Data Analysis: Collecting, Summarizing, and Analyzing Statistics - Descriptive & Inferenti, Study notes of Statistics

Download Data Analysis: Collecting, Summarizing, and Analyzing Statistics - Descriptive & Inferenti and more Study notes Statistics in PDF only on Docsity!

Statistics Test # 1 Chapter 1 ---  Statistics – Science of collecting, summarizing, analyzing, an d interpreting data (info, usually in the form of numbers) o Descriptive Statistics – Summarizing the data o Inferential Statistics – Analyzing and interpreting data. Inductive thought process  Probability – Field of mathematics involved with determining the relative frequency of certain events. Deductive thought process  Population – Collection of all elements (individuals or items) under consideration o Example: All the possible tosses of a coin  Sample – A part of the population from which information is obtained  Parameter – A numerical characteristic (descriptive measure) of the population  Statistic – A numerical characteristic (descriptive measure) of a sample  Statistical Inference – Inductive thought process – Based on observation o Either experimental or hypothesis testing  Census – 100% enumeration of a population  Why take a sample instead of a census? o Convenience, Necessity, and Accuracy o Random Sample – Elements are drawn at random with replacement o Simple Random Sample – Elements are drawn at random without replacement o Sampling Frame – List of the elements in the population from which the sample will be drawn (n= # of elements in population) Chapter 2 ---  Observational Unit – The elements or objects described  Variable – The measured characteristic for an observational unit o Qualitative – simply classifies elements into categories or classes  Example: non-numeric, numeric but used to rename object, ordinal values o Quantitative – This type of data is numerical and such that differences in the vales have meaning  Example: values are finite or countably infinite, positive values is an interval  Frequency Distribution – Two column table including the values of the variable and the frequency of each value

 Relative Frequency distribution – Two column table including the values of the variable and the relative frequency (frequency divided by the number of observations) of each value o Relative Frequency always totals 1, write as a decimal  Bar Chart – Graph with values of a qualitative variable on the horizontal axis and either the frequencies or relative frequencies on the vertical axis o *** Bars don’t touch each other!!  Stem and Leaf Diagram – Used for displaying the distribution of the values of a quantitative variable. Leading digits are used as stems and the next digits as leaves o Gives a quick way to look at the main features of the distribution  Center, Spread, Shape, Outliers  To determine shape (skewed to right/left or symmetric) turn graph on side and skewness is to side with longest tail o Use for small sets of data  Classes – Categories for grouping data  Frequency – The number of observations that fall in a class  Frequency Distribution – A listing of all classes and their frequencies  Relative Frequency – The ratio of the frequency of a class to the total number of observations  Relative-frequency distribution – A listing of all classes and their relative frequencies  Lower cutpoint – The smallest value that could go in a class  Upper cutpoint – The smallest value that could go in the next higher class (equivalent to the lower cutpoint of the next higher class)  Midpoint – The middle of the class ,found by averaging its cutpoints  Width – The difference between the cutpoints of a class  Histogram – graph with values of a quantitative variable on the horizontal axis and either the frequencies or the relative frequencies on the vertical axis o **** Bars touch each other!!!! o Use for large data sets o Want 5-12 bars  Measures of center of a distribution o Mean – Arithmetic Average of the measurements (Notation:  More susceptible to extreme measurements o Median – The number such that half of the measurements are greater and half are smaller than the number (Notation: m)  Measures of Variation o Range – The distance between the smallest and the largest measurements (Notation: range = lgest observation – smest observation ) o First quartile – the value such that one fourth of the measurements are less than that

value (Notation: Q 1 = First Quartile)

o Third Quartile – the value such that one fourth of the measurements are greater than

that value (Notation: Q 3 = Third^ Quartile

o IQR – The distance between the first and third quartiles (Notation: IQR = Q3 – Q1)

 Rule of thumb for outliers: Less than Q1 – 1.5 x IQR, or greater than Q3 + 1.5 x IQR  Five-Number Summary – Describe the distribution with the numbers: minimum, Q1, m, Q3, maximum  Boxplot – graphical display of the five-number summary o Good for comparing several distributions  Measures of Spread o Variance – Measures spread as a function of the distance of measurements from the mean (Notation: o Standard Deviation – The square root of the variance (Notation:  Measuring Center and Spread in populations o Population – o Population Variance – o Population standard deviation –  Chebyshev’s Theorem – For any distribution, a proportion of at least 1 – 1/k^2 of the measurements must lie within k standard deviations of the mean ( for k > 1)  Empirical Rule – For the normal distribution, approximately 68% of the measurements are within one standard deviation of the mean, approximately 95% of the measurements are within two standard deviations, and approximately 99.7% of the measurements are within three standard deviations of the mean  Z score – measures the number of standard deviations a measurement, x, is from the mean (Notation:  Scatterplot – plotting each element as a point on the two –dimensional axis (x on horizontal axis, y on vertical) o Linear relationship – points fall along a line with a slope not equal to 0 o Positive linear relationship – points fall along a line with slope greater than 0 o Negative linear relationship – points fall along a line with a slope less than 0  Linear correlation coefficient – measures the strength of the linear relationship between two variables x and y (Notation: r =