AEM 201 1st Edition Lecture 4PREVIOUS LECTUREI. Descriptive Statistics-Organization and DisplayII. Graphical Displays of Frequency DistributionsIII. Summarizing Quantitative DataCURRENT LECTUREI. Summarizing Quantitative DataII. Summary of Tabular and Graphical DisplaysIII. Simultaneous Display of Multiple Variables-Two Qualitative VariablesIV. Simultaneous Display of Multiple Variables-One Qualitative One Quantitative VariableV. Simultaneous Display of Multiple Variables-Two Quantitative VariablesSUMMARIZING QUANTITATIVE DATA- When we summarize quantitative data into classes, we don’t know what the values are. We take quantitative data and turn it into qualitative data- You can learn something from frequencies not so much about datao Sometimes we have to sacrifice information in summarizing data for the understanding we gain from it- Absolute frequency has the most information and can be used to create the relative and absolute frequency- If a data point falls into two classes because it is on a boundary you have to decide which classes the data will fall into (you must make a plan BEFORE you start classifying data)o Data points on the border may all go in the lower classo Data points on the border may all go in the higher classo You may decide to subtract a small amount (say 0.1) from each upper class limit to correct for the overlap between classeso You may decide to add a small amount (say 0.1) to each upper class limit to correct for the overlap between classes- Dot Plot: a tabular summary in which the relative number of elements in a data set that take on each potential value of the variable are represented by dots (use when comparing frequencies of values for a quantitative variable)o Can be used to recreate to original datao Doesn’t work well fro large amounts of dataThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Histogram: bar chart for the frequency distribution of a quantitative variable (used when comparing frequencies of categories of values for a quantitative variable)o Lack of gaps between bars because it indicates the order of the categories matter- What you do with frequency distribution can effect the display of your graph. You MUST decide class width and what you are doing for the values that fall into two classes BEFORE you make your graph- Line Graph: connected points used to identify trends in the consecutive values of the data (used to show trends in values of a quantitative data set)- Ogive: line graph of a cumulative frequency distribution of quantitative variable that are greater than a given value)- Density Curves: line graph for which the y-axis represents relative (proportional) or percentage frequency (used to show distribution of values of a quantitative variable)o Area under the density curve must equal 1- Stem and Leaf Plot: display by class, of the actual values in a data set in a histogram-like manner dots (use when comparing frequencies of categories of values for a quantitative variable)o Steps to make a stem and leaf plot: Record the leading digit(s) that occur in the data set of the left side of a vertical line (‘Stems’) Record the trailing digit that occurs in the data set on the right side of a vertical line (‘leaves’)o Can recreate the original data from a stem and leaf ploto Is a lot like a histogram except shows exact valuesSUMMARY OF TABULAR AND GRAPHICAL DISPLAY- Qualitativeo Tabular Frequency distribution Cross tabulationo Graphical Pie chart Bar chart- Quantitativeo Tabular Frequency distribution Cross tabulationo Graphical Histogram Stem and leaf plot Ogive Dot plot Scatter diagramSIMULTANIOUS DISPLAY OF MULTPILE VARIABLES-TWO QUALITATIVE VARIABLES- We can look at two different variables occurrence’s simultaneously- Cross Tabulation: a table displaying the frequency of occurrence for classes of values for two (or more) variables simultaneously- Bar Chart: we could display the frequency of the two variables in a side-by-side mannero one variable and its classes on the x-axis, one variable and its classes represented by the bars - Stacked Bar Charts:we could display the frequency of the two variables in a stacked mannero one variable and its classes on the x-axis, and one variable and its classes represented bythe bars - Pie Charts: we could display side-by-side pie charts to show the frequencies of the two variableso Very hard to compareo Sometimes groups are not the same size, so pies should not be the same sizeSIMULTANEOUS DISPLAY OF MULTIPLE VARIABLES-ONE QUALITATIVE AND ONE QUANTITATIVE VARIBALE- Data Array: we can use an array of data to display. We can use color, bolding, italics, and differentfontsect.to distinguish the different qualitative categories- Dot Plot: we can a dot plot to display. We can use color, different shapes, bolding ect. to distinguish the different qualitative categories- Frequency Distributions: cross tabulation can also be used to display the frequency- Line Charts: We can use line charts as a display. Can distinguish different periods of time- Stem and Leaf Plots: we can use a stem and leaf plot to display data. Color, font, bolding, italics ect can be used to distinguish the different qualitative variablesSIMULTANEOUS DISPLAY OF MULTIPLE VARIABLES-TWO QUANTITATIVEVARIABLES- Frequency Distribution: a cross tabulation can also be used to display the frequency of occurrence for classes of values for two (or more) quantitative variables simultaneously- Scatter Diagram: a graphical simultaneous presentation of the values of two variables on a Cartesian coordinate system (use when showing the nature of the relationship between values for two quantitative variableso Shows relationships between variables  Positive, negative, or no relationship at allo Only display that shows relationship between two quantitative variableso Interpretations mean what is the graph showing us?- The only way to show causality is experimentation. Relation does NOT imply causation- Line Graphs: can use line graphs to display data. Over lapping lines of quantitative data on the same