CALCULATING STANDARD DEVIATION WORKSHEET



Name: October 23rd 2015Stats 1Stats.21 - Notes and Practiceleft40195500CorrelationWhat sort of correlation would you expect to find between:a person's age and their house number? ___________________________a child's age and their height? ___________________________an adult's age and their height ? ___________________________1885950-111760Sort the different Analysis ToolsMean, Tables, Median, Scatter Plots, Mode, Correlation, Range, Line of Best Fit, Quartiles, Standard Deviation, Bar Graphs, Pie Charts, HistogramsUnivariate DataBivariate DataMean, Tables, Median, Mode, Range, Quartiles, Standard Deviation, Pie Charts, HistogramsTables, Scatter Plots, Correlation, Line of Best Fit, Bar Graphs, 0-635003457575150495We can calculate the correlation coefficient to describe exactly how strong or weak a correlation is!What type of correlation would you expect to find between each of the following quantities:Age and pocket money? _______________________________ IQ and height? _______________________________ Price of house and number of bedrooms? _______________________________ Person's height and shoe size? _______________________________r=i=1n(xi-x)(yi-y)i=1nxi-x2i=1nyi-y2The first x valueThe second x valueThe ith x valueMean of all of the x valuesMean of all of the y valuesDifference between the value of x and the mean of the x valuesSquared difference between the value of y and the mean of the y valuesProduct of the differences from the meansProduct of the sums of the squared differences from the meansThe correlation coefficientr tells us…A positive value of r indicates…A negative value of r indicates…General Guidelines:If |r| is greater than 0.8, then it is considered _________________________If |r| is less than 0.5 then it is considered ______________________Describe a correlation if r = 0.71 ______________________________________________________Describe a correlation if r = -0.83 ______________________________________________________Describe a correlation if r = 0.83 ______________________________________________________Describe the correlation if r = - 0.23 ____________________________________________________Describe the correlation if r = -0.93 ____________________________________________________Describe the correlation if r = 0.13 ______________________________________________________center-101600Calculate the correlation coefficient! r=i=1n(xi-x)(yi-y)i=1nxi-x2i=1nyi-y2ixiyixi-xyi-y(xi-x)(yi-y)xi-x2yi-y212345678x=i=1nxin = y=i=1nxin = i=1n(xi-x)(yi-y)= i=1nxi-x2= i=1nyi-y2= r=i=1n(xi-x)(yi-y)i=1nxi-x2i=1nyi-y2= What does this correlation coefficient tell us about this bivariate data?center-209550Calculate the correlation coefficient! r=i=1n(xi-x)(yi-y)i=1nxi-x2i=1nyi-y2ixiyixi-xyi-y(xi-x)(yi-y)xi-x2yi-y21234567x=i=1nxin = y=i=1nxin = i=1n(xi-x)(yi-y)= i=1nxi-x2= i=1nyi-y2= r=i=1n(xi-x)(yi-y)i=1nxi-x2i=1nyi-y2 What does this correlation coefficient tell us about this bivariate data?0000Calculate the correlation coefficient! r=i=1n(xi-x)(yi-y)i=1nxi-x2i=1nyi-y2Use calculator’s STAT functions to speed up this process by automating the basic calculations for you ixiyixi-xyi-y(xi-x)(yi-y)xi-x2yi-y2nL1L2L3L4L5L6L6 **we will reuse list 6 since the calculator can only store 6 listsright2730500Enter data into lists… STAT 1:Edit…Find the sum of lists…522922516510002nd LIST MATH 5:sum( 2nd L1Calculate new lists from other lists… STAT 1:Edit… press up arrow to select the name of the list you want to editenter the formula for new list (example: L1-100) ENTERx=i=1nxin = y=i=1nxin =i=1n(xi-x)(yi-y)= i=1nxi-x2= i=1nyi-y2= r=i=1n(xi-x)(yi-y)i=1nxi-x2i=1nyi-y2 What does this correlation coefficient tell us about this bivariate data?00Use your calculator to calculate to help you calculate the correlation coefficient! Use calculator’s STAT functions to speed up this process by automating the basic calculations for you ixiyixi-xyi-y(xi-x)(yi-y)xi-x2yi-y2nL1L2L3L4L5L6L6 **we will reuse list 6 since the calculator can only store 6 listsx=i=1nxin = y=i=1nxin =i=1n(xi-x)(yi-y)= i=1nxi-x2= i=1nyi-y2= r=i=1n(xi-x)(yi-y)i=1nxi-x2i=1nyi-y2 What does this correlation coefficient tell us about this bivariate data? ................
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