Pocket money II

Pocket money II

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about reading information from a histogram.

Connor did a survey of 9-year-olds and 11-year-olds to find out how much pocket money they were given each week. He spoke to 50 children of each age group. When the tally was completed the results looked like this:

graph of pocket money for year 9 and year 11 students


a)
i)
What is the most frequent amount of pocket money for 11-year-olds? $__________
   
ii)
 
How does that compare with the 9-year-olds most frequent amount?

 

 
 
 
b)		  
i)		  
What percentage of 9-year-olds got $2 or less? __________%
   
ii)		  
What percentage of 9-year-olds got more than $10? __________%
 
c)		  
How does the percentage of 9-year-olds compare with the percentage of 11-year-olds who got more than $10?

 

 
 
 
 
d)
What is one problem with the way this histogram has been set up?
 
 
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Statistics, Statistical investigations
Key Competencies: 
Thinking, Using language, symbols, and texts
Keywords: 
histograms, graph interpretation, percentages, bi-variate data
Description of task: 
Students interpret information presented in a composite histogram to answer questions involving percentages and comparisons.
Curriculum Links: 
This resource can be used to help to identify students' ability to interrpret a histogram.
Key competencies
This resource involves exploring and using patterns and relationships in data and communicating findings. 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
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 
Y8 (11/1997)
a) i)
ii)		 $10
It is more for 11-year-olds. ($5 for 9-year-olds compared with $10 for 11-year-olds). [Other answers acceptable if they compare the modes].		 easy
difficult
b) i)
ii)		 40%
10%		 difficult
difficult
c)   It is less for 9-year-olds. (10% for 9-year-olds compared with 28% for 11-year-olds). [Other answers acceptable if they compare the percentages getting more than $10. Do not accept "11-year-olds get more money" or equivalent statements]. very difficult
d)  
Any 1 of:
  • x-axis values should increase by the same amount (even intervals).
  • the start of the x-axis is not even (e.g., 1,2 then 5 and then goes up in 5s)
  • hard to see the distribution of pocket money within an interval, e.g., having both Y9 and Y11, what were the values within 2-5, 5-10, 10-15? [perhaps the best way to present this data is to stack Y9 and Y11 in the same bar]
  
Diagnostic and formative information: 
  Common error Likely reason
a) i) 15 Confuses frequency with amount (in $).
b) i) 20 Confuses percentage with frequency.
b) ii) 5 Confuses percentage with frequency.