PSYCH 210 1st Edition Lecture 5Outline of Last Lecture I. Percentiles and Percentile Ranksa. InterpolationII. Central Tendencya. Modeb. MeanOutline of Current Lecture I. Central Tendencya. MedianII. Relation between Mean, Median and ModeIII. VariabilityCurrent LectureI. Mediana. How to calculate with SFD with ties near middleb. Interpolationi. Median = 50th percentile rankii. Data must be continuousiii. Same method as Lecture 4c. Disadvantagesi. Doesn’t include all values of dataset in calculation (unlike Mean)d. Advantagesi. Can be used in situations when mean cannot1. Mean is normally first choice for Central Tendencye. Four Situations when you can’t use mean i. Ordinal Data1. Not ‘allowed’ to use mean – nonparametric statisticsii. Skewed Distribution1. Outliers will pull mean up (if positively skewed)a. Mean is sensitive to outliersThese 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.iii. Opened-ended distributions1. Frequency Distribution open at one side2. Ex) X= # of Beers consumed = 0, 1, 2, 3+3. Ex) X= <2, 3, 4, 5, 6i. Impossible to calculate mean because we don’t know every raw score of data setiv. Undetermined scores1. Background Psychology Informationa. Kitty Genovese Story:i. Raped in NYC in daylight with many witnesses and nobody called policyii. Sparked widespread interest in research, etc.iii. Bystander Effect: as the number of bystanders increases, the likelihood that any one person will help decreases1. Diffusion of Responsibility2. Ex) Field Study @ Memorial Uniona. As soon as elevator closes, actress drops all her coinsi. IV = # of bystanders with actressii. DV = # coins picked upDV= Latency to start helping (sec)X=Latency f=Frequency6 15 24 63 32 2Didn’t Help 2iii. Problem: Cannot throw out this data, but also cannot assign them 0.iv. Solution: Group at bottom or top and calculate Median (since we cannot calculate Mean)II. Relationship Between Mean, Median and Modea. Knowledge of Relationship can help us know the shape of data without seeing its graphi. Helpful for future calculations (Inferential Statistics)b. Unimodal Symmetricali. Mean, median and mode are equalc. Bimodal Symmetricali. Mean and median equal and in center, 2 modesd. Positively Skewedi. Mode=peak, mean highest, median in betweene. Negatively Skewedi. Mode=highest, Mean lowest, median in betweenf. Ex) Mean = 30, Median = 27i. Good guess: positive skewg. Ex) Mean = 10, Mode = 25i. Good guess: negative skewIII. Variabilitya. Another category of Descriptive Statisticsb. Measures spread or dispersionc. Four Typesi. Rangeii. Semi-Interquartile Range (SIQ)iii. Variance iv. Standard Deviationd. Two Data Sets for examples:i. Graph A ii. Graph Be. Rangei. Difference btwn highest and lowest scoreii. With real limits: URL x max – LRL x miniii. Graph A) 125-25 = 100125.5-24.5 = Range = 101iv. Disadvantage1. Doesn’t tell us what’s happening in middle a. no difference btwn A & B!2. Too basic to be used often f. Semi-interquartile range (SIQ)i. Way to measure distance without influence of extremes on either endsii. SIQ = (Q3-Q1) / 2iii. Use Percentiles to split data into Quartiles1. 50th percentile = Q22. 25th percentile = Q13. 75th percentile = Q34. Graph a. Measure distance btwn Q1 & Q3 (Interquartile Range, IQ = Q3-Q1)5. Ex)a. GFD (Continuous data)b. Q1=59.5 (already listed on tablec. Q3 = ?d. Interpolationi. Q3= 89.1e. (Q3-Q1)/2= (89.1-59.5)/2 = SIQ =14.8iv. What does SIQ tell me?1. The higher the value, the more the spread2. See handout from class – detailed