Interpreting bar graphs & histograms

Interpret a given bar graph or histogram -- read values directly, add frequencies across categories or intervals, calculate a weighted average across groups of different sizes, and (for higher-ability students) estimate a mean or median from grouped data, read a cumulative frequency table, and explain why comparing histogram bar heights directly requires equal class widths.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

Terminology

  • Bar graph
  • Histogram
  • Frequency
  • Modal class
  • Class interval
  • Weighted average
  • Cumulative frequency
  • Frequency density

Task goals

  • Read individual values directly from a bar graph or histogram, and add values across categories or intervals to find a total or a difference.
  • Identify the modal category or modal class, and read a cumulative frequency table to find how many values lie within a given interval.
  • Calculate a weighted average across groups of different sizes, rather than averaging the group averages directly.
  • Estimate a mean from grouped data using class midpoints, and estimate a median from a grouped frequency table or a cumulative frequency graph.
  • Explain why comparing histogram bar heights directly is only valid when every class has the same width, and use frequency density when it is not.

Key skills

  • Interpret bar graphs
  • Interpret histograms
  • Calculate weighted average
  • Estimate mean median grouped data
  • Read cumulative frequency graphs

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included
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For teachers

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