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York University
Administrative Studies
ADMS 2320
Michael Rochon

CHAPTER#1 & CHAPTER#2 & CHAPTER#3: GRAPHICAL DISCRP. Statistics: a way to get to transfer data into useful information Population is entire set of obv. descriptive measure is called a parameter Sample is a subset of population, descriptive measure is called statistics. Descriptive statistics: arrangement, summary, presentation of data DS methods: GRAPHICAL TECHNIQUES&NUMERICAL DESCRIPTIVE MEASURES Variable: a characteristic of population or sample of interest to us. Values of a variable are all possible observations EX. Cereal brand, weight ETC Data: observed values of variable Ex. Marks (67,74,71,83,48) àInterval: real# Ex.Weight. also quantitative or numerical • Histograms: all data are interval, with class intervals àOrdinal: categorical in nature but have an order (ranking) Ex. Poor=1 fair good=2 good=3 excellent=4 à BAR CHART   àNominal: categories (qualitative/categorical) ex.single=1 married=2 widowed=3 etc. àIf a distribution is symmetrical, the mean, median and mode maybe coincide. - can be treated as ordinal àIf the distribution is non symmetrical, and skewed to the left or the right, the • Allowed only FREQ OR RELATIVE FREQ= freq/total freq • Pie chart à relative frequencies Bar chart àbin and frequency three measure differ. Histogram: important graphical method for single set of interval data, it doesn’t only summarize interval data but also explain probabilities. • Number of classes intervals= 1+3.3 log (n) • Class Width = (largest observation- Smallest observation)/ # of classes Shapes of Histograms: • Symmetry: two sides are identical in shape and size. • Skewness: histogram with a long tail extending to either right or left • Modality: unimodal is one single peak, while bimodal is one with two peaks. • Bell shape: a special symmetric unimodal histogram. OGIVE: graph of a cumulative relative frequency distribution. Ex. Histogram is extremely skewed yields mean and standard deviation of 70 and Two Nominal variables: contingency table and bar chart (two dimensional) Two Interval Variables: scatter diagram : relationship between 2 interval data 12, what is min proportion of observations at? (cheby theorem) 70+(2)(12)= 94 70-(2)(12)= 46 • Independent variable X = horizontal axis, dependent Y= vertical axis à 75% lies between 46 and 94. Linear relationship: positive, negative, weak, non-linear 70+(3)(12)=106 70-(3)(12)=34 à88.9% lies between 34 and 106. Mean/Variance/SD use this form of chart to solve easier: • Positive linear- both XY increasing or decreasing together • Negative linear- XY going opposite directions Measures of Relative Standing: designed to provide info about position of particular Cross-sectional: observations measures at the same point in time (multi bar charts) values relative to entire data set. Percentile (Ph) is value for which P% are less than Time-series: observations measured at successive points in time (OGIVE ) that value and (100-P)% or (1-p) is greater than that value. th CHAPTER#6: PROBABILITY CHAPTER#4: NUMERICAL DISCRIP. TECHNIQUE EX. Score in 60 percentile means 60% of other score were below you, and 40% A Random Experiment: process that leads to one of several possible outcomes. GM takes consideration of time and all ur data. If not given the rates of return you have were above you. (rule#1) outcomes must be exhaustive and (rule#2) must be mutually exclusive to calculate “annual rate of return”: Annual rate= new-old/old investment for each st nd Sample Space: (Rule#1&2) The probability of any outcome is between 0 and 1, sum of year. EX. Invrdted 1,000 4yrs ago was worth 1,200 after 1 yr, 1,200 after 2 yr, probabilities of all outcomes equals 1. S={O1,O2,..O }k0≤ P(O ) i1 and ∑p(O )=1 i 1,500 after 3 yr, & 2,000 today. Three ways to assign a probability to an outcome: • Classical Approach: counting approach used effectively in game of chance • Relative Frequency: assigning probabilities based on history of outcomes. % Interquartile range= Q3- Q1 (measure the spread of the middle 50% of observation) • Subjective Approach: assigning probabilities based on a degree of belief. Location of a percentile: L =p(n+1) P/100, where L is phe location of the p th An Event: collection (all outcomes) of one or more simple events in a sample space. percentile. A Simple Event: is individual (SINGLE) outcome of a sample space. A Complementary Event: the opposite of the event. P(A)+P(A )= 1 c Intersection of Events (joint probability): intersection of event A and B is the event that occurs when both A and B occur. Denoted as P(A and B). Marginal probabilities: are computed by adding across rows and down columns Conditional Probability: used to determine how two events are related. We can determine probability of event A given t
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