Chapter 1: Exploring Data
Section 1.1: Displaying Data
Individuals: The objects being described by the data
Variable: Any characteristic of an individual
Distribution of variable:
 pattern of variation
 tells what values the variable takes AND how often each value occurs
Who?
Individuals, #
What?
variables, units
Categorical
 place in a group (category)
Why?
did we gather the data
Quantitative
● take numerical values for which it makes sense to do
arithmetic
DISPLAYING CATEGORICAL DATA
*Bar Graph
 Categorical data
 Bars don’t touch
 Can rearrange categories
 Scale may be in counts or percents
50%
8
40%
6
30%
4
20%
2
10%
Truck
Van
Car
(Scale in percents)
Percentage of People
(Scale in counts)
Number of People
 What kind of car do you drive? (example only)
- Truck
3
15%
- Van
0
0%
- Car
9
45%
- SUV
2
10%
- Other
4
20%
- None
2
10%
10
SUV Other None
Type of Car
(Categories)
*Pie Graph (Chart)
 Categorical Data
 Must be Out of a Whole (100%)
*Bar graphs are more flexible since you don’t necessarily
need the whole (but you must be using the counts side
unless the counts are in percentages – Example 1.3 p. 10)
DISPLAYING QUANTITATIVE DATA
 How tall are you in inches?
Class Heights (example only)
59
63
65
67
68
60
64
67
67
68
62
64
67
67
68
62
65
67
67
68
62
65
67
68
69
69
69
70
70
70
71
71
71
72
72
72
72
73
73
74
*Dotplot
 Quantitative data
 Values at the bottom
 Each dot = 1 piece of data
 Heights are how many at each value
59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74
Height of students
(values)
*Stem plot
 Quantitative data
 Around 5 stems is good minimum
 May have to split (high/low)
 Numbers listed in increasing order
 Each stem must have an equal # of
possibilities
 May need to round data (5.3 ≈ 5)
 Leaves can only be one digit
Heights of Students
55-59
60-64
65-69
70-74
75-79
5H
6L
6H
7L
7H
5
6
6
7
7
9
0222344
5557777777788888999
0001112222334
Key: 6 | 0 means 60 inches
Read Example 1.5 on p. 13 – 14.
 Comparative Stem plot: used to compare two groups
o For example: boys height vs. girls height
Boys
Girls
5 9
442 6 0223
9998887777755 6 577788
4332222100 7 011
7
Example 1.6 on page 19 
14
(Scale in counts)
Number of Presidents
*Histogram
 Bars touch
 “Classes” need to have equal widths
 5 “classes” is a good minimum
 Label & scale axes
 Frequency can be in counts or %
12
10
8
6
4
2
0
40
45
DESCRIBING DISTRIBUTIONS
50
55
60
Age of Inauguration
65
70
Use SOCS – Shape, Outliers, Center, Spread
Outlier: an individual observation in any graph of data that falls outside the overall pattern of the graph.
5
6
6
7
7
9
0222344
5557777777788888999
0001112222334
59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74
Height of students
(values)
Shape: Peak at 67
Outliers: None
Center: 67
Spread: 59 – 74
Key: 6 | 0 means 60 inches
Shape: Peak at 65 to 69
Outliers: None
Center: 67
Spread: 59 – 74
 Kinda like range
Shape: Roughly symmetric, one peak
Outliers: none
Center: About 55 years
Spread: 42 – 69
(Scale in counts)
Number of Presidents
14
12
10
8
6
4
2
0
40
45
50
55
60
Age of Inauguration
65
70
MORE ON SHAPE
- Peaks are always good to mention
*Symmetric: roughly the same on both sides
*Uniform: roughly the same height everywhere
*Skewed
Skewed Right
Skewed Left
Direction towards tail
Modifiers:
 Roughly
 Approximately
 Somewhat
 Clearly
 Slightly (used more with skewed)