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# Statistics for Business and Economics Notes- Weeks 1 and 2 STAT 1051

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This 7 page Class Notes was uploaded by Oya Zaimoglu on Tuesday January 26, 2016. The Class Notes belongs to STAT 1051 at George Washington University taught by Zhang, P in Fall 2015. Since its upload, it has received 36 views. For similar materials see Introduction to Business and Economic Statistics in Statistics at George Washington University.

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Date Created: 01/26/16

Statistics for Business and Economics The Science of Statistics Collecting, classifying, summarizing, organizing, analyzing and interpreting numerical and categorical information. Sampling: A process of selecting data from larger sets of data whose characteristics we wish to estimate. Statistics: -Describing sets of data -Drawing conclusions about sets of data on sampling basis Descriptive Statistics: uses numerical and graphical methods to explore data (i.e. patterns, create a more convenient way to present info) Inferential Statistics: uses sample data for estimates, generalizations etc. The main difference between these two is that DS is to present patterns of a data set conveniently; no analysis. IS is to present analysis results using probability theory; primary theme of text. Experimental Units: an object (i.e. person, thing, transaction, event) about which we collect data. Population: set of units, collection of all experimental units. Sample: subset of a population. Variable: characteristic or property of an individual experimental unit (i.e. height). The name variable is derived from the fact that any particular characteristic may vary among the units in a population. Measurement: process used to assign numbers to variables of individual population units. Census: used to measure a variable for every unit of a population. Statistical Inference: estimate/prediction/generalization about a population based on information in a sample (to learn about the larger set). Measure of reliability: statement (usually quantitative) about the degree of uncertainty associated with a statistical inference -Sample size (larger=better) -Representative Sample: selected completely at random (better to have >30) Four Elements of Descriptive Statistical Problems 1. The population/sample of interest 2. One or more variables (characteristics of the population or sample units to be investigated) 3. Tables, graphs, or numerical summary tools 4. Identification of patterns in the data Types of Data Quantitative: measured on a naturally Qualitative: cannot be measured Occurring numerical scale i.e. height, on a natural numerical scale; can GPA, unemployment rate… only be classified into one group of categories; nominal/ordinal i.e. gender, race, size of car… 2 Conversion: We assign arbitrary numerical values to qualitative data for ease of computer entry and analysis. Three Ways to Collect Data 1. From a published source (i.e. book, journal) 2. From a designed experiment (i.e. control group and treatment) 3. From an observational study (i.e. an opinion poll/survey) Observational Study: data collection method where the experimental units sampled are in their natural setting. Representative Sample: A (simple) random sample of n experimental units is a sample selected from the population in such a way that every different sample of size n has an equal chance of selection. -sampling with replacement -sampling without replacement Selection Bias: subset of experimental units in the population is excluded so that these units have no chance of being selected in the sample. Nonresponse Bias: researchers conducting a survey or study are unable to obtain data on all experimental units selected for the sample. Measurement Error: inaccuracies in the values of the data collected. Statistical Thinking: involves applying rational through and the science of statistics to critically assess data and inferences. Fundamental to the thought process is that variation exists in populations and data. CHAPTER 2- DESCRIBING QUALITATIVE DATA Used to provide insights about the data that cannot be quickly obtained by looking only at the original data. 3 Numerical: -Class Frequency: number of observations in the data set in a particular class. Shows how observations in a sample are distributed. -Class Relative Frequency: Class frequency divided by the total number of observations in the data set (Class percentage= CRF x 100). Graphical (non-numerical features) Class: One of the categories into which qualitative data can be classified i.e. how many number of stars hotels have. Graphical Methods 1. Bar graphs: categories of the qualitative variable represented by bars, where the height of each bar is either the class frequency, class relative frequency, or class percentage. 2. Pie Chart: qualitative variable represented by slices of a pie (360). The size (angle) of each slice is proportional to the class relative frequency. 3. Pareto Diagram: A bar graph with he categories (classes) of the qualitative variable (i.e. the bars) arranged by height in descending order from left to right. *Frequencies are in descending order in Pareto (difference between bar graph); it helps us find the most significant class of the data. Graphical Methods for Describing Quantitative Data 1. Dot Plot: the numerical value of each quantitative measurement in the data set is represented by a dot on a horizontal scale when data values repeat, the dots are placed above one another vertically. S = {1, 3, 2, 3, 4, 0, 2, 3, 2, 1, 4, 1} 0 1 2 3 4 4 2. Stem-and-Leaf Display: numerical value of quantitative value is partitioned. The possible stems are listed in order in a column. The leaf for each quantitative measurement in the data set is placed in the corresponding stem row. Leaves for observations with the same stem value are listed in increasing order horizontally. S = {1.2, 1.7, 2.8, 2.3, 1.5, .9, 1.3, 2.1, .6} Stem Leaf 1 69 2 2357 3 138 3. Histogram: Possible numerical values of the quantitative variable are partitioned into class intervals, each of which has the same width. These intervals form the scale of the horizontal axis. The frequency/relative frequency of observations in each class interval is determined. A vertical bar is places over each class interval, with the height of the bar equal to either the class frequency or class relative frequency (using bar graph for quantitative data). [max−min] number of classes Methods for Describing Sets of Data Histograms The sum of all class frequencies will always equal the sample size. 5 The sum of all class relative will always equal to 1. The sum of all class percentages will always equal to 100%. Interpreting a Histogram The proportion of the total area under the histogram that falls above a particular… Interval on the x-axis: relative frequency of measurements falling into that interval. As the number of measurements increase, we can obtain a better description of data. Numerical Measures of Central Tendency Measures to make inferences about the corresponding measures for a population. Data Characteristics: -Central tendency: to cluster/center about certain numerical values -Variability: spread of data Measure of Central Tendency: The most popular and bet understood measure of central tendency for a quantitative data is the arithmetic mean. Mean: sum of all measurements divided by the number of measurements contained in the data set. Two Factors: The accuracy of an inference depends on two factors 1. Size of the sample. The larger the sample, the more accurate the estimate will tend to be. 2. The variability of the data. The more variable the data, the less accurate is the estimate. 6 Median: Middle number when the measurements are arranged in ascending (or descending) order. The symbols for the median are m=sample median; n=population median. 1. Arrange them in order If n is odd, m is the middle number. If n is even, m is the mean of the middle two numbers. *In certain situations, the median may be a better (more robust) measure of central tendency than the mean, because the median is less sensitive than the mean to extremely large or small measurements (outliers). Skewness If one tail of the distribution has more extreme observations than the other tail. 1. Rightward Skewness: median<mean 2. Leftward Skewness: median>mean 3. Symmetric: median=mean Mode: Most frequent. In a relative frequency histogram, the measurement class obtaining the largest relative frequency is called the modal class (emphasizes data concentration). Variability Comparison Range: equal to the largest measurement minus the smallest measurement Deviation: directed distance between measurement and the mean. 1. Take the average of the absolute value of the deviation (no statistical meaning). 2. Eliminate the negative signs by squaring the deviations. Sample variance: n=sum of the squared deviations from the mean, divided by (n-1). 7

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