Teacher salaries

Teacher salaries

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
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Further Resources
This task asks questions about a box-and-whisker graph.
 
Here is a box-and-whisker plot of the salaries of 48 new graduates at Bluntley High School.

 

Salaries of new graduates at Bluntley High School
 
 
 
a)
 
 What is the median salary? $ __________
 
b)
 
 How many of the 48 staff have salaries below $46 000? __________
 
c)
 
 The inter-quartile salary range for the staff is $ __________.
 
d)
 
 Another staff member has a salary of $82 000.
 
 
i)
 
Plot this point with an asterisk (*) directly above the whisker of the graph.
  
  ii)
This point is called an "outlier".
Give a likely reason why this point is an outlier.
 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Statistics, Statistical investigations
Keywords: 
box-and-whisker graphs, graph interpretation, outliers
Description of task: 
Students study a box-and-whisker graph and answer questions on median, quartile and outliers.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
Scoring:   Y10 (06/2000)
1 mark a) 50 000 moderate
1 mark b) 12 difficult
2 marks
or
1 mark		 c) 9000 [Accept numbers between 8500 and 9500]
46 000-55 000		 2 correct -
very difficult 
1 correct -
difficult 
1 mark
1 mark

 

 d) i)
ii)		 Point correctly plotted
Any 1 of: 

  • He/she is the principal or the boss, etc.
  • This person earns a much higher salary than the rest of the staff.
  • Other similar explanations.

[Do not accept a definition of an outlier.]

 easy
difficult
 
NOTE: 
  1. Neither of the whiskers on a box-and-whisker plot should be longer than 1.5 times the inter-quartile range (upper quartile – lower quartile i.e. the length of the box). Points further away than this from the box are outliers and should be drawn as dots or asterisks. This means that the whiskers are not artificially stretched by an extreme value.
  2. The end of each whisker is usually finished with a line rather than a dot.
  3. The inter-quartile range is a single number, but partial credit is given to students who identify the range as a correct interval.
Diagnostic and formative information: 
  Common error  Likely reason
c) 9 Quotes correct answer but in units, not thousands.
c) 22 000 (or 22)
42 000 to 64 000		 Gives range rather than interquartile range.