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Tools - Math 'Reasoning from Evidence' Ordering a Cab, Example #3 (solution)


Testing a New Deodorant, Example #1 (solution) || Emergency 911!, Example #2 (solution)
Ordering a Cab, Example #3 (solution) || Traffic Accidents, Example #4 (solution)

Malcolm Swan
Mathematics Education
University of Nottingham
Malcolm.Swan@nottingham.ac.uk

Jim Ridgway
School of Education
University of Durham
Jim.Ridgway@durham.ac.uk


The aim of this assessment are to provide the opportunity for you to:
  • use appropriate calculations to analyze data
  • use appropriate graphs and/or diagrams to analyze data
  • reason clearly and convincingly.

Sunshine cabs and Bluebird cabs are rival companies.

Each claims that their cab company is better than the other.

A picture of a woman on the phone calling for a cab.
A dialogue bubble saying, 'Hi, I need a cab to pick me up at 7:00 am tomorrow.'

Sarah has to take a cab to work each day. She wants to compare the two companies.

Over several months Sarah orders each cab 20 times. She records how early or late they are when arriving to pick her up from her home.

Her results are shown on the next page...

Cab data sheet
A two column table, one column for each cab company: Sunshine Cab and Bluebird Cab. The data shows how many minutes and seconds the cab was either early or late for the assigned pick up.
Click on this image to open a new window with a larger version of this image.


  1. At the moment, it is hard to see which company is the best.
      Use appropriate calculations, graphs and/or diagrams to analyze the data so that comparisons are easier to make. Show all your reasoning.

  2. Present a reasoned case for Sunshine cabs being the better company.
    Present your reasoning as fully and as clearly as possible.

  3. Present a reasoned case for Bluebird cabs being the better company.

  4. Which argument do you think is the most convincing? Why?


Ordering a Cab - Sample Solution

The data may be analyzed and graphed as follows.

Cab data sheet
 Two different bar graphs, one for each cab company. Each bar graph is a plot of frequency versus minutes early or late.
Click on this image to open a new window with a larger version of this image.

Company Sunshine Cabs Bluebird Cabs
Mean time late 2 mins 3 secs 3 mins 14 secs
Median time late 1 min 53 secs 3 mins 15 secs
Range 12 mins 45 secs 6 mins 30 secs
Standard Deviation 3 min 11 secs 1 min 40 secs

Whereas Sunshine cabs are, on average, earlier, they are less consistent in their arrival times than Bluebird cabs. It may therefore be better to book with Bluebird cabs, making sure that the cab is called about 5 minutes before it is needed.



Testing a New Deodorant, Example #1 (solution) || Emergency 911!, Example #2 (solution)
Ordering a Cab, Example #3 (solution) || Traffic Accidents, Example #4 (solution)


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