Lecture 9

Histograms

DATA 8

Summer 2017

Slides created by John DeNero (denero@berkeley.edu), Ani Adhikari (adhikari@berkeley.edu), and Sam Lau (samlau95@berkeley.edu)

Announcements

Bar Charts (Review)

Types of Data

All values in a column should be both the same type and be comparable to each other in some way

• Numerical — Each value is from a numerical scale
• Numerical measurements are ordered
• Differences are meaningful
• Categorical — Each value is from a fixed inventory
• May or may not have an ordering
• Categories are the same or different

“Numerical” Data

Just because the values are numbers, doesn’t mean the variable is numerical

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• Census example had numerical SEX code (0, 1, and 2)

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• It doesn’t make sense to perform arithmetic on these “numbers”, e.g. 1 - 0 or (0+1+2)/3 are nonsense here

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• The variable SEX is still categorical, even though numbers were used for the categories

Bar Charts

Compare some quantity across categories

• % of smartphone owners who have used their phone for the following in the last year: online banking, job search, etc.
• Gross ticket sales for individual movies

(Demo)

Discussion Question

Top 10 highest grossing movies

How long ago each one was released

Bar Charts of Counts

Distributions:

• The distribution of a variable (a column) describes the frequency of its different values
• The group method counts the number of rows for each value in a column

Bar charts can display the distribution of categorical values

• Proportion of how many US residents are male or female
• Count of how many top movies were released by each studio

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(Demo)

Binning

Binning Numerical Values

Binning is counting the number of numerical values that lie within ranges, called bins.

• Bins are defined by their lower bounds (inclusive)
• The upper bound is the lower bound of the next bin

188, 170, 189, 163, 183, 171, 185, 168, 173, ...

The [185,190) bin

Histogram

Chart to display the distribution of numerical values using bins

(Demo)

Attendance

bit.ly/at-d8

The Density Scale

Histogram Axes

By default, hist uses a scale (normed=True) that ensures the area of the chart sums to 100%

• The horizontal axis is a number line (e.g., years)
• The vertical axis is a rate (e.g., percent per year)
• The area of a bar is a percentage of the whole

(Demo)

How to Calculate Height

The [20, 40) bin contains 59 out of 200 movies

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• “59 out of 200” is 29.5%
• The bin is 40 - 20 = 20 years wide

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29.5 percent

Height of bar = --------------------------

20 years

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= 1.475 percent per year

Height Measures Density

% in bin

Height = ---------------------

width of bin

• The height measures the percent of data in the bin relative to the amount of space in the bin.

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• So height measures crowdedness, or density.

(Demo)

Area Measures Percent

Area = % in bin = Height x width of bin

• “How many individuals in the bin?” Use area.
• “How crowded is the bin?” Use height.

Chart Types

Bar Chart vs. Histogram

Bar Chart

• 1 categorical axis &�1 numerical axis
• Bars have arbitrary �(but equal) widths and spacings
• For distributions:�height (or length) of bars are proportional to the percent of individuals

Histogram

• Horizontal axis is numerical, hence to scale with no gaps
• Height measures density; areas are proportional to the percent of individuals

Overlaid Graphs

For visually comparing two populations

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(Demo)