Chapter 1: Looking at Data  Distributions
Readings: Sections 1.1, 1.2
September 1, 2009
1
Introduction
Important vocabulary
:
•
Individuals
: objects being described by a set of data (people, households, cars, animals, corn,
etc.)
•
Variables
: characteristics of individuals (height, yield, length, age, eye color, etc.)
– Categorical
: places an individual into one of several groups (gender, eye color, college major,
hometown, etc.)
– Quantitative
: attaches a numerical value to a variable so that adding or averaging the values
makes sense (height, weight, age, income, yield, etc.)
•
Distribution of a variable
: describes what values that variable takes and how often it takes on
that value.
–
If you have more than one variable in a problem, look at each variable by itself first, then look
for any relationships between the variables.
Example 1
: Identify whether the following questions would give you categorical or quantitative
data. If it is categorical, state the possible answers.
a. What letter grade did you get in your Calculus class last semester?
b. What was your score on the last exam?
c. What is your GPA?
d. Did you vote for Barack Obama?
e. How many votes did George W. Bush get?
2
Visual display of data
2.1
Categorical variables
•
Bar graph
•
Pie chart
Example 2 (
Messy room example
)
: In a poll of 200 parents of children ages 6 to 12, respondents were
asked to name the most disgusting things ever found in their children’s rooms. The results are below
(J&C 2005)
Most disgusting thing
# of parents
% of parents
Foodrelated
106
53%
Animal and insectrelated nuisances
22
11%
Clothing (dirty socks and underwear especially)
22
11%
Other
50
25%
1
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Pie chart (needs % of parents)
2.2
Quantitative variables
Stemplot
(also known as the stemandleaf plot)
Four steps to create a stemplot
:
1. Sort the data from the smallest to largest
2. Choose the “stem”; usually all but the last one or two decimal places of data. Round the trailing
digits to create “leaves”
3. Write stem in a vertical column with the smallest at the top, and draw a vertical line.
There
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