Bags of marshmallows

Bags of marshmallows

Auto-markingPencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about mean and distribution of data. 

Question 1Change answer

Jenny buys a bag of marshmallows every week. They come in bags stating "20 marshmallows" in each. For 10 weeks Jenny counts and writes down the number of marshmallows in each bag. This is what she found:  

 20,     21,     19,     20,     23,     18,     20,     20,     19,     20 

a)  What is the average (mean) number of marshmallows per bag?

 

b)  What percentage of bags have less than 20 marshmallows? %

 

c)  Jenny is unhappy with the number of marshmallows she gets in the bags. Explain why.

     

Task administration: 
This task can be completed with pencil and paper or online (with SOME auto marking).
Level:
4
Curriculum info: 
Maths, Statistics, Statistical investigations
Key Competencies: 
Thinking, Using language, symbols, and texts
Keywords: 
mean, distribution, percentages
Description of task: 
Students calculate an average and a percentage from raw data and comment on these findings.
Curriculum Links: 
This resource can be used to help to identify students' ability to interpret a table of data, and to show an understanding of the mean (average) and distribution of the data.
 
Key competencies
This resource involves relating the mean and the overall distribution of data, and communicating this. These relate to the Key Competencies: Thinking and Using language, symbols and text.
For more information see http://nzcurriculum.tki.org.nz/Key-competencies
 
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) 20 [200/10] very easy
b) 30% moderate
c) Statements which indicate the key idea that some bags have fewer than 20 or she expected at least 20 per bag.
NOTE: If the student makes errors in calculation in a) or b), this mark can still be obtained by a reasonable deduction from incorrect figures.		 easy

 

Diagnostic and formative information: 
  Common error Likely reason
b) 3% Confuses percentage and frequency.
b) 3/10 Confuses fraction and percentage.
b) 33% Interprets 3/10 as 1/3 , i.e., 33%.