Ordered Array (nib) Frequency Distribution. Chapter 2 Descriptive Statistics: Tabular and Graphical Methods

Transcription

1 Chapter Descriptive Statistics: Tabular and Graphical Methods Ordered Array (nib) Organizes a data set by sorting it in either ascending or descending order Advantages & Disadvantages Useful in preparing tables and charts in Chapter and numerical summary measures in Chapter What scale (level) of data is required? Frequency Distribution A grouping of data into mutually exclusive categories that shows the number of observations in each category Can be prepared for either qualitative or quantitative variables Class Frequency Relative Frequency (RF) Percent Frequency 1

2 Frequency Distribution: Qualitative Variables Example: A sample of runners were asked to indicate their favorite brand of running shoe. Asics Converse Brand Asics Other Total # of Runners 1 RF PF Dewey, Cheatham and Howe assignment Pie Chart Effective at showing the proportion of the total each category contributes How construct for the Running Shoe example? Brand # of Runners RF PF Asics 1.. Other.. Total 1.. Asics Other Frequency Distribution: Quantitative Variables Construction of: 1) how many classes? c >n ) classes must be mutually exclusive and all inclusive ) class interval width = (Max Min)/c then round up - Advantages & Disadvantages

3 Frequency Distribution: Quantitative Variable Class Limits upper and lower Class Frequency Class Midpoint Relative Frequency (RF) Cumulative Frequency (CF) less-than orientation must have at least ordinal-level data Cumulative Relative Frequency (CRF) Pictorial Displays Advantages & Disadvantages of graphs Frequency Hours spent studying Histogram Bar graph of a frequency distribution Can plot frequencies and/or relative frequencies Frequency.%.%.%.%.% Relative Frequency Class Interval (Cents per gallon).%

4 Frequency Polygon (nib) Plot of class midpoints vs. frequencies Frequency Midpoint (Cents per Gallon) Skew Characterizes a distribution s shape by describing its degree of horizontal balance Figure., page general cases Symmetrical Negative Skew Positive Skew 11 Dotplot (nib) Just like it sounds! No arbitrary decisions to make regarding the number of classes and class limits {,,,, } Gas Price 1 1

5 Ogive Line graph of cumulative frequencies or cumulative relative frequencies CumulativeFrequency Less Than (Cents Per Gallon) Cumulative Relative Frequency 1 Percentile (Chapter ) Indicates the proportion of observations whose value is less than or equal to a specified value Easy to estimate from an ogive in the Gas Price data set, cents per gallon is approximately percentile 1 Exploratory Data Analysis Techniques that employ simple arithmetic and easy - to-draw pictures to summarize data quickly Stem-and-Leaf Display -Number Summary (Ch ) Box Plot (Ch ) 1

6 Stem-and-Leaf Display A hybrid of an Ordered Data Array and Histogram Advantages & Disadvantages note the leaves are sorted and aligned Stem Leaf Crosstabulation aka Contingency Table Cross-classifies two variables What are the two variables? Column percentages or row percentages can reveal relationships (interactions) between two variables Does market share vary by gender? Hormel Anti-Spam assignment Textbooks America assignment Brand Male Female All Runners Asics 1 Other Total 11 column percentages Brand Male Female All Runners Asics.1.. Other... Total... 1 Scatter Plot Graphs the value of one quantitativevariable vs. value of another quantitative variable Bivariate data Y-axis plots the dependent (response) variable X-axis plots the independent (explanatory) variable Can reveal relationships (interactions) between two quantitativevariables A trend line can estimate the relation between variables direct relation vs. inverse relation Amount of scatter around the trend line indicates strength of relationship 1

7 Scatter Plot hours score Exam Score Do you detect a pattern? A scatter plotand trend line can help Absences and Score assignment 1 Hours Studied 1