Statistics: Descriptive and Inferential Methods and Distributions - Prof. Chung-Ching Wang, Study notes of Data Analysis & Statistical Methods

Download Statistics: Descriptive and Inferential Methods and Distributions - Prof. Chung-Ching Wang and more Study notes Data Analysis & Statistical Methods in PDF only on Docsity! Chapter 1 Descriptive statistics: utilizes numerical and graphical methods to look for patterns in a data set, to summarize information revealed in a data set, and to present that information in a convenient form Inferential statistics: utilizes sample data to make estimates, decisions, predictions, and other generalizations about a large set of data Population: a set of units that we are interested in studying Sample: a subset of the units of a population Census and Sample: Measurement is a process we use to assign numerical values to variables of individual population units. When we measure a variable for every unit of a population, the result is a census of the population. If we only measure part of the units in a population, the result is a sample of the population. Elements of inferential statistics:  The population or sample of interest  One or more variables that are to be investigated  Tables, graphs, or numerical summary tools  Identifications of patterns in the data Elements of interferential statistical problems:  The population of interest  One or more variables that are to be investigated  The sample of population units  The inference about the population based on information contained in the sample  A measure of the reliability of the inference Quantitative data: measurements that are recorded on a naturally occurring numerical scale Qualitative data: measurements that cannot be measured on a natural numerical scale; can only be classified into one group Representative sample: exhibits characteristics typical of those possessed by the target population Measure of reliability: a statement (usually quantitative) about the degree of uncertainty associated with a statistical inference Chapter 2 Box-Plot: distance between points is figured out by 1.5*IQR Quantile-Quantile Plot: the dot chart Stem-and Leaf Display: all the numbers lying out Mean: average Median: the middle number when the numbers are in order Mode: number that occurs the most Range: largest number minus smallest number Standard Deviation (s): defined as the positive square root of the sample variance (s2) or s=√s2 Variance (s2): equal to the sum of the squared distances from the mean, divided by (n-1) or s2= ∑ i−1 n x i 2 − (∑ i=1 n xi) 2 n n−1 Upper Quartile: the 75th percentile Lower Quartile: the 25th percentile IQR: distance between the lower and upper quartile Chebyshev's Rule: Generally, at least I 1/k2 of the measurements will fall within k standard deviations of the mean for any number of k greater than 1,regardless of the sharp of the frequency distribution.(a) At least 3/4 of the measurements will fall within the interval (x-2s, x+2s) for samples and (μ-2σ, μ+2σ) for populations. (b) At least 8/9 of the measurements will fall within the interval (x-3s, x+3s) for samples and (μ-3σ, μ+3σ) for populations. Empirical Rule: the empirical rule is a rule of thumb that applies to samples or populations with frequency distributions that are mound- shaped. (a) Approximately 68% of the measurements will fall within the interval (x-s, x+s) for samples and (μ-σ, μ+σ) for populations. (b) Approximately 95% of the measurements will fall within the interval (x-2s, x+2s) for samples and (μ-2σ, μ+2σ) for populations. (c) Approximately 99.7% of the measurements will fall within the interval (x-3s, x+3s) for samples and (μ-3σ, μ+3σ) for populations Z-Score: suppose x is a measurement from a sample with mean x and standard deviation s. The sample Z score of x is ¿ ( x−x ) s . Symmetric: Skewed: one tail of the distribution has more extreme observations than the other tail; if the lower part is on left it’s a right skew and vice versa Mound-Shaped distribution: the mean, median, and mode are all about the same Chapter 3 Definitions: Experiment: An experiment is an act or process of observation that leads to a single outcome that cannot be predicted with certainty.