WEEK 3 Features of distributions (Metric) Central tendency · provides a statistic that defines the centre of the distribution (mean/median/ mode) categorical . the values that are ' most typically most representative of the entire group Variability Measures the degree to which scores are spread out / clustered together Shape: symmetric / screwed · extreme scores: any very ?/ values Measuring the amount of variability in a distribution of scores How different are the scores? · Are the scores spread out or closely clustered together? Distance between scores Provides info about the "amount of error " we can expect between a sample and a population
Measures of Variability: - Range - Standard - Varience Deviation 1. Range - Distance covered by X max - X min scores - Not a reliable measure of variab- ility L> extreme scores (outliers) eg. Scores of 1, 16 , 18 , 19 XC Max - Xmin Max = 19-1 = range of 18 BUT there are 3 values between 16 and 19 Deviation - distance from mean (value of X- M Interest - population mean) Varience - mean of squared deviations - Just adding deviation scores = 0 - average of squared distance from mear - definitional Computational calculation
Standard Deviation-square root of varience varience - Average distance from mean Calculating Deviation score for populations Deviation = distance from the mean » Deviation = X - u [Value of interest minus population mean] » Values: 2, 1, 9, 4 Scores [X] X - u 2 2 - 4 -2.00 1 1 - 4 -3.00 9 4 Deviation 9 - 4 5.00 4 - 4 0.00 Deviation Score Total = 16 N = 4 u = 4 Deviation scores should add to zero, but this does not give us a measure of the variation, so ... We will use the Sum of the Squared Deviations - SS KNOW Calculating Varience for populations - Varience = mean of squared deviations Definitional formula: SS = > ( JC - M) 2 ( sum of squares = sum of squared deviation scores) Computational formula Minimises errors SS = EX 2 - (EX)2 N