Lecture 4 Outline of Last Lecture I Scales of Measurement II Review of Mathematical Operations III Symbols IV Descriptive Statistics V Frequency Distributions Outline of Current Lecture I Histogram II Polygon III Bar Graphs Psych 311 1nd Edition IV Graphs for Population Distributions V Shapes of Distributions VI Measures of Central Tendency VII Characteristics of Mean Current Lecture I Histogram Type of bar graph representing frequency of scores on interval or ratio scale of measurement Two characteristics Height of bar corresponds to frequency in that category Width of bars extend to real limits of boundaries of categories bars touch one another bars touching indicates interval or ratio scale of measurement II Polygon 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 Type of line graph used for interval or ratio scales of measurement Three characteristics dot centered above each score corresponding with frequency of that category the dots are connected line extends to x axis at real limit III Bar Graphs Type of graph used to represent frequency scores on nominal or ordinal scales of measurement Two characteristics height of bar corresponds to frequency of category bars do not touch their spaces represent discrete categories IV Graphs for Population Distributions When pop is too big we can construct relative frequency distributions and smooth curves this is representative of the population Relative Frequency bar graph with no numbers bars are approximately representable nominal or ordinal data Smooth Curves line graphs used when pop consists of scores indicates that we are showing relative changes from one category to another this is normal distribution bel curve describes distribution normal describes shape symmetrical greatest frequency is in middle fewer frequency towards extremes most psychological characteristics are measured under normal distribution V Shapes of Distributions theses representational aides all describe frequency distributions distributions can take on a number of shapes or forms Unimodal Distribution mode most frequently occurring score single well defined mode Multimodal Distribution 1 modes exist approximately so 1 modes exist relative to other frequencies Symmetrical Distribution if cut down middle would be symmetrical balanced can be normal or any other distribution Skewed Distribution unbalanced scores are more weighted towards one end direction tail points determines positive vs negative skewed data VI Measures of Central Tendency How can we summarize distribution efficiently using quantitative methods describe data using numbers Central Tendency most typical or common score of entire group best representative of entire data set mode median mean Mode most frequently occurring score tallest point on graphs ex 10 20 30 40 40 60 mode 40 Median value at which half of the ordered scores fall above and half fall below must always order scores first Odd number of data average score of middle two numbers Even number of data find middle number ex 10 20 30 40 median 25 average score of middle s ex 10 20 30 40 50 median 30 middle score Mean arithmetic average balancing point for set of scores balances distances between scores and mean population is X X individual scores number scores sample X Sigma or sum of scores ex X important to understand SD X deviation score as many deviation scores as values of X s we ve arrived at correct mean when of total deviation scores is 0 00 VI Characteristics of Mean most often used central of tendencies takes into account every single score if you change one value the mean will change if you introduce or remove a score the mean will change if you add or subtract a constant the mean will change by that constant if you multiply or divide by a constant the mean will multiple or divide by that constant