Box plots & stem & leaf diagrams

The box-and-whisker diagrams below show the masses of the tomatoes.

What is the range of the masses for the Sungold tomato plants?

How many of the Roma plants produced 22 kg or less of tomatoes?

Geraint has collected data on some adult gulls.

He weighed 400 slender-billed gulls, 400 little gulls, and 400 black-headed gulls.

He has constructed box-and-whisker diagrams to display the masses of the gulls.

Slender-billed gulls

Black-headed gulls

What is the range of the masses of the slender-billed gulls?

Range of the masses_{………..………........ ………} g

How many of the little gulls have a mass greater than or equal to 96 g?

Write down the percentage of little gulls that have a mass greater than or equal to 168 g.

From the box-and-whisker diagrams, Geraint notices that two of the types of gull have the same median mass. He makes the following statement about these two types of gull.

“The diagrams suggest that one of these two types of gull generally has a greater mass than the other.”

Which type of gull appears to have the greater mass?

Geraint based his statement on one of the following measures. Which measure did Geraint use?

Circle your answer.

Range Median Lowest mass Lower quartile Upper quartile

On 1st June last year, 200 customers used cash to pay at Shop Lil. The cumulative frequency diagram represents the time each of these 200 customers waited to be given change at the checkout.

How many of these customers waited between 30 and 50 seconds for their

change?

Use the graph to estimate the median time these 200 customers waited for their change.

Circle your answer.

24 seconds 32 seconds 38 seconds 80 seconds 100 seconds

Calculate the fraction of these 200 customers who waited 40 seconds or longer for their change.

Give your answer in its simplest form.

On 1st June this year, the manager at Shop Lil drew a box-and-whisker plot of the times 200 customers waited for their change at the checkout.

Based on the results of these 200 customers, the manager made the following statements. Complete the statements.

“On 1st June this year, 50% of our customers were given their change in

........ seconds or less.”

“On 1st June this year, the interquartile range of the times taken to give

customers their change was........ seconds.”

Consider the 50 customers waiting the longest times to get their change on 1st June last year and this year. Has the speed of giving change at the checkout improved since last year?

Yes No

You must give a reason for your answer.

Eva grows three varieties of organic potato on her farm: Maris Piper, King Edward and Desiree.

She weighs and records the masses of 400 potatoes of each of the 3 varieties.

Eva constructs box-and-whisker diagrams for the masses of the potatoes weighed.

Complete each of the following statements.

The_........ potatoes have the highest median mass.

The median mass of these potatoes is_........ g.

The range of the masses recorded for the Maris Piper potatoes

In the future, Eva wants to grow potatoes that are quite similar in size.

Use the box-and-whisker diagrams to advise Eva which of these three varieties of

potato she should grow.

Select which variety of potato she should grow.

Maris Piper
King Edward
Desiree

Select the measure you used to help you decide.

Median
Interquartile range
Lower quartile

Select a reason for your choice of measure.

The measure is greater than for the other 2 varieties

The measure is less than for the other 2 varieties

Eva grows three varieties of organic potato on her farm: Maris Piper, King Edward and Desiree.

She weighs and records the masses of 400 potatoes of each of the 3 varieties.

Eva constructs box-and-whisker diagrams for the masses of the potatoes weighed.

Complete each of the following statements.

The_........ potatoes have the highest median mass.

The median mass of these potatoes is_........ g.

The range of the masses recorded for the Maris Piper potatoes

In the future, Eva wants to grow potatoes that are quite similar in size.

Use the box-and-whisker diagrams to advise Eva which of these three varieties of

potato she should grow.

Select which variety of potato she should grow.

Maris Piper
King Edward
Desiree

Select the measure you used to help you decide.

Median
Interquartile range
Lower quartile

Select a reason for your choice of measure.

The measure is greater than for the other 2 varieties

The measure is less than for the other 2 varieties

Dafydd works in a call centre.

On Monday, he made 200 phone calls. He recorded the length of time he spent on each of these phone calls.

Dafydd noted the following about the times spent on each phone call. • The greatest time was 2 minutes 10 seconds. • The range of the times was 2 minutes. • The median time was 84 seconds. • The upper quartile was 108 seconds. • The interquartile range was 68 seconds.

Use the graph paper to draw a box-and-whisker diagram to represent Dafydd’s data.

Length of time on each of 200 phone calls

Dafydd was set a target. He had to complete half of his phone calls in less than 1 minute 30 seconds each. By how many seconds did Dafydd beat this target?

Circle your answer.

4 seconds 6 seconds 10 seconds 12 seconds 18 seconds

On Monday, how many of Dafydd’s phone calls lasted less than 108 seconds?

The shortest yacht has a length of 3 m. The longest yacht has a length of 22 m.

Use the information above to complete a box-and-whisker diagram on the graph paper

The lengths of the 68 yachts in Clwyd Marina were measured.

For these yachts: • the lower quartile of their lengths is 10 m • 25% have lengths greater than 18 m • the median length is 11·6 m.

Calculate how many of the yachts in Clwyd Marina have lengths greater

than 10 m.

Use the cumulative frequency diagram to give the best estimates for the answers to the following questions.

What is the median length of these ray fish?

How many of these ray fish have lengths greater than 72 cm?

Draw a box-and-whisker plot of this data on the grid below.

How many of the sample of 60 guppies have a length greater than or equal to

2. 4 cm?

Calculate the mass of the carp in November 2021.

Use the cumulative frequency diagram to give the best estimates for the answers to the following questions.

What is the median length of these ray fish?

How many of these ray fish have lengths greater than 72 cm?

Draw a box-and-whisker plot of this data on the grid below.

Calculate the mass of the carp in November 2021.

On Wednesday, there were no cars in a car park when it opened at 7:00 a.m.

From 7:00 a.m., the number of cars entering the car park was recorded.

The cumulative frequency diagram has been drawn from the results.

How many cars had entered the car park by 7:35 a.m.?

The first car entered the car park at 7:21 a.m. The last car entered the car park at 7:44 a.m.

Draw a box-and-whisker plot using this information and the data from the cumulative

frequency diagram.

On Wednesday, there were no cars in a car park when it opened at 7:00 a.m.

From 7:00 a.m., the number of cars entering the car park was recorded.

The cumulative frequency diagram has been drawn from the results.

How many cars had entered the car park by 7:35 a.m.?

The first car entered the car park at 7:21 a.m. The last car entered the car park at 7:44 a.m.

Draw a box-and-whisker plot using this information and the data from the cumulative

frequency diagram.

On 1st July every year, Trefor estate agents record the time from when a phone rings to when it is answered.

The time taken to answer the phone is recorded in seconds.

Trefor displays the data for their agents to see. The displays for 1st July 2018 and 1st July 2019 are shown below.

1st July 2018

Cumulative frequency

Use the diagrams on the previous page to answer the following questions.

What is the range of times taken to answer the phone for 1st July 2018?

Circle your answer.

101 seconds 80 seconds 78 seconds 106 seconds 104 seconds

What is the maximum possible range of times taken to answer the phone for 1st July 2019?

Circle your answer.

86 seconds 106 seconds 80 seconds 56 seconds 83 seconds

The manager of Trefor estate agents claims that there has been an improvement in the median time taken to answer the phone from 1st July 2018 to 1st July 2019. Is this true?

Yes No

You must show all your working.

Complete the following statements.

‘On 1st July 2018, 75% of the phone calls were answered within........

seconds.’

‘On 1st July 2019, 75% of the phone calls were answered within........

seconds.’

On 1st July every year, Trefor estate agents record the time from when a phone rings to when it is answered.

The time taken to answer the phone is recorded in seconds.

Trefor displays the data for their agents to see. The displays for 1st July 2018 and 1st July 2019 are shown below.

1st July 2018

Cumulative frequency

Use the diagrams on the previous page to answer the following questions.

What is the range of times taken to answer the phone for 1st July 2018?

Circle your answer.

101 seconds 80 seconds 78 seconds 106 seconds 104 seconds

What is the maximum possible range of times taken to answer the phone for 1st July 2019?

Circle your answer.

86 seconds 106 seconds 80 seconds 56 seconds 83 seconds

The manager of Trefor estate agents claims that there has been an improvement in the median time taken to answer the phone from 1st July 2018 to 1st July 2019. Is this true?

Yes No

You must show all your working.

Complete the following statements.

‘On 1st July 2018, 75% of the phone calls were answered within........

seconds.’

‘On 1st July 2019, 75% of the phone calls were answered within........

seconds.’

Maesystrad, Rhewlteg and Glanmawr are three colleges. Each college recorded the times Year 12 students took to travel to college. The results are displayed in the box-and-whisker plots below.

Which of the three colleges has the greatest range of times?

What is the range of times for this college?

College_{………………………........ ……………} Range_{………………………........} minutes

On average, in which college did Year 12 students have the longest travel times?

You must give a reason for your answer.

Which college has the greatest difference between the median and the lower quartile?

What is this difference?

College_{………………………........ ……………} Difference_{…………………........} minutes

Which of the three colleges has the greatest number of Year 12 students?

Give a reason for your answer.

Maesystrad Rhewlteg Glanmawr Don’t know

At another college, Wynne College, there are 240 students in Year 12.

The interquartile range of the times taken for these students to travel to college is 32 minutes.

How many of these students have travel times within this interquartile range?

75% of the Year 12 students at Wynne College take less than 55 minutes to travel to college. Complete the following statement.

‘25% of the Year 12 students at Wynne College take less than

........ minutes to travel to college.’

Maesystrad, Rhewlteg and Glanmawr are three colleges. Each college recorded the times Year 12 students took to travel to college. The results are displayed in the box-and-whisker plots below.

Which of the three colleges has the greatest range of times?

What is the range of times for this college?

College_{………………………........ ……………} Range_{………………………........} minutes

On average, in which college did Year 12 students have the longest travel times?

You must give a reason for your answer.

Which college has the greatest difference between the median and the lower quartile?

What is this difference?

College_{………………………........ ……………} Difference_{…………………........} minutes

At another college, Wynne College, there are 240 students in Year 12.

The interquartile range of the times taken for these students to travel to college is 32 minutes.

How many of these students have travel times within this interquartile range?

75% of the Year 12 students at Wynne College take less than 55 minutes to travel to college. Complete the following statement.

‘25% of the Year 12 students at Wynne College take less than

........ minutes to travel to college.’

Gwen records the time she spends writing each of 240 text messages.

She finds the following. • The greatest time is 1 minute 5 seconds. • The range of the times is 60 seconds. • The median is 45 seconds. • The lower quartile is 23 seconds. • The interquartile range is 32 seconds.

Use the graph paper to draw a box-and-whisker diagram to represent Gwen’s data.

How many of these text messages took Gwen more than 23 seconds to write?

There are two entrances to a stadium, North Entrance and South Entrance.

At each entrance, 3000 people queued to pass through security. The length of time each of these people spent in the queue was recorded. The box-and-whisker diagrams show the results.

At the North Entrance, how many people had to queue for more than 44 minutes?

You must show all your working.

Number of people is_........

For the South Entrance, calculate an estimate of the number of people who had to queue there for between 40 and 60 minutes.

You must show all your working.

Number of people is_........

There are two entrances to a stadium, North Entrance and South Entrance.

At each entrance, 3000 people queued to pass through security. The length of time each of these people spent in the queue was recorded. The box-and-whisker diagrams show the results.

At the North Entrance, how many people had to queue for more than 44 minutes?

You must show all your working.

Number of people is_........

For the South Entrance, calculate an estimate of the number of people who had to queue there for between 40 and 60 minutes.

You must show all your working.

Number of people is_........

Complete each of the following statements.

‘Apples from the_........ apple tree have the least median width.

The median width of apples recorded for this tree is_........ mm.’

‘The range of the widths of apples recorded for the Gala apple tree

is_........ mm.’

‘The_........ apple tree has apples with the greatest interquartile range of widths.

The interquartile range of the widths of apples recorded for this tree

is_........ mm.’

Which tree has a higher proportion of larger apples?

You must give a reason for your answer.

Complete each of the following statements.

‘Apples from the_........ apple tree have the least median width.

The median width of apples recorded for this tree is_........ mm.’

‘The range of the widths of apples recorded for the Gala apple tree

is_........ mm.’

‘The_........ apple tree has apples with the greatest interquartile range of widths.

The interquartile range of the widths of apples recorded for this tree

is_........ mm.’

Which tree has a higher proportion of larger apples?

You must give a reason for your answer.

The following box-and-whisker plots illustrate the daily rainfall for April 2016 in Trefwen and in Nawrby.

April rainfall in Trefwen

April rainfall in Nawrby

Iona is going on holiday next April. She is hoping for good weather, with hardly any rain. She decides to go to Nawrby. Give a reason to support Iona’s decision.

Include values for both Trefwen and Nawrby.

The following box-and-whisker plots illustrate the daily rainfall for April 2016 in Trefwen and in Nawrby.

April rainfall in Trefwen

April rainfall in Nawrby

Iona is going on holiday next April. She is hoping for good weather, with hardly any rain. She decides to go to Nawrby. Give a reason to support Iona’s decision.

Include values for both Trefwen and Nawrby.