Slide 1Practice ProblemsAdditional Reading and ExamplesSlide 4Motivating ExampleDescriptive StatisticsDescriptive StatisticsSlide 8Purpose of Graphical ProceduresQualitative VariablesQuantitative VariablesExampleExampleStem-and-Leaf PlotStem-and-Leaf PlotStandard Stem-and-Leaf PlotStandard Stem-and-Leaf PlotStandard Stem-and-Leaf PlotStandard Stem-and-Leaf PlotStandard Stem-and-Leaf PlotStandard Stem-and-Leaf PlotStandard Stem-and-Leaf PlotSlide 23Example 7Example 7Example 7Example 7Example 7Example 7Example 7Standard Stem-and-Leaf PlotStandard Stem-and-Leaf PlotStandard Stem-and-Leaf PlotExample 8Example 8Example 8Example 8Example 8Example 8Example 8Example 8Slide 42Extended Stem-and-Leaf PlotExample 9Example 9Example 9Example 9Example 9Example 9Example 9AdvantagesDisadvantagesSlide 53Motivating ExampleMotivating ExampleMotivating Example - SolutionSlide 57STAT 210Lecture 7Graphically Displaying DistributionsSeptember 12, 2016Practice ProblemsPages 65 through 68Relevant problems: III.1, III.3 – III.7, III.11, III.12 and III.13 (a) onlyRecommended problems: III.1, III.5, and III.13 (a)The “use the plot to describe the distribution” part ofthe problems can be postponed until after Thursday’s class.Additional Reading and ExamplesRead pages 61 and 62ClickerMotivating ExampleSeveral students, when asked to list their three favorite things to do, included “playing video games” on their list. Suppose you are interested in the typical cost of video games.You select a sample of 20 video games and record their costs. How would you display and describe the distribution of these costs?Descriptive StatisticsThe branch of statistics concerned with numerical and graphical techniques for analyzing and describing one or more characteristics of a population and for comparing characteristics among populations.Descriptive StatisticsWhen describing a distribution we usually describe four things:(1) the center of the distribution(2) the spread of the distribution(3) the shape of the distribution(4) any unusual features in the distributionClickerPurpose of Graphical Procedures•Simplify the data•Make it easy to describe distributions•Make it easy to make statistical inferencesQualitative VariablesVariables whose measurement vary in name or kind only, and cannot be ranked in anyorder of magnitude.Pie chartsBar graphsQuantitative VariablesVariables in which measurements vary in magnitude from trial to trial, meaning some order or ranking canbe applied.Possible measurements are divided into class intervals.Each measurement should fall in one and exactly one interval.Example 0 - 1011 - 1615 - 2018 - 3034 - 5051 - 80 BadIn what interval does 19 fall? What about 32?Example 0 - 1011 - 1615 - 2018 - 3034 - 5051 - 80 0 - 1011 - 1516 - 2021 - 3031 - 5051 - 80 Bad GoodIn what interval does 19 fall? What about 32?Stem-and-Leaf PlotCan be used to sort a large list of data.More importantly, also can be used to graphically display the distribution of the data so that the distribution can be described.Stem-and-Leaf PlotDetermine the center of the distribution.Determine the range or spread of the data.Determine the shape of the distribution.Determine any range of values not represented.Determine if there is a concentration of data.Determine if there are any outliers (extreme values).unusualStandard Stem-and-Leaf PlotIf necessary, modify the numbers in the data set so that each has the same number of digits.For example, if the data ranges from 23 to 4320, two-digit numbers like 23 would become 0023, three-digit numbers like 567 would become 0567, and four-digit numbers like 4320 would remain unchanged.Standard Stem-and-Leaf PlotDivide each number in a data set into two parts: a “stem” and a “leaf”. With two digit numbers, the digit in the ten’s place is the stem and the digit in the one’s place is the leaf.Example: 95 9 is the stem 5 is the leafStandard Stem-and-Leaf PlotNext determine what the possible stem values are and list them vertically from smallest to largest. Draw a vertical line to the right of the stems.Example: If the data ranges from 43 to 98, then we have: 456 789Standard Stem-and-Leaf PlotFor each number in the data list, write the leaf digit next to the correct stem.Example: Consider 95 and 63456 789 5Standard Stem-and-Leaf PlotFor each number in the data list, write the leaf digit next to the correct stem.Example: Consider 95 and 63456 3789 5Standard Stem-and-Leaf PlotState a defining rule which indicates how the stem-and-leaf plot should be interpreted. This allows someone to easily determine what each value represents.Example: 9|5 = 95 as opposed to 9|5 = 9.5Standard Stem-and-Leaf PlotOnce completed, for each stem order the leaves from smallest to largest. This is optional, but makes sorting of the data easier.Example 7Example 70123456789Example 70 123456789 2Example 70 12345678 29 2Example 70 12345678 2,09 2Example 70 123456 878 2,09 2Example 70 123456 878 2,09 2,1Example 7 0 8 where 3|7 = 37123 74 3,4,85 6 87 7,9,7,6,5,4,88 2,0,8,0,5,4,5,5,3,3,6,4,8,7,6,3,99 2,1,4,5,1,2,3Standard Stem-and-Leaf PlotThis procedure can also be used with three, four, five, etc. digit numbers, and numbers with decimals.In this situation, we must spend more effort determining how the stems and leaves should be separated.Example: 436 could be written 4|36 or 43|6Standard Stem-and-Leaf PlotThis procedure can also be used with three, four, five, etc. digit numbers, and numbers with decimals.For moderate size data sets less than 6 stems is too few and more than 20 stems is too many; between 10 and 15 stems is often considered ideal.Standard Stem-and-Leaf PlotThis procedure can also be used with three, four, five, etc. digit numbers, and numbers with decimals.For moderate size data sets less than 6 stems is too few and more than 20 stems is too many; between 10 and 15 stems is often considered ideal.The defining rule allows us to display numbers containing decimals, as the decimal location is made part of the defining rule.Example 8Example 8The data range from 09.5 to 93.6. This suggests using:a) one-digit stems and two-digit leaves orb) two-digit stems and one-digit leaves ???ClickerExample 8The data range from 09.5 to 93.6. This suggests using:a) one-digit stems and two-digit leaves Stems of 0
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