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# Math 181 Chapter 2 MATH 181

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This 3 page Class Notes was uploaded by Courtney Erickson on Monday January 25, 2016. The Class Notes belongs to MATH 181 at Ball State University taught by Dr. Pierce in Spring 2016. Since its upload, it has received 14 views. For similar materials see Elementary Probability and Statistics in Math at Ball State University.

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Date Created: 01/25/16

Frequency Distributions Chapter 2 Math181 Spring 2016 Distribution a way to describe the structure of a data set or population Frequency Distribution display of the values that occur in a data set and how often each value or range of values occurs Frequencies f numbers of data values in the categories of a frequency distribution Class category of data in a frequency distribution Constructing a frequency distribution 1 Decide how many classes should be in the distribution 2 Choose an appropriate class width 3 Find the class limits a Lower Class Limit smallest number that can belong to a class b Upper Class Limit largest number that can belong to a class 4 Determine the frequency of each class Class Width the difference between the lower limits OR upper limits of two consecutive classes of a frequency distribution Class Boundary the value that is halfway between the upper limit of one class and the lower limit of the next class ex Class Frequency 1019 5 2029 10 3039 7 Class Width 2010 10 Class Boundary the lower class boundary of the 2nCI class is 195 halfway between 19 amp 20 Midpoint aka Class Mark Lower Limit Upper Limit 2 Relative Frequency the percent of the data set that falls into a particular class Relative Frequency f f gt class frequency n n gt sample size n 2fi sum of the frequencies Cumulative Frequency the sum of all the frequencies of a given class and all previous classes the cumulative frequency of the last class sample size Graphical Displays of Data Pie Charts Qualitative Display qualitative data by showing each category39s relation to the whole when constructing a pie chart round each angle to the nearest whole degree Bar Graphs Qualitative Use bars to represent the data in each category Generally one axis displays categories while the other displays frequency Bar graphs include Pareto Charts Sidebyside Bar Graphs and Stacked Bar Graphs Pareto Chart bar graph where the bars are in descending order SidebySide Bar Graph bar graph that compares the same categories for 2 samples Stacked Bar Graphs bar graph that shows compiled data from 2 samples Histograms Quantitative A bar graph of frequency distribution aka Frequency Histogram Relative Frequency Histograms show relative frequencies rather than frequencies Polygons Quantitative A frequency polygon is created by plotting a point at the frequency of each class above each class midpoint Points are connected with straight lines Ogives Quantitative A graph that shows the cumulative frequency of each class from a frequency distribution StemandLeaf Plot Quantitative A graph of quantitative data similar to a histogram Must have a legend key How to construct a StemandLeaf plot 1 Create two columns left for stems and right for leaves 2 List each quotstemquot that occurs in the data set in numerical order 3 List each quotleafquot next to its stem 4 Create key to guide interpretation of stemandleaf plot 5 Put the leaves in numerical order to create an ordered stemandleaf plot optional Dot Plots Dot plots retain the original data in the chart Only data that are the same appear together Line Graphs Best representation of data measurements over time iar Graph arat Sidabyaaa Staalitad Chant Ear Graph F ia Shari ualitativa ata i lialntitatitra Data Histagiam Fr aquanatr Dgitra Lina Eurph Palygan Starna l Laavaa r A Etanit El g I 5 5 lat Plat Leaf Pit Analyzing Graphs 0 All Graphs should be labelled with title axes and source where the data comes from 0 Graphs should also be appropriate to their data 0 Timeseries Graph is a line graph showing a variable that changes over time 0 Crosssectional Graph is a graph of data collected at one point in time 0 Pictograph is a bar graph that uses pictures rather than bars often misleading 0 Graphs should be scaled properly to represent data well 0 Overall Shape of the graph can be useful 0 Uniform each class has similar frequencies 0 Symmetric data is even on both sides of the distribution 0 Skewed to the right most of the data is on the left outliers on the right 0 Skewed to the left most data is on the right outliers on the left 0 UnimodalBimodal data has onetwo modes main peaks

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