Histogram

A histogram is a graph grouping data into intervals, and drawing a bar for each interval, shows the empirical distribution

• It’s a discrete distribution, where events are intervals but not values

For example, the frequency histogram of data 50, 51, 53, 55, 56, 60, 65, 65, 68 with binwidth = 5.

Elements

• Boundaries
  • Specify the boundaries to eliminate the confusion
  • You can choose boundaries to be NON-round numbers, to make sure no data lie on the boundaries
• Bin width ^e0e0f4
  • Choose the right bin width to better present the data
    • thin width will provide more details, but may not be necessary and give gaps
      • thin bins are useful for looking for gaps and heaping
    • wide width will wipe out much information
  • Changing the bin width can help discover the rounding pattern
  • Uneven bin widths
    • When using uneven bin widths, use a density histogram ^904jrz
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Types

In a histogram, the x-axis is the Continuous Variable to be inspected. And Different y-scales give types of histograms.

• Frequency histogram
• Density histogram
  • In a density histogram, the area of a bar equals the relative frequency; thus the y-scale is the density: $\text{relative frequency}/\text{binwidth}$
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  • In ggplot2, use y = ..density.. to specify this scale
  • It is also very useful to overlay a Density Curve (geom_density())
• Cumulative frequency histogram
  • is suitable when some frequencies are small to present
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