0580

Statistical Diagrams

Statistics

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
Exam tip

Put the key on any stem-and-leaf diagram you draw, units included — the syllabus requires it and it carries a mark. Bar charts have gaps between equal-width bars, which is what separates them from histograms, and a pie chart shows proportions only, so two drawn from different totals cannot be compared sector by sector. When comparing two sets, quote one average and one measure of spread, and interpret both in context.

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
  • Naming the numbers alone — "A's median is 62 and B's is 55" — is not a comparison and scores nothing
  • The word "average" must be tied to a named measure, and "spread" to a named one, before either is interpreted