chapter 5.3 - variability

measures of variability

summarize and describe extent to which scores in a distribution differ from each other and the mean

range

distance from lowest to highest score, problematic because lacks precision and extreme scores distort variability

interquartile range

range of the middle 50% of observations (25th to 75th percentile), attempts to get around problem of range being dependent on extreme scores, to compute find median and use median to split into 2 halves and then find the difference in the two half’s medians, problematic because eliminates half the data

variance

an index that reflects the degree of variability in a group of scores, average of the squared deviations (distances) about the mean, larger variance=more spread out scores

sample variance (s²)

sum of the squared deviations about the mean divided by samplesize-1

population variance (σ²)

very similar to sample but not samplesize-1

standard deviation

take square root of the variance, is a measure of the average deviation of each score of the mean

• approx. 68% scores will fall within 1 SD of mean

• approx. 95% falls within 2 SD of mean

• approx. 99.7% falls within 3 SD of mean