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

Stem and Leaf Plots-I This is a key to how the stem 4 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.

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

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.

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.

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.

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

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?

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

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

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