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# Statistical Methods Notes Week 1 2100-01

Marketplace > Rensselaer Polytechnic Institute > 2100-01 > Statistical Methods Notes Week 1
John.Danison
RPI
Statistical Methods
Yingda Lu

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Covers the first week of notes for Statistical Methods
COURSE
Statistical Methods
PROF.
Yingda Lu
TYPE
Class Notes
PAGES
0
WORDS
KARMA
Free

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This 0 page Class Notes was uploaded by John.Danison on Monday February 1, 2016. The Class Notes belongs to 2100-01 at Rensselaer Polytechnic Institute taught by Yingda Lu in Spring 2016. Since its upload, it has received 6 views.

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Date Created: 02/01/16
Statistical Methods Notes 212016 Types of Data 0 Data can be quantitative or qualitative o Qualitative data are categorical eg marital status gender laptop brand name 0 Quantitative data are numerical eg height income age 0 Quantitative data can be further characterized as either continuous or discrete 0 Continuous data are the result of a measurement process while discrete data are the result of a counting process llatiea and intervals are well de ned 7 a namnlea mane distance age 39 e Data lame q Liantltatlne Meaningful inteniala but net ratins ne true mere Enann piles ill sent ea Temperature aealea 7 Data wee anantitaitl39ii39e llI39I1E1 Ei l by internals are meaningless IEnamplea aatlsfaetien ranka level if education 3 glllata tyne qnalita ljve n ave ne tinder enly names er labels are assigned nannplea ear cellars enunn39y ei erigln 39 IIIuata tyne qualitative Frequency 0 Frequency refers to the number of times a value occurs in a data set 0 For example in the small dataset below the frequency of the color White is 5 and of the color Red 3 0 Blue Blue White Red Red White Green White Red Yellow White White Yellow Quantitative Data Quantitative data are numerical and can be either discrete countable or continuous non countabe For the most part with quantitative data we cannot simply list all the values in our data set since often that would result in very large frequency tables With quantitative data we more commonly group values into classes before constructing a frequency table Classes must be mutually exclusive and exhaustive Mutually exclusive means that each value falls in only one class Exhaustive means that all values are represented in the table Creating Classes 0 Step 1 Number of classes 0 Step 2 Class width interval 0 Step 3 Assign data values to classes Number of classes 0 Guided by the number of observations in the data set the researcher s knowledge of the domain of the data or other research requirements 0 As a general rule of thumb any number between 5 and 20 classes is acceptable depending on the above considerations 0 Alternatively Sturges formula offers a way to calculate the number of classes as Number of classes 133logn Class Width 0 The class interval de nes the boundaries for the values to be included in each class 0 We aim to create our classes with more or less equal intervals so that no one interval is arti cially over or under represented by being larger or smaller than the others 0 Divide the range of the data by the number of classes Range largest minus the smallest value in our data set Practice A bank branch manager tracks her employees performance by measuring the time it takes each employee to serve a customer The time it took to serve each of 50 customers at the branch are shown below Create a frequency table for the service times at the branch 2 4 2 2 9 11 2 5 10 8 3 2 11 7 2 6 7 3 6 3 11 10 6 11 10 9 5 5 8 7 8 7 7 9 3 2 10 11 6 4 6 8 5 3 5 5 3 9 7 5 Graphing Continuous Data 0 Histogram a graph which displays the classes on the Xaxis and the frequencies on the yaxis 1 KDCOICD H C 0 to 9 10 to 19 20 to 29 30 to 39 40 to 49 50 to 59 60 to 69 70 to 79 80 to 89 90 to 100 Total 0 0 1 4 4 13 11 13 3 1 l50 20 10 m Frequency 0 9 O 0 V 19 b9 lt09 lt2 Classes Histograms are important in visualizing the shapes of the distribution 0 We look for symmetry and skewness 0 Negative left skew means the peak is on the right side 0 Positive right skew means the peak is on the left side Stern and Leaf Plot 0 A different way of graphing quantitative data 0 Stem and Leaf plot displays data broken into the stem which is on the left hand side of the line and represents the grouping level of the data and the leaves shown on the right hand side of the line Sten1 4 DU hJ US 00 J on L Leaf CD CD CD CD CD 4 CH 5 am 3999 45 FJ DU hJ LU Ch Stemandleaf displays provide another way to look at frequencies 0 To construct the stemandleaf display you split the data into the stem and the leaf Relative Frequency Describes the frequency of occurrence of speci c values as percent out of the total number of observations To create the relative frequency table we divide the frequency of each class by the total number of observations WORKS CITED Lu Y 2016 February 1 Data Presentation Lecture presented at Statistical Methods Class 2 in Pittsburgh Building RPI Campus Troy

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