MathematicsExam code: 0580

Statistical Diagrams

Statistics

PractiseFlashcards

Drawing conclusions properly

  • Comparing two data sets needs both an average and a measure of spread, and a comparison using only one of them is incomplete
  • Say what the comparison means in the context of the question rather than only quoting numbers
  • The syllabus asks you to appreciate the restrictions on what data can show
    • A small sample may not represent the whole population
    • A diagram showing proportions, such as a pie chart, hides the actual totals
    • A correlation between two things does not establish that one causes the other
  • Check the scale on any printed diagram before reading values, since axes do not always start at zero
A time series graph of temperature against the days of the week, each day's reading marked with a cross and consecutive crosses joined by straight lines, showing a fall to Wednesday, a rise on Friday and a fall again over the weekend
Source: Reading & interpreting statistical diagrams by Save My Exams

Worked example

Comparing two sets properly

Class A has median 62 marks and range 30. Class B has median 55 marks and range 12. Compare the two classes.

Solution:

  • A comparison needs one statement about average and one about spread, each interpreted in context
  • The medians: 62 is higher than 55
  • In context: on average, Class A scored higher marks than Class B
  • The ranges: 30 is larger than 12
  • In context: Class B's marks were more consistent, because a smaller range means the marks were closer together
  • Writing only "A's median is 62 and B's is 55" lists the numbers without comparing them: say which is higher, name the measure, and say what it means for the two classes

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