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SECTION 1.1 
LOOKING AT DATA
SECTION 1.2  DESCRIBING DISTRIBUTIONS WITH NUMERICAL SUMMARIES
TYPES OF VARIABLES
*
Quantitative (or numerical) variables
take numerical values for which arithmetic operations such
as adding and averaging make sense (age, GPA, numeric total score for this course, height).
*
Categorical variables
place an individual into one of several groups or categories (major, eye color,
hometown, favorite ice cream flavor, etc.)
EXAMPLE
Identify whether the following questions would give you categorical or quantitative data.
a)
What letter grade did you get in your Calculus class last semester?
b)
What was your score on the last exam?
c)
Did you vote for Barack Obama?
DISTRIBUTION OF VARIABLES
The distribution of a variable
describes the values the variable takes and how often it takes on each value.
Suppose that we wanted to find the distribution of eye color in group of 20 people.
The distribution of the
variable “eye color” would be the number of times each eye color is represented out of the 20.
Brown = 11/20
Blue = 5/20
Hazel = 3/20
Green = 1/20
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.
GRAPHING CATEGORICAL VARIABLES
1.
Bar graph
2.
Pie charts
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%
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Bar graph
(can use either # of parents like below or % of
parents): Typically with bar graphs, the yaxis represents
the frequency (number of observations) in the categories.
Units can give multiple answers or no answer.
Pie Chart
: Percents must add to 100%.
Each
unit must give one and only one answer.
Pie chart
(needs % of parents):
GRAPHING QUANTITATIVE VARIABLES
1.
Stemandleafplots
display actual values of all observations and are good for small amounts of data.
2.
Histograms
are used for large amounts of data and display only summary information.
Steps for Creating StemandLeafplots:
1.
Put data in numerical order from smallest to largest.
2.
Separate each observation into a “stem” and a “leaf” (Note:
leaf = final digit, stem = remaining digits.
In the case of a single digit number like 7, use 07 so that 0 is the stem.)
3.
Write stem numbers in order in a vertical column with the smallest at the top.
Do not skip numbers.
Draw a vertical line next to the stem.
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 Spring '08
 Staff

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