Variability 2011, 10, 4

Learning Topics  Variability of a distribution: The extent to which values vary –Range –Variance** –Standard Deviation**

Lab 1 X(n=10)fP%c% %100% %90% %70% %30% %10%X(n=10)fP%c% %100% %90% %80% %60% %40% %20% %10% Lab 2

Lab 1 Lab 2 Mean = 94

Variability of a Distribution  Variability provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together –Range –Variance –Standard Deviation

Range  Range = Maximum Value - Minimum Value –Lab 1: = 4 –Lab 2: = 12 –How many values the range is based on? –Weakness of range? X(n=10)f X(n=10)f Lab 1 Lab 2

Standard Deviation  In essence, the standard deviation measures how far off all of the individuals in the distribution are from the mean of the distribution. Essentially, the average of the deviations. 

Student Score (N=10) Total---- Mean Mean Square Root Square Root Lab 1

Lab 2

Steps, Formulas and Notations Step 1. Compute the mean Step 2. Compute deviation scores Step 3. Compute the Sum of Squares Step 4. Determine the variance Step 5. Determine the standard deviation

Use a Sample to Estimate the Population Standard Deviation

Why do we need to consider the variability of a distribution? ConditionMeanSD Happy Face 18%5% No Happy Face 21%12% Application: Draw a Happy Face?

Lecture Recap Variability of a Distribution  Compute range  Compute variance and standard deviation –Population vs. sample  Why do we need variability measures?