Tramping times

Tramping times

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about creating and interpreting a stem-and-leaf graph.

Some students went to Mauao. One group climbed to the top of the mountain and back, and the other group walked around the base.
Here are all the times it took to the nearest minute.
 
Climbing to the top and back:

71, 52, 37, 62, 52, 43, 54, 57, 74, 63, 57, 65, 91, 43, 82, 58, 22
 
Walking around the base:
 
40, 61, 48, 26, 32, 34, 50, 35, 49, 37, 38, 96, 38
 
a)
Put the data on the back-to-back stem-and-leaf plot below. 
 
 
Walking times at Mauao
 
Climbing                                                                                Walking around
 
b)
i)
 
ii)
Which walk generally takes longer?   Climbing   /   Walking around   (Circle one)
 
Explain your answer to question b) i) without doing any calculations.
 
 
 
 
 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Statistics, Statistical investigations
Key Competencies: 
Thinking, Using language, symbols, and texts
Keywords: 
composite graphs, stem-and-leaf graphs, graph construction, bi-variate data, graph interpretation
Description of task: 
Students display data on a back-to-back stem-and-leaf graph to show the times taken to complete two walks. The longer of the two walks is then identified.
Curriculum Links: 
This resource can be used to help to identify students' ability to construct and interpret a back-to-back stem-and-leaf graph.
 
Key competencies
This resource involves comparing distributions visually to identify patterns variations and relationships and explaining their rationale. These relate to the Key Competencies: Thinking and Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 5
Statistical investigations, set 6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

 

  

Y11 (03/2001)

2 marks
(for all correct)
or
1 mark
(1-2 errors)

a)

 

Climbing

Walking around

NOTE: Include as 1 error

  • transposing climbing and walking.
  • writing the actual times on the graph rather than only the ones digit.

[Accept if leaves are arranged in other orders].

2 marks – easy

1 mark – easy

1 mark
(for both correct)

b)

i)
ii)

Climbing
Any 1 of:

  • Most of the data on the stem-and-leaf is higher for climbing.
  • Most climbers take more than 45 minutes but most walking around have finished by then.
  • The median is higher for climbers.
  • The mode for climbers is 50 to 59 min. but for walking around it is 30 to 39 min.
  • Other similar statements that compare the two distributions.
Do NOT accept:
  • "Because climbing takes longer."
  • "Because the quickest person climbed."
  • "Because the slowest person walked around."
  • "Because the numbers are bigger/higher (or smaller/lower)", without comparing the two distributions.

moderate