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Figure out your �row letter (row) & seat # (column)

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Lecture 8

Histograms

DATA 8

Fall 2017

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

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Announcements

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Bar Charts (Review)

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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

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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)

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Binning

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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, ...

160

165

170

175

180

185

190

The [185,190) bin

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Histogram

Chart to display the distribution of numerical values using bins

(Demo)

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Attendance for Odd Seats

bit.ly/attend8

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The Density Scale

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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)

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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

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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)

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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.

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Discussion Question

What's the height of each bar in these �two histograms?

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actress.hist(1, bins=[0,15,25,85])

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actress.hist(1, bins=[0,15,35,85])

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What are the vertical axis units?

Name

2016 Income (millions)

Jennifer Lawrence

61.7

Scarlett Johansson

57.5

Angelina Jolie

40

Jennifer Aniston

24.75

Anne Hathaway

24

Melissa McCarthy

24

Bingbing Fan

20

Sandra Bullock

20

Cara Delevingne

15

Reese Witherspoon

15

Amy Adams

15

Kristen Stewart

12

Amanda Seyfried

10.5

Tina Fey

10.5

Julia Roberts

10

Emma Stone

10

Natalie Portman

8.5

Margot Robbie

8

Meryl Streep

6

Mila Kunis

4.5

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Attendance for Even Seats

http://bit.ly/attend8

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Chart Types

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Bar Chart Versus 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

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Overlaid Graphs

For visually comparing two populations

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(Demo)