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# Principles of Statistics STAT 121

BYU

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This 4 page Class Notes was uploaded by Sydney Clark on Friday September 2, 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.

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Date Created: 09/02/16

Stats 121: Principles of Statistics week 1 Section 1 Population is a compilation of ALL things Sample is a small group pf the population The P rocess of Statistics o Collect data o Summarize data o Interpret data Probability and inference The process of statistics start when we identify what group we want to study or learn something about. Population is the entire group of individuals that is the target of our interest In the Gallup Election prediction, the population of interest is all eligible American voters. A Sample is asubgroup of the population which we can examine or observe and collect data from. o You can create a good or a bad sample Choosing a sample and collecting data from it is called Producing Data, the first step of the big picture. Data without identifiers are useless o Need to know Who? What? Why? Who is being interviewed? What are we interviewing? How are we doing it? Individual is an entity that is observed o Ex: student, person, rat Variable is characteristic that is measured on each individual o Height, age Categorical Variable is a variable whose possible values are non-quantitative categories. (you can't take an average) o Gender, opinion, favorite color, race, social security card, phone# Quantitative variable is variable whose possible values are meaningful numbers o Cost, height, age Measurement is value of a variable for an individual o Textbook costs for Nathan Data is measurements for a set of individuals o Textbook costs for samples of students Single variable patterns is looking at one column or category at a time Organize and summarize data Discover: features, patterns, striking deviations Distribution of a variable=summary of data one variable at a time o Listing of all values of that variable AND how often the values occur All of the heights in the class and how many occur at a specific height Vocab o Collect data o Summarize data o Exploratory data analysis o Inference Visual display of data o Represent numerical quantities with visual elements(length, area, position, darkness.) Visual element consistent and proportional to quantity Make easy for viewer to see and understand Bar Chart o Represent categories by arbitrary positions on a horizontal line o Construct bar over each category such that height is proportional to number/percent in category o In a bar chart the height of the bar is proportional to the number in each category. Pie Chart o Represent categories by arbitrary positions in a pie o Construct pie chart over each category such that height is proportional to number/percent in category Pictogram= picture enhanced bar (misleading) o Problems: only account for one dimension when they often are two dimensions Analysis of Distribution for Quantitative data o 1.) Always plit your data first o 2.) Look for an overall pattern and for striking deviations such as outliers o 3.) Look at shape, center and spread of distribution o 4.) Add numerical summaries to supplement the graph o 5.) If the pattern is regular use a mathematical model Histogram Construct horizontal line with consistent scale such that range is greater than or equal to range of data Divide range into classes of equal width Construct bar over each class such that height is proportional to number/percentage of class. Center, spread, shape Frequency= count NOT percentage Histogram Bar Graph Represents categorical variable Represents quantitative variable Order of categories are arbitrary Order of classes are essential Bars separated by spaces Bars are adjacent o Can NOT describe center, shape and spread of bar chart!! Stem Plot o Separate measurements into digits Stem= all but final digit Leaf=final digit Write each leaf to right of stem Can be horizontal or vertical Can describe center, shape, and spread Can split stems into two or more What is the advantage of Histograms over stem plots? o The data set can be ANY sze Dotplots o Similar to histogram but with dots o Center, spread, shape, modes, outliers G Shape of the distribution o Symmetric and bell shape o Right skewed (ex. Income, anything with money) o Left skewed o Bimodal o Flat or uniform Center o Look for value with half of the data to the left and half to the right Spread o Distance from lowest to highest Outliers o Far away from the rest of the pack o Do NOT get rid of outliers VOCAB o Bar graph o Categorical variable o Data o Distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence o Histogram o Individual o Quantitative variable o Measurement o Pie chart o Stem plot o Table o Variable o Shape o Center o Spread o Outlier

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