Variability Measures of spread of scores range: highest - lowest standard deviation: average difference from mean variance: average squared difference from mean
Range Subtract lowest score from highest score For continuous variables, add a point for real limits EXAMPLE: Find the range of this set of scores: 3,7,8,10,15,17 Range = = 14 (for discrete variable) Range = = 15 (for continuous variable)
Population or Sample Standard Deviation EXAMPLE: Find the population standard deviation for this set of scores: 3,7,8,10,15,17
STEP 1: Calculate the mean. = ( ) / 6 = STEP 2: Subtract the mean from each score. x x -
STEP 3: Square each (x- ). x x - (x - )
STEP 4: Sum the (x - ) 2 x x - (x - ) = (x - ) 2
STEP 5: Divide by N and take the square root.
Population or Sample Variance Same as x or S x, but don’t take the square root. EXAMPLE: Calculate the population variance of this set of scores: 3,7,8,10,15,17
Estimated Population Standard Deviation or Variance Same as x and x 2, but divide by N-1 instead of N. EXAMPLE: Calculate the estimated population standard deviation. 3,7,8,10,15,17
More about deviating from standards... Why are the formulae different for estimating? - sample variability is usually less than the population variability -dividing by N-1 compensates for that - unbiased estimate
Comparing Measures of Variability range: easy to compute highly unstable standard deviation: very commonly used takes all scores into account variance: used in inferential statistics hard to interpret