CK-12 Probability and Statistics - Advanced

(Marvins-Underground-K-12) #1

http://www.ck12.org Chapter 2. Visualizations of Data


First of all, it appears as if there was a shift to the right in all the data, which is explained by realizing that all of the
countries have significantly increased their consumption. The first peak in the lower consuming countries is almost
identical but has increased by 20 liters per person. In 1999 there was a middle peak, but that group showed an even
more dramatic increase in 2004 and has shifted significantly to the right (by between 40 and 60 liters per person).
The frequency polygons is the first type of graph we have learned that make this type of comparison easier and we
will learn others in later lessons.


The Mantra of Descriptive Statistics: Shape, Center, Spread


In the first chapter we introduced measures of center and spread as important indicators of a data set. We now have
the tools to include the shape of a distribution of data as being very important as well. The “big three”:Shape,
Center, and Spreadshould always be your starting point when describing a data set. If a statistician had to wear a
uniform, it should probably say: shape, center, and spread.


If you look back at our imaginary student poll on using plastic beverage containers, A first glance would allow us to
conclude that the data isspreadout from 0 up to 9. The graph illustrates this concept, and we have a statistic that
we used in the first chapter to quantify it: the range. Notice also that there is a larger concentration of students in the
5 , 6 ,and 7 region. This would lead us to believe that the center of this data set is somewhere in that area. We also
used statistical measures to quantify this concept such as the mean and the median, but it is important that you “see”
the idea of the center of the distribution as being near the large concentration of data.


Shapeis harder to describe with a single statistical measure, so we will describe it in less quantitative terms. A very
important feature of this data set, as well as many that you will encounter is that it has a single large concentration
of data that appears like a mountain. Data that is shaped in this way is typically referred to asmound-shaped.
Mound-shaped data will usually look like one of the following three pictures:


Think of these graphs as frequency polygons that have been smoothed into curves. In statistics, we refer to these
graphs asdensity curves.Though the true definition of a density curve will come in a later chapter, we should start
to get used to the correct terminology now. The most important feature of the first density curve is symmetry. A
concise description of the shape of this distribution therefore, would besymmetric and mound shaped. Notice

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