Interpreting Data (DP IB Maths: AI HL)

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Dan

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Dan

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Interpreting Data

How do I interpret statistical measures?

  • The mode is useful for qualitative data
    • It is not as useful for quantitative data as there is not always a unique mode
  • The mean includes all values
    • It is affected by outliers
    • A smaller/larger mean is preferable depending on the scenario
      • A smaller mean time for completing a puzzle is better
      • A bigger mean score on a test is better
  • The median is not affected by outliers
    • It does not use all the values
  • The range gives the full spread of the all of the data
    • It is affected by outliers
  • The interquartile range gives the spread of the middle 50% about the median and is not affected by outliers
    • It does not use all the values
    • A bigger IQR means the data is more spread out about the median
    • A smaller IQR means the data is more centred about the median
  • The standard deviation and variance use all the values to give a measure of the average spread of the data about the mean
    • They are affected by outliers
    • A bigger standard deviation means the data is more spread out about the mean
    • A smaller standard deviation means the data is more centred about the mean

How do I choose which diagram to use to represent data?

  • Box plots
    • Can be used with ungrouped univariate data
    • Shows the range, interquartile range and quartiles clearly
    • Very useful for comparing data patterns quickly
  • Cumulative frequency graphs
    • Can be used with continuous grouped univariate data
    • Shows the running total of the frequencies that fall below the upper bound of each class
  • Histograms
    • Can be used with continuous grouped univariate data
    • Used with equal class intervals
    • Shows the frequencies of the group
  • Scatter diagrams
    • Can be used with ungrouped bivariate data
    • Shows the graphical relationship between the variables

How do I compare two or more data sets?

  • Compare a measure of central tendency
    • If the data contains outliers - use the median
    • If the data is roughly symmetrical – use the mean
  • Compare a measure of dispersion
    • If the data contains outliers - use the interquartile range
    • If the data is roughly symmetrical – use the standard deviation
  • Consider whether it is better to have a smaller or bigger average
    • This will depend on the context
      • A smaller average time for completing a puzzle is better
      • A bigger average score on a test is better
  • Consider whether it is better to have a smaller or bigger spread
    • Usually a smaller spread means it is more consistent
  • Always relate the comparisons to the context and consider reasons
    • Consider the sampling technique and the data collection method

Worked example

The box plots below show the waiting times for the two doctor surgeries, HealthHut and FitFirst.

4-1-7-we-imageCompare the two distributions of waiting times in context.

4-1-7-ib-ai-aa-sl-interpreting-data-we-solution

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Dan

Author: Dan

Expertise: Maths

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.