Vehicle speeds

Vehicle speeds

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 graph.
 
Number of Vehicles Travelling at Different Speeds
A speed camera was on a road with a speed limit of 50 km/h. The graph above shows the speeds of 80 vehicles as they passed the camera.
Answer the following questions about this graph.
 
a)
How many vehicles were travelling within the speed limit? __________
 
b)
What percentage of vehicles were going faster than 30 km/h? __________ %
 
c)
If the police department allows a margin of error of 10 km/h before giving out a speeding ticket, how many drivers would receive a speeding ticket? __________
 
d) The median speed of vehicles passing the camera is in which of these ranges?
 
(A)
(B)
(C)
(D)
(E)

31-35 km/h
36-40 km/h
41-45 km/h
46-50 km/h
It is impossible to tell.
 
e)
One car passed the speed camera at 100 km/h. Why can you not tell this from the graph?
 
 
 
f)
What are two problems with the way this histogram has been set up?
 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Statistics, Statistical investigations
Keywords: 
histograms, graph interpretation
Description of task: 
Students interpret a histogram showing the number of vehicles travelling at different speeds past a speed camera. Students need to calculate a percentage and the median to complete this task.
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: 
  
Y10 (08/1999)
a) 53 easy
b) 90 moderate
c) 15 easy
d) C [41-45 km/h] moderate
e) Any 1 of:

•   Because the data are grouped into intervals.
•   Because the last interval is open-ended.
•   Because individual speeds are not given.
•   Any other similar explanations.

 easy
f) Any 2 of:

  • the intervals should be the same size.
  • the first interval (30 and below) is much larger interval (30) than the following intervals (5).
  • the last interval (70 plus) is much larger interval (?) than the preceding intervals.
  • x-axis values should be numbers on a scale (continuous data), rather than intervals. 
  
Diagnostic and formative information: 
  Common error
e) "Speeds are only shown up to 70 km/h."
"Speeds do not go to 100 km/h."