1. Descriptive Statistics-II (More on Graphs and Data Summaries)
QSCI 381 – Lecture 3
(Larson and Farber, Section 2.2)

2. Stem and Leaf Plots-I This is a key to how the stem4 1 5 6 7 8
1,3,3,4,4,5,5,6,7 9
1,3,3,7 10
0,1,9 11
1,6 12
1,3,7 13
0,1,3,4,8,9 14
1,2,3,4,6,9 15
0,2,2,2,5,7 16
2,3,5,8 17
2,4
This is a key to how the stem
and leaf plot is structured
Each number to be plotted is separated
into a stem (e.g. the number’s first
two digits) and a leaf (e.g. the number’s
rightmost digit).
A stem and leaf plot is similar to a
histogram, but has the advantage that
the graph still contains the basic data.
Note that I have sorted the data within
each stem.

3. Lengths (cm x 10) of 48 bowhead whales harvested off Alaska
Stem and Leaf Plots-II
Lengths (cm x 10) of 48 bowhead whales harvested off Alaska 85 84
138 93 97
163
152 87 91
172
157
147
155
168
142
162
100 83 86 41
174
150
130
123
165
139
148
141
146 77
144
127
121
134
143 81
111
133
101
131
116
109
Identify the minimum and maximum values
Select a definition for the stem.
Assign each data entry to a stem.
Sort the leaves for each stem

4. Stem and Leaf Plots-III
An extension to stem and leaf plots is to split some of the stems further to better identify the structure of the data.

5. Pie Charts Pie charts can be used to summarize qualitative data.
Pie charts are over-used;
often the same information
can be represented better
using other graph and
table styles.

6. Pareto Plots
A Pareto chart is a vertical bar graph in which the height
of each bar represents the frequency (or relative frequency).
The bars are ordered in decreasing height.

7. Graphing Paired Data Paired data: For each value in one data set,
there is a value in the other.
Note: Just because there is a
pattern in the plot does not
imply a causal relationship!
“Scatter plot” in EXCEL was
was used to construct this plot
Bowhead age and length data.
The estimates of age were obtained
using the acid racemization method

8. Gray whales off the west
Time Series Plots
When data are collected on regular (or irregular) intervals over a period of time, the data set is referred to as a time-series. We plot such data using a time-series plot.
Gray whales off the west
Coast of North America
Can we explain this?

9. The Curse of Zero-I
When data are based on ratio measurements how zeros are represented on graphs can substantially impact how the results are interpreted.
Consider a data set in which the percentage of a (fish) population which spawns successfully was measured in areas that differ in terms of the impact on the habitat. The basic data are:
Extent of Damage
High
Medium
Low 92 95 97

10. The Curse of Zero-II
Percentage spawning
This is the default EXCEL bar chart. What is the immediate visual interpretation of the data?

11. The Curse of Zero-III The plot now includes zero.
How has the interpretation of
the information changed?