II Lecture 5 Outline of Last Lecture I Histogram II Polygon III Bar Graphs Psych 311 1nd Edition IV V VI VII Graphs for Population Distributions Shapes of Distributions Measures of Central Tendency Characteristics of Mean Outline of Current Lecture I Selecting a Measure of Central Tendency II Central Tendency and Shape of Distribution III Measures of Variability IV Quantifying Variability V and s VI Samples as Biased and Unbiased Estimates of Population Current Lecture I Selecting a Measure of Central Tendency Choose the median appropriet study when you have extreme scores or skewed distribution or open ended distributions or ordinal scale Chose the mode when dealing with nominal scale or discrete variables or describing shape of distribution Mean is most commonly used central tendency because it uses every single score in data set it can be easily algebraicly manipulated it s related to varience and standard deviation measures vaiability II Central Tendency and Shape of Distribution When distribution of scores is symmetical and normal mean median mode When distribution of scores is symmetrical but not normal mean median 2 modes When distribution is positively skewed mean median mode When distribution is negatively skewed mean median mode III Measures of Variability These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Descriptive statistics describes variability within data Variability the degree to which differences exist among set of scores measures of variability quantifies the degree of differences how spread apart or close together the scores fall the more variability the more the scores are spread apart vice versa No matter what measure of variability you use the larger the value the greater the spread of the scores IV Quantifying Variability We quantify variability by calculating varience and SD varience the average of squared distances from mean SD the square root of average squared deviations or variences We want to know on average how far a score falls from the mean X how far an individual score falls from mean X N on average how far the sum of the scores fall from the mean X N mean usually X 0 so you must X sum of squares ss X N population can t have squared varience in psych X N X N on average how far do individual scores fall from mean above and below Ex On an exam there is a mean of 70 and X 65 which values for SD would give you the highest position in the class a 1 b 5 c 10 C would be correct because 65 60 which is 1 below V and s and population s and s sample s and s use df degrees of freedom n 1 as denominator VI Samples as Biased and Unbiased Estimates of Population sampling error descrepency bias or unbias estimate of population assumption characteristics of sample approximately characteristics of population assumption is that sample provides an unbiased estimate of population but samples can provide biased estimate variability is biased because it always underestimates population varience impossible to over estimate df allows us to correct the bias III