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Tools - Math 'Fault Finding and Fixing' Interpreting and Misinterpreting Data Tasks, Set #3

Percentages, Set #1 (solutions) || Combinations and Chance, Set #2 (solutions)
Interpreting and Misinterpreting Data: Set #3 (solutions) || Set #4 (solutions)

Malcolm Swan
Mathematics Education
University of Nottingham

Jim Ridgway
School of Education
University of Durham

Each question contains a selection of errors or misleading interpretations of data.

The aim of this assessment is to provide the opportunity for you to:

  • explain clearly the source of each error or misinterpretation.
  • rectify the errors and produce correct interpretations.

1. Along a country road

This graph shows a car and a motorbike travelling along a country road.

What is wrong with the following statement?

I think that they are travelling at the same speed after 4 seconds. You can tell that because the graphs cross.

Graph of distance along the road in meters versus time for a motor bike and car.  The car's plot is linear, starts at 10 meters and ends at 75 meters in about 6 seconds.  The motor bike is initially at a shorter distance than the car until 4 seconds and then is at a greater distance after that.

2. Swimming pool

The graph above shows the progress of a swimming race.

Here is a commentary of the race.

Highlight the mistakes in this commentary and write a better one.

    Sam goes quickly into the lead.

    He is swimming at 15 metres per second.

    Janet is swimming at only 10 metres per second.

    After 22 seconds, Janet overtakes Sam.

    Janet swims more quickly than Sam from 25 seconds until she turns at 50 seconds.

    Sam overtakes Janet after 55 seconds, but she catches up again.

    5 seconds later, Janet is in the lead until right near the end.

    Sam swims at a steady 30 metres per second after the turn, until 80 seconds, while Janet is gradually slowing down.

    Sam wins by 10 seconds.

Graph of distance from start in meters versus time for 2 swimmers, Janet and Sam.  Graphs for both swimmers increase from time equals zero, peak at 50 meters, and drop to 0 meters.  Janet reaches 50 meters in 50 seconds and is back at zero meters in 100 seconds.  Sam's times are longer.

Explain clearly how you know that an error has been made.

Show how the error should be put right.

3. College magazine

Karl is thinking of producing a college magazine.

He produces a prototype of the magazine and conducts a small survey to compare male and female opinions of it. He asks the following question among a random sample of students:

    Would you pay a dollar for this magazine?

The results are shown below.

Bar graph of Frequency versus males and females responding Yes or No to the question above.  In both cases, the No response is greater than the Yes.  The female responses are greater than the male responses.

He concludes that females are less likely to buy the magazine than males.

Explain why Karl is wrong and say what a sensible conclusion would be.

4. Car and Bicycle Production

The diagram below shows how the world production of cars and bicycles has changed from 1965 to 1995.

Graphic showing car and bike production in 1965 and 1995.  For bikes, production was 21 million in 1965 and 114 in 1995.  For cars, production was 19 million in 1965 and 36 in 1995.  Graphic includes pictures of various sized bikes and cars not corresponding to production volume.

Explain, with reasons, whether or not you think that this diagram fairly represents the numerical information given

Percentages, Set #1 (solutions) || Combinations and Chance, Set #2 (solutions)
Interpreting and Misinterpreting Data: Set #3 (solutions) || Set #4 (solutions)

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