STATS 250 1st Edition Lecture 1 Outline of Last Lecture** no last lectureOutline of Current Lecture I. Syllabus InformationII. Definition of StatisticsIII. Raw DataIV. Types of VariablesV. Summarizing One or Two Categorical VariablesVI. Exploring Features of Quantitative Data with PicturesCurrent LectureI. Syllabus Informationa. Course Goal: Learn various tools for using data to gain understanding and make sound decisions about the world around usII. Definition of Statisticsa. Statistics: numbers measured for some purposeb. Statistics: a collection of procedures and principles for gathering data and analyzing information in order to help people make decisions when faced with uncertaintyIII. Raw DataThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.a. Raw data: numbers and category labels that have been collected or measured, but not processed in any wayb. Variable: a characteristic that differs from one individual to the nextc. Sample data: collected from a subset of a larger populationd. Population data: collected when all individuals in a population are measurede. Statistic: summary measure of sample dataf. Parameter: summary measure of population dataIV. Types of Variablesa. Categorical variable: place an individual or item into one of several groups or categoriesi. Ordinal variable: when the categories have an ordering or rankingb. Quantitative variable: takes numerical values for which arithmetic operations make sensei. AKA measurement variable or numerical variableV. Summarizing One or Two Categorical Variablesa. Numerical Summariesi. Count how many individuals/items fall into each categoryii. Calculate the percent, or proportion, of individuals/items falling into each categoryiii. Count: frequency distributioniv. Percent: relative frequency distributionb. Visual Summariesi. Chartsii. Bar graphsiii. Pie chartsVI. Exploring Features of Quantitative Data with Picturesa. Graph with a histogrami. Find the smallest and largest values (minimum and maximum)ii. Find the range (maximum-minimum)iii. Determine what are reasonable intervals to break up data into – usually between 6 and 15 intervalsiv. No spaces between bars!v. Histograms show the distribution of a quantitative variable, or the overall pattern of how often the possible values occurvi. Can be either frequency (count) or percentage on the y-axis; personal preference, but it is better to use relative frequencies on the y axis when comparing 2 or more sets of observationsvii. Usually include measurements for mean (xbar), sample size (n), and standard deviation (s)b. How to interpret?i. Look for overall pattern1. Shapea. Symmetrical?b. Bell-shapec. Uniformd. Skewedi. Skewed to the right = positive skew1. Few high outliers pull mean rightii. Skewed to the left = negative skew1. Few low outliers pull mean left2. Locationa. Where is the mean (µ)?b. Where is the median?3. Spreada. What is the standard deviation (s)?ii. Look for deviations from overall pattern1. Outliers: a data point that is not consistent with the bulk of the data2. Outliers should not be discarded without