MTH 232
Section 13.1
Organizing and Representing Data
Key Ideas
• Statistics is a way to organize, present, and
represent data through a variety of methods.
• The various numerical definitions of the
center (mean, median, and mode) or a set
give different insights into which measure of
the center of the data is most revealing.
• Prior to the middle grades, students should
have had experiences collecting, organizing,
and representing sets of data.
Dot Plots
• Used to summarize relatively small sets of
data.
• Dots are placed above the number line.
• At a glance, certain information—range of
scores, where most scores are located, what
the “typical” score is, which scores are
atypical, or outliers.
Example
• Test scores from a recent MTH 100 test:
• 90, 73, 78, 80, 64, 48, 58, 61, 88, 49, 39, 49,
48, 80, 55, 84, 53, 64, 78, 82, 58, 76, 51, 54,
52, 15, 89
Stem-and-Leaf Plots
• Similar to dot plots
• Especially useful for comparing two sets of
data.
• One part of the data value is the “stem” and
the other part is the “leaf”
• Data must first be grouped by the “stem”,
them ordered by the “leaf”
Another Example
• Another set of MTH 100 test scores:
• 46, 56, 71, 96, 46, 72, 88, 97, 70, 78, 84, 92,
86, 97, 73, 45, 41, 85
Histograms
• Scored are grouped into intervals.
• The height of the rectangle constructed on an
interval indicates the number of data points in
that interval (frequency).
• In a histogram, detail about the data is
exchanged for the ability to visualize larger
sets of data.
Line Graphs
• Especially useful for showing changes in data over
time.
Average Temperature in Tuscaloosa, Alabama
Month
Temp
Month
Temp
Jan
48
Jul
80
Feb
48
Aug
81
Mar
58
Sep
75
Apr
64
Oct
63
May
71
Nov
53
Jun
79
Dec
48
Bar Graphs
• Similar to histograms, but the horizontal axis
contains categorical (non-numeric) data.
• The height of the bar indicates the frequency
of the particular category.
• Random Question: which color of M&M’s is
most occurring in a bag?
The answer may surprise you…