05:00
Numerical and Visual Summaries
STAT 20: Introduction to Probability and Statistics
Agenda
Agenda
Announcements
Conceptual Review: bringing three reading notes together (mini-lecture/chart)
Coding Review
Break
Concept Questions
Work time on assignments
Announcements
Announcements
- Quiz 1 on Monday. Covers Understanding the World with Data through Summarizing Numerical Data.
- Problem Set 1 can now be turned in through Friday night for full credit.
- Lab: Getting Started is due Monday, June 24 at 12pm. Make sure you read the Lab Submission Guidelines posted to Ed.
Concpetual Review
Break
Concept Questions
Concept Question 1 - Taxonomy of Data
Images as data
Images as data
Images are composed of pixels (this image is 1012 by 1520)
The color in each pixel is in RGB
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Each band takes a value from 0-255
This image is data with 1020 x 1520 x 3 values.
Grayscale
- Grayscale images have only one band
- 0 is black, 255 is white
- This image is data with 1020 x 1520 x 1 values.
To simplify, assume our photos are 8 x 8 grayscale images.
Images in a Data Frame
If you were to put the data from these (8 x 8 grayscale) images into a data frame, what would the dimensions of that data frame be in rows x columns? Answer at pollev.com/jeremysanchez.
03:00
Concept Questions 2 and 3 - Summarizing Categorical Data
Concept Question 2a
The table below displays data from a survey on a class of students.
What proportion of the entire class was in the marching band?
01:30
Concept Question 2b
What were the dimensions of the raw data from which this table was constructed? (rows x cols)
01:30
Concept Question 3
Below is a two-variable bar chart describing affiliation and college degree status of 500 survey participants.
Concept Question 3 (cont.)
Based off of the graphic on the previous slide, which group is largest?
- Democrats with no college degree
- Democrats with a college degree
- Republicans with a college degree
- Republicans without a college degree
02:00
Concept Question 3 (cont.)
The regular stacked bar chart of counts preserves original counts and thus is good at comparing joint proportions.
- The stacked, normalized bar chart shows conditional proportions and thus is good for showing associations between variables.
Concept Activity 4 - Summarizing Numerical Data (Measures of Center)
Mean, median, mode: which is best?
It depends on your desiderata: the nature of your data and what you seek to capture in your summary.
Get out a piece of paper. You’ll be watching a 3 minute video that discusses characteristics of a typical human. Note which numerical summaries are used and what for.
General Advice
- Means are often a good default for symmetric data.
- Means are sensitive to very large and small values, so can be deceptive on skewed data. > Use a median
- Modes are often the only option for categorical data.
But there are other notions of typical, depending on the context.
Wrapup - Summarizing Distributions of Data
- You can construct a statistical graphic to show the shape, which you can describe in terms of modality and skew
- you can calculate a measure of center to convey a sense of a typical observation
- and you can calculate a measure of spread to capture how much variability there is in the data
Free time
05:00
Numerical and Visual Summaries STAT 20: Introduction to Probability and Statistics