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.

Current NZC (2007)
  • S5-1
  • S4-1
New NZC (2026)
  • NZC26-P4-STA-VIS-K-Y9-01

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.

Where this fits

What leads into this objective, and where it goes next.

Before

Constructing and Selecting Statistical Displays

Constructing and Selecting Statistical Displays

You are here

Interpreting bar graphs & histograms

Interpreting bar graphs & histograms

Know

A distribution is formed from all the possible values of a variable and their frequencies. It can be shown using data visualisations that show patterns, trends, and variations and that include dot plots, bar graphs, frequency tables, box plots, histograms, time-series graphs, scatter plots, and two-way tables.

Statement▸
Year 9 · Statistics · Visualisation of data
NZC26-P4-STA-VIS-K-Y9-01

Next

Selecting appropriate displays

Selecting appropriate displays

Interpreting data from Scatter plot - TARSOG

Interpreting data from Scatter plot - TARSOG

Analysing scatter plots (i.e. bivariate) - TARSOG

Analysing scatter plots (i.e. bivariate) - TARSOG

Also under S5-1:

Also under S4-1:

Explore the whole sequence →

For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.