STT 201 Ch 1 2 10 21 2014 I Statistics art and science of designing studies and analyzing the data from those studies i Goal translating data into knowledge II Inference making decisions and predictions based on data III Design planning how to obtain data to answer the questions of interest IV 2 types of Statistics i Descriptive Statistics pictures tables charts plots diagrams ii Inferential Statistics drawing conclusions about a population based histograms displays on information from a sample V Parameter numerical summary of the population VI Statistic numerical summary of a sample taken from the population VII Data systematically recorded information numbers of labels VIII Context tells who what when where how and why the information is IX Raw Data numbers and category labels that have been collected but not together with its context being measured recorded yet processed X Variables characteristics recorded about each individual i Categorical qualitative consist of group that doesn t necessarily have logical ordering a Ex eye color country of residence b Ordinal variables categorical variables that have a logical order ex T shirt size highest education level ii Quantitative numerical consist of numberical values taken on each individual numbers a Discrete if it takes its value from a countable or finite set of b Continuous if it takes its possible values from an interval or continuum like 2 7 XI Mean the sum of the observations divided by the number of observations XII Median the midpoint of observations when in order XIII Mode number that occurs most frequently in a number set XIV Outliers unusual or extreme values that do not appear to belong with the rest of the data XV Measure of Spread numberical summary of how tightly the values are clustered around the center i Standard deviation ii Interquartile range iii Range i Calculate x the sample mean ii For each observation calculate the difference between data value XVI Steps of how to find Standard Deviation and the mean iii Square each difference in step 2 iv Sum the squared differences in step 3 then divide this sum by n 1 v Take the square root of the value in step 4 Interquartile Range IQR distance between Q1 and Q3 i Q3 ii Q1 upper quartile median of upper half of ordered data lower quartile median of lower half of ordered data XVII XVIII 5 Number Summary i max min median Q1 Q3 XIX Upper fence Q3 1 5 IQR XX Lower Fence Q1 1 5 IQR XXI Describing Histograms i Unimodal one mode ii Bimodal two modes iii Multimodal more than 2 modes iv Uniform no modes all data is about same length v Skewed Right tail on right side vi Skewed Left tail on left side XXII Stem and Leaf Plot i Stem leading numbers ii Leaves last digit on the number only 1 digit Chapter 3 10 21 2014 I Skewed Right mean median tail is on right II Skewed Left mean median tail is on left III Linear Relationships i Explanatory variable x ii Response variable y IV Correlation coefficient r numerical measure of the direction and strength of a linear association i From 1 to 1 positive slope r negative slope r ii Closer to 1 and 1 you are stronger the association is iii 0 is no correlation iv units do not effect it v only used in QUANTATIVE variables not categorical V Residuals e discrepancy between data and model difference between observed value and value predicted by regression line i Observed y predicted y ii E y y hat iii If e 0 no error iv Positive e overestimate v Negative e underestimate VI Coefficient of Determination r2 i The proportion of the variation in the y values that is accounted for by the linear relationship of y with x ii Number from 0 to 1 iii R2 1 IF all points line on a lie 10 21 2014