Lecture 1 -011910 - Simple Visual Summaries of Data Sets

Lecture 1 -011910 - Simple Visual Summaries of Data Sets -...

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1/17/2010 1 STAT 3704 Sections 2.1-2.3 ` Introduction ` Stem-and-Leaf Plots Construction Interpreting Depth ` Boxplots Construction Interpreting ` Summary 2

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1/17/2010 2 ` What do we actually do with a data set when it’s handed to us? Most data sets are too large to be able to draw any useful conclusions from just by staring at the list of numbers and characters. We need some way of summarizing the data in an informative form that is easy on the eyes. 3 ` This chapter covers several ways of creating visual summaries of data sets. These methods are designed for a data set consisting of one variable; other methods for two or more variables will be discussed as they come up. ` Using these visual tools is a critical first step when analyzing data, to be done before doing anything else! 4
1/17/2010 3 ` By observing visual summaries of the data, we can… Determine the general pattern of data Pick out any outliers that seem like they don’t belong Check whether the data follow some theoretical distribution Make quick comparisons between groups of data. ` All of this can be done before any formal analysis, and it can often be sufficient in its own right! 5 ` There are several types of visual summaries. The ones we’ll cover in this chapter include… Stem-and-leaf plots Boxplots Histograms Time series plots (or time plots) ` The first two are usually pretty easy to draw by hand, so we’ll start with them. A computer software package makes life easier for all four displays. We’ll discuss some of these next time. 6

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1/17/2010 4 ` The first visual display we will look at is a stem-and-leaf plot . This graph sorts the data in order by grouping elements with similar sizes together. ` An example will be the easiest way to illustrate a stem plot. 7 ` Example: Suppose that the homework scores (out of 100) for a statistics class (after sorting) are as follows: 50 56 58 59 59 60 61 67 67 68 72 72 72 74 75 76 76 77 79 80 80 81 83 85 86 ` Notice how we have several values sharing a digit in the 10’s place. We can group these together as follows: 5 | 06899 6 | 01778 7 | 222456679 8 | 001356 8
1/17/2010 5 ` Notice how the digit in the 10’s place is “pulled out” to the left, while all the corresponding digits in the 1’s place are grouped together. ` We say that the column on the left is the 5 | 06899 6 | 01778 7 | 222456679 8 | 001356 We say that the column on the left is the stem , while each of the leaves to the right represents an element of the data set when paired with its stem number. 9 ` It’s a judgment call as to what place to pick for the stem values. Generally, we try to pick the stem so that no one stem element has all the leaves or that each stem only has one or two leaves on it. Computer software packages will tend make this selection automatically.

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This note was uploaded on 02/23/2010 for the course STAT 3704 taught by Professor Talaura during the Spring '07 term at Virginia Tech.

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Lecture 1 -011910 - Simple Visual Summaries of Data Sets -...

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