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Statistical Analysis for Categorical and Quantitative Variables: Lecture 2, Study notes of Statistics

University of Illinois - Urbana-ChampaignStatistics

An introduction to the statistical analysis of categorical and quantitative variables. It covers the use of graphical displays, such as bar graphs, pie charts, stem-and-leaf plots, and histograms, to understand the distribution of data. Examples of analyzing categorical data from student majors and quantitative data from shark lengths.

Typology: Study notes

Pre 2010

Uploaded on 03/10/2009

koofers-user-4j2
koofers-user-4j2 🇺🇸

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STAT 200, S1 Lecture 2
P. 6-21
Categorical Variables
Graphical Displays: enable us to see the distribution of the variable
• Bar Graphs
• Pie charts
To find the distribution of the variable:
1. List Categories
2. Indicate count or percent of individuals in each category
Example:
You are interested in studying the distribution of various majors of 400
students enrolled in an undergraduate program at a small university.
The following data is provided for you.
Major Number of Students Percent of Students
Math 65 16.25%
Stat 20 5%
Engineering 250 62.5%
Health Sciences 65 16.25%
[R command page 32-37 on R book]
numstudent <- c(65,20, 250, 65)
names(numstudent)<-c("math", "stat", "eng", "health")
barplot(numstudent)
pf3
pf4
pf5

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Download Statistical Analysis for Categorical and Quantitative Variables: Lecture 2 and more Study notes Statistics in PDF only on Docsity!

STAT 200, S1 Lecture 2

P. 6-

Categorical Variables

Graphical Displays: enable us to see the distribution of the variable

• Bar Graphs

• Pie charts

To find the distribution of the variable:

1. List Categories

2. Indicate count or percent of individuals in each category

Example:

You are interested in studying the distribution of various majors of 400

students enrolled in an undergraduate program at a small university.

The following data is provided for you.

Major Number of Students Percent of Students

Math 65 16.25%

Stat 20 5%

Engineering 250 62.5%

Health Sciences 65 16.25%

[R command page 32-37 on R book]

numstudent <- c(65,20, 250, 65)

names(numstudent)<-c("math", "stat", "eng", "health")

barplot(numstudent)

barplot(numstudent, ylab="frequency")

pie(numstudent)

Quantitative Variables

Distribution:

• What values a variable takes

• How often the variable takes those values (frequency)

Graphical Displays:

• Stem-and-leaf plots

• Histograms

attach(Shark) length [1] 18.7 12.3 18.6 16.4 15.7 18.3 14.6 15.8 14.9 17.6 12.1 16.4 16.7 17.8 16.2 12.6 17. 13.8 12.2 15.2 14.7 12.4 13.2 15.8 14.3 16.6 9.4 18.2 13.2 13. [31] 15.3 16.1 13.5 19.1 16.2 22.8 16.8 13.6 13.2 15.7 19.7 18.7 13.2 16.

sort(length) [1] 9.4 12.1 12.2 12.3 12.4 12.6 13.2 13.2 13.2 13.2 13.5 13.6 13.6 13.8 14. [16] 14.6 14.7 14.9 15.2 15.3 15.7 15.7 15.8 15.8 16.1 16.2 16.2 16.4 16.4 16. [31] 16.7 16.8 16.8 17.6 17.8 17.8 18.2 18.3 18.6 18.7 18.7 19.1 19.7 22.

Stem - and-leaf plot

stem(length, scale=2)

The decimal point is at the |

9 | 4 10 | 11 | 12 | 12346 13 | 22225668 14 | 3679 15 | 237788 16 | 122446788 17 | 688 18 | 23677 19 | 17 20 | 21 | 22 | 8

Histograms

Steps to constructing a histogram:

1. Order data

2. Divide data into intervals of equal width

To chose interval width:

Range Number of intervals(5 or 6)

3. Count the number of observations in each interval

4. Graph

> hist(length)

Interpreting histograms :

Overall pattern

  • Shape: single peak (or uni-modal, bi-modal, multi-modal) , symmetric
  • Center: the middle point
  • Spread: range
  • Outliers: falls outside of pattern

Symmetric and skewed distribution:

  • Symmetric: left and right are mirror to each other
  • Skewed to right: right side of histogram extends further than left side
  • Skewed to left: left side of histogram extends further than right side