Measures of Central Tendency and Variability Handout
Measures of Central Tendency
- Central tendency refers to the "average" score in a set of scores.
- Trying to specify a "representative" value of a set of scores
Mode à Score that occurs most frequently
- Problem of bimodal or multimodal distributions
- Two or more modes
- No unique value – lose effectiveness as measure of central tendency
Median à point in distribution that divides distribution into two equal parts.
- Two approaches:
Even number of scores: Median is arithmetic average of two middle scores
Odd number of scores: Take the middle score
Mean à arithmetic average of scores (sum all scores and divide by total number of scores)
- Equation: 
Measures of Variability
- Variability refers to extent to which scores differ from one another
Range à highest score minus lowest score
- Not a very good index of variability because can be misleading
Interquartile Range (IQR) à Represents the middle 50% of scores
- Order from lowest to highest, arrange into four "quartiles" of three scores each
- Eliminate top and bottom groups, have middle 50% of scores
- Some people prefer IQR because not as sensitive to distortions of extreme cases
- But criticized because it does not take into account all the scores in the distribution
Sum of Squares à How far do scores vary from mean score
- Gets its name because it is the sum of squared deviations from the mean
where
= the sum of the squared X scores and 
= square of the summed X scores
- Size of SS depends not only on amount of variability, but also on number of scores
Variance à takes into account the number of cases in each set in computing index of variability
- Formula: 
Standard Deviation à Represents the average deviation from the mean
– most easily interpreted measure of variability
- Formula: 
