The mean height of a sample of Mexican pyramids is 53.5 m.

Tachi says, “On average these Egyptian pyramids are twice as high as the Mexican pyramids.”

Is Tachi correct? You must show working to support your answer.

The range of heights for the Mexican pyramids is 45 m. The lowest height of the Mexican pyramids is 30 m.

Work out the greatest height of the Mexican pyramids.

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.

Zack is comparing the players from the England Rugby Union team with the players from the Welsh Rugby Union team. The players are listed as Rugby Union Forwards or Rugby Union Backs.

Here are the weights, in kilograms, of the England Rugby Union team players who are listed as Backs.

(Source: www.englandrugby.com/england/senior‑men#squad)

The back‑to‑back stem and leaf diagram gives the weights, in kilograms, of the Welsh Rugby Union Backs.

Complete the back‑to‑back stem and leaf diagram with the weights, in kilograms, of the England Rugby Union Backs.

(Source: www.wru.wales/fixtures‑and‑teams/teams/wales/)

Work out the median weight for the Welsh Rugby Union Backs.

Work out the interquartile range for the Welsh Rugby Union Backs.

The table gives information about the weights for the England Rugby Union Backs.

Zack thinks that the Welsh Rugby Union Backs are heavier and have less consistent weights than the England Rugby Union Backs.

Do the statistics support these conclusions? You must give reasons for your answer.

Amy wants to use the median and interquartile range statistics in a news article for a sports magazine. The article will compare the players on the two teams who are Backs.

Comment on the appropriateness of using the median and the interquartile range in the article.

Give a limitation of using Zack’s statistics to compare all the players on the two teams.

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.

Logan is investigating the heights of male adult giraffes and the heights of female adult giraffes.

He records the height, in metres, of each of a sample of male adult giraffes and the height, in metres, of each of a sample of female adult giraffes.

He draws the box plot below for the recorded heights of the male adult giraffes.

The table gives information about the recorded heights of the female adult giraffes.

Logan makes the following two conclusions.

1. Male adult giraffes are generally taller than female adult giraffes.

2. The heights of the female adult giraffes are more consistent than the heights of the male adult giraffes.

Assess Logan’s two conclusions. You should show clearly the values of any statistics you use in your answer.

The cumulative frequency step polygon shows information about the number of goals scored in each of 28 matches played by the German women’s national football team.

(Source: www.worldfootball.net/teams/deutschland‑frauen‑team/)

Give a reason why a cumulative frequency step polygon is used to represent this information rather than a cumulative frequency curve.

Find the mode of the number of goals scored.

Find the number of these matches where

exactly 6 goals were scored,

more than 6 goals were scored.

In 24 matches fewer than n goals were scored.

Find the value of n

Klara tries to calculate the interquartile range of the number of goals scored.

She gets an answer of 14

Explain how you know that her answer is incorrect.

Jane is a car mechanic at MPG Autos.

Jane recorded the time, in minutes, that she took to change a tyre on each of 9 cars.

Here are her results.

25 32 19 27 17 24 35 29 15

Explain whether or not her results have a mode.

Find the median of her results.

Show that the range of her results is 20 minutes.

The range of the times that Jane took to change the oil in each of these 9 cars is 28 minutes.

Are the times that Jane took to change a tyre on each of these 9 cars more consistent than the times that she took to change the oil in each of these 9 cars? Give a reason for your answer.

Huan has applied for a job at a college. As part of the interview process all candidates must take a numeracy test and a literacy test.

The table below gives Huan’s score for the numeracy test and his score for the literacy test. The table also gives the mean and the standard deviation of the scores for each of these two tests for all candidates who were interviewed for the job.

Huan concludes that because he scored a higher mark in literacy than in numeracy he performed better in literacy than in numeracy as compared to the other candidates.

Use statistical calculations to assess Huan’s conclusion.

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.

Bill investigated the heights of females competing in different sports.

Using data from the internet, he recorded the height, in cm, of each female in a sample of 15 female rugby players and the height, in cm, of each female in a sample of 15 female basketball players.

He drew the box plot below for the recorded heights of the 15 female basketball players.

(Source: englandrugby.com, gbbasketball.com)

The table gives information about the recorded heights of the 15 female rugby players.

Using the information in the table, draw on the grid above a box plot for the recorded heights of the 15 female rugby players.

Compare the two distributions of heights. Give three comparisons and interpret one of your comparisons.

Considering the method that Bill used to collect his data, comment on the reliability of your comparisons in part (b).

Bill investigated the heights of females competing in different sports.

Using data from the internet, he recorded the height, in cm, of each female in a sample of 15 female rugby players and the height, in cm, of each female in a sample of 15 female basketball players.

He drew the box plot below for the recorded heights of the 15 female basketball players.

(Source: englandrugby.com, gbbasketball.com)

The table gives information about the recorded heights of the 15 female rugby players.

Using the information in the table, draw on the grid above a box plot for the recorded heights of the 15 female rugby players.

Compare the two distributions of heights. Give three comparisons and interpret one of your comparisons.

Considering the method that Bill used to collect his data, comment on the reliability of your comparisons in part (b).

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.

Aminah collected information about the mean daily temperature, in C, in August in Scotland for the years 1910 to 2018

The table shows a summary of the data produced by statistical software.

(Source: https://www.metoffice.gov.uk/climate/uk/summaries/datasets)

On the grid below, draw a box plot for the information in the table.

Calculate the interquartile range for the data in the table. You must show your working.

Describe the skew of the distribution represented by the box plot. Give a reason for your answer.

The cumulative frequency graph gives information about the area, in square kilometres, of the 48 counties in England.

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

Find an estimate of the 75th percentile of this information.

_........ square kilometres

Interpret this value in context.

Half of the counties in England have an area between 2000 square kilometres and k square kilometres.

Work out an estimate for the value of k.

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).

Birgitta works in a wildlife reserve. She has been researching the size of tiger feet in order to help in the identification of animal tracks.

The table gives information about the front pad width of adult tigers.

(Source: keywordsuggest.org)

Compare in context the distribution of the front pad widths of adult male tigers with the distribution of the front pad widths of adult female tigers.

Explain when it would be more appropriate to use the median rather than the mean in describing a distribution.

The table gives the standardised scores for Brinn Bevan in three of the gymnastic apparatus used in the men’s all‑around final in the 2018 Artistic Gymnastics World Championships.

(Source: worldgymdoha18.com)

Use the standardised scores to compare Brinn Bevan’s performances relative to the other competitors in the floor exercise, in the pommel horse and in the rings. Give reasons for your comparisons.

The raw score for each apparatus is also known. Each apparatus had the same maximum raw score.

Explain why it is appropriate to use standardised scores rather than raw scores to compare performances.

The table below shows Brinn Bevan’s standardised score for the parallel bars.

It also shows the mean and the standard deviation of the number of points awarded in the parallel bars to all the gymnasts who completed the men’s all‑around final.

(Source: worldgymdoha18.com)

Work out the number of points awarded to Brinn Bevan for the parallel bars. Give your answer correct to one decimal place.

The glucose level in blood is measured in milligrams per 100 millilitres (mg/100 ml).

A doctor is investigating the glucose levels in blood of some adult females at the end of 12 hours of not eating or drinking.

The incomplete histogram and the incomplete grouped frequency table give information about the glucose levels in the blood of these adult females.

Glucose level in blood (mg/100 m l)

Glucose level in blood x (mg/100 ml)	Frequency
40 x 60	5
60 x 70	11
70 x 75	11
75 x 80	13
80 x 85	16
85 x 90
90 x 110

(Source: college.cengage.com)

Use the information in the histogram to complete the table.

Use the information in the table to complete the histogram.

The doctor used statistical software to produce the following summary statistics for his data.

By calculating limits for outliers using the mean and the standard deviation, explain whether or not there could be any outliers in the doctor’s data.

A second doctor is investigating the glucose levels in the blood of some adult males at the end of 12 hours of not eating or drinking.

The following summary statistics were calculated.

Calculate the skew for the distribution of the adult male glucose levels in blood and interpret this value in context. Give your answer correct to 2 decimal places.

Explain how the pie chart shows that fish made up the largest proportion of the total pet population of the UK in 2017

_........

The total pet population in the UK in 2017 was estimated to be 54 million.

Calculate an estimate for the number of fish in the total pet population of the UK in 2017

Melanie takes a random sample of 30 pet owners in her town and records the number of pets they each have.

She produced the following table for her results.

For Melanie’s sample, find the upper quartile of the number of pets owned.

Give an interpretation of the value of the upper quartile.

From this sample, Melanie concluded that everyone in her town owns at least 1 pet.

Comment on the validity of Melanie’s conclusion.

Cindy works in a library. She recorded the number of books borrowed by each person in a random sample of 20 people who borrowed books from the library one Monday. The table gives information about her results.

Cindy also recorded the number of books borrowed by each person in a random sample of 20 people who borrowed books from the library one Friday. The table gives two summary statistics for her results.

She claims that the mean number of books borrowed from the library on a Monday is greater than the mean number of books borrowed from the library on a Friday. Cindy also claims that there is a smaller spread in the number of books borrowed from the library on a Monday than on a Friday.

Comment on whether each of Cindy’s claims is supported by her results. You must give reasons for your answers.

Suzanne suggests repeating the investigation with a larger number of Mondays and Fridays.

Give a reason why Suzanne’s suggestion may be appropriate.

Joel is investigating the heights of buildings in Paris and in London. He collects data on the heights of the tallest buildings in Paris and in London.

Joel decides to remove the height of the tallest building from each of his two data sets before carrying out the investigation.

Suggest a reason why it may be appropriate for Joel to do this.

The cumulative frequency diagram shows information about the heights, in metres, of a sample of 50 of the tallest buildings in Paris.

The box plot shows information about the heights, in metres, of a sample of 50 of the tallest buildings in London.

­ Height (metres)

Compare the distribution of the heights of the tallest buildings in Paris with the distribution of the heights of the tallest buildings in London.

You should give the value of any statistic that you use in your comparisons.

The cumulative frequency graph shows information about the maximum daily temperature, in °C, in Bingley for the 30 days of June 2018

Find the 90th percentile.

Interpret your 90th percentile in context.

For Bingley in June 2018, the lowest maximum daily temperature was 13 °C and the greatest maximum daily temperature was 28 °C.

Show that the greatest maximum daily temperature in June is not an outlier.

The box plot below shows information about the maximum daily temperature, in °C, in Aultbea for each day of June 2018

On the grid above, draw a box plot for the maximum daily temperatures in June 2018 for Bingley.

Compare the distributions of maximum daily temperatures in June 2018 for Aultbea and for Bingley.

The table shows information about the performance of students in a Maths examination and in a Statistics examination.

Freya scored 62 marks in her Statistics examination.

Show that Freya’s standardised score for Statistics is 0.5

Freya’s Maths examination mark was 59 giving her a standardised score for Maths of 0.7

She thinks she did better in the Statistics examination than in the Maths examination.

Explain whether or not Freya is correct.

Freya also took a French examination. She says that her mark in this examination is below average.

Explain how Freya’s standardised score for French can be used to confirm this.

Some people were asked to complete three puzzles, Puzzle X, Puzzle Y and Puzzle Z.

The table shows some summary statistics about the times taken, in minutes, to complete Puzzle X and Puzzle Y.

The shortest time taken to complete Puzzle X was 26 minutes.

Work out the longest time taken to complete Puzzle X.

Use the information in the table to compare the median time to complete Puzzle X with the median time to complete Puzzle Y. You should interpret your comparison.

The list below gives the times taken, in minutes, for these people to complete Puzzle Z.

25 27 31 39 32 32 37 34

38 31 46 45 47 42 41

Work out the range of these times.

Which puzzle, X, Y or Z, is completed with the most consistent times by these people? Explain your answer.

Hannah wants to find the median of the 15 times taken, in minutes, to complete Puzzle Z.

She draws this stem and leaf diagram for these 15 times.

She says that as there are 15 values, the median is the 8th value, which is 34 minutes.

Explain what Hannah has done wrong. You should give the correct value of the median.

Here are the weights, in kilograms, of 10 dogs.

9.2 4.3 68.2 12.3 6.5 10.6 14.2 16.0 9.1 8.5

Work out the range.

Work out the median.

The median is more appropriate than the mean to summarise the data.

Explain why.

The cumulative frequency diagram gives information about the heights, in metres, of a sample of 100 oak trees in Camden, London.

Using the cumulative frequency diagram, complete the table below for the heights of

The box plot shows information about the heights, in metres, of a sample of maple trees in Camden, London.

For the sample of oak trees the least height is 2.0 m the greatest height is 22.3 m

On the grid above, draw a box plot for the heights of the sample of oak trees.

Compare the two distributions of heights. Give three comparisons and interpret one of these comparisons.

Diana is a journalist working for a local newspaper.

She is writing a newspaper article about how house prices in the local area have changed.

Diana has house price data for 1996 and for 2016

She plans to include in her article the median house price for 1996 and the median house price for 2016

Mika thinks that Diana should also include in her article the interquartile range of house prices for 1996 and the interquartile range of house prices for 2016

Give one reason why including the interquartile ranges in the article would be appropriate.

Give one reason why including the interquartile ranges in the article would not be appropriate.

The cumulative frequency diagram gives information about the heights, in metres, of a sample of 100 oak trees in Camden, London.

Using the cumulative frequency diagram, complete the table below for the heights of

The box plot shows information about the heights, in metres, of a sample of maple trees in Camden, London.

For the sample of oak trees the least height is 2.0 m the greatest height is 22.3 m

On the grid above, draw a box plot for the heights of the sample of oak trees.

Compare the two distributions of heights. Give three comparisons and interpret one of these comparisons.

Diana is a journalist working for a local newspaper.

She is writing a newspaper article about how house prices in the local area have changed.

Diana has house price data for 1996 and for 2016

She plans to include in her article the median house price for 1996 and the median house price for 2016

Mika thinks that Diana should also include in her article the interquartile range of house prices for 1996 and the interquartile range of house prices for 2016

Give one reason why including the interquartile ranges in the article would be appropriate.

Give one reason why including the interquartile ranges in the article would not be appropriate.

The table shows some of the expected percentile weights (kg) for babies up to 6 months old, based on data collected from the World Health Organisation.

Antonia says,

“An estimate of the expected 30th percentile for a 3 month old boy is 5.8 kg”

Explain why this is not a good estimate.

Compare the expected 9th to the 91st interpercentile range for 5 month old girls with the expected 9th to the 91st interpercentile range for 5 month old boys. You must show your working.

Give an interpretation of your comparison in part (b).