Stats 101 Week 2 Notes
Stats 101 Week 2 Notes STAT 121
Popular in Principles of Statistics
verified elite notetaker
Popular in Department
This 4 page Class Notes was uploaded by Sydney Clark on Friday September 9, 2016. The Class Notes belongs to STAT 121 at Brigham Young University taught by Dr. Christopher Reese in Winter 2016. Since its upload, it has received 5 views.
Reviews for Stats 101 Week 2 Notes
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 09/09/16
Stats week 2: Examining Distributions with numerical measure *Important* *Sample test questions* Numerical summary o Summarize the distribution of a quantitative variable with measure of: Center Shape Spread IQR range Measure of center o Mode=peak of distribution, most frequently occurring value o Median= middle value *most important* Divides data in half (half are less than the number, half are more) If “n” is odd, pick middle value If “n” even, take average of 2 middle vales Denote by Mmedian o Mean=average value *most commonly used* Traditional measure of center Computing the media o 1.) order the data o 2.) if the number of observations is odd, median equals the middle observation Mean vs. Median o Consumer alert: either one might be called “average” in media o Depends on shape If histogram is symmetric use mean If you have skews or outliers use median Mean is dragged in direction of the tail The median is resistant to outliers, unlike the mean Mean is larger than median when skewed Two aspects of spread o Overall and central clustering Measure of spread o Range AND interquartile range Range: maxmin IQR= 3 quartile1 quartile 3 is median of the largest half of data, 1 quartile is smallest half of data Resistant to outliers Standard deviation= ”average distance” of value from mean Quartiles o Q1: Value that has approximately 25% of the observations in the ordered data set below it and 75% above. “Median” of observations below the median. o Q2: The median o Q3: Value that has approximately 75% of the observations in the ordered data set below it and 25% above. “Median” of observations above the median. o When “n” is odd, median is NOT included in either bottom or top half of data o When ‘n” is even, data are naturally divided in two halves o Standard deviation= “average distance” of values from mean Outliers o DON’T ALWAYS THROW THEM AWAY o How to find an outlier The 1.5 (IQR) criteria 1) Calculate IQR Q3Q1 2) Q3 + 1.5(IQR) If less than original Q3 than the Original Q3 and anything to the right is an outlier. 3) Q1 − 1.5(IQR) If higher that original Q1 than the original Q1 and anything to the left is an outlier. Describe a distribution o Shape, center, spread o If skewed, best measure of center is median. Median, range and IQR determined by 5 number summaries o 1) center: median o 2)Spread Central/Overall: maxmin Clustering: Q1Q3 o 3) Shape med Q1 versus Q3 med med min versus max med o Gives a graphical representation to tell shape of distribution Boxplot o o About what Percent of years have average January temperatures above freezing (32 degrees F)? A) 50% B) 37%*** C) 20% D) 12% o (a) Standard deviation only measures clustering False o (b) Standard deviation cannot be 0 False o (c) Standard deviation has same units as data True o (d) Standard deviation resistant to outliers False o (e) Standard deviation should be paired with mean True Report median as measure of center use median Risk is directly equivalent to standard deviation because the upside is indeed larger Risk=standard deviation Choosing measures of center and spread o Report median and IQR and Range if skewed o Symmetric report mean Give exact measure o ALWAYS PLOT DATA! For distributions that are normal (bell shape or symmetric) o Take mean and go down on standard deviation and up on standard deviation is 68% o Go down two standard deviations and up two standard deviations is 95% of data o Go down 3 standard deviations and up 3 standard deviations is 99.7% of data
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'