Ch4: Central Tendency and Variability

Central Tendency

descriptive statistic that best represents the center of a data set

mean: average, best used for symmetric distributions

median: middle score, best for a skewed distribution or one w/ 1+ outliers

mode: most common score, repeats, used when:

• one particular score dominates a distribution

• distribution is bimodal or multimodal

• data is nominal

parameter

number based on the whole population (mean of a population); represented with greek letters such as mew (upside down h)

statistic

mean of a sample; symbol: M or X bar

mode(s)

unimodal distribution: one mode, most common score

bimodal distribution: two modes, most common scores

multimodal distribution: more than two modes

outlier

extreme score that is either very high or very low

usually doesn’t affect the media in a drastic way

variability

numerical way of describing how much spread there is in a distribution

• range: measure of lowest to highest score, subtract lowest from the highest score

• variance: average square deviation from the mean

  • calculate by subtracting the mean from every score, square every deviation, sum all of the squared deviations, divide the SS by the total number in the sample

• standard deviation: variation from the sample mean, square root of the variance

interquartile range

completely dependent on the maximum and minimum scores

measure of distance between the first and third quartiles

• 1st quartile: 25th percentile of data set

• the median: marks 50th percentile of data set

• 3rd quartile: 75th percentile of data set

find all scores below (Q1) and above (Q3) the median, IQR=Q3-Q1

deviation from the mean

the amount that a score in a sample differs from the mean of the sample; aka deviation

sum of squares

symbolized as SS, is the sum of each scores squared deviations from the mean