descriptive statistics

measures of location

where the distribution is on the number line (range from min. to max. possible score on the x-axis)

measures of central tendency

single-value summaries that describe the "middle" of a distribution differently

- mean, median, mode

mean

the arithmetic average of the values, dividing the distribution in half in terms of magnitude

- minimizes the sum of squared deviations

- very much affected by outliers

median

the value that corresponds to the 50th percentile, dividing the distribution in half

- minimizes the sum of absolute deviations (closest value to all other values)

- not much affected by outliers

mode

the most frequently occurring value(s)

- the tallest bar(s) in a histogram

- not much affected by outliers

(can be unimodal, bimodal, trimodal, or multimodal)

measures of dispersion

how spread out the scores are for a distribution of a random variable

- range, IQR, variance, SD

range

magnitude reflecting the difference between the min. and max. values of a distribution

interquartile range (IQR)

magnitude of difference between the 75th and 25th percentiles of the distribution

(divide the distribution in half, then find median for both)

variance

average of the squared deviations from the mean

standard deviation

avg distance of measurements from the mean

- standardized version of the variance (square root of the variance)

measures of shape

skewness and kurtosis

skewness (g1)

symmetry of a distribution

- negatively or positively skewed / no skew

symmetrical distribution

distribution of one half is a mirror image of the other

- mean = median

kurtosis (g2)

peakedness of a distribution

- narrowness or wideness

mesokurtic

normal distribution

- equals 0

leptokurtic

taller and narrower peaks

- greater than 0

platykurtic

flatter and boxy peaks

- lesser than 0

boxplots

help identify outliers

- consists of a box and whiskers (up to 1.5 x IQR)

aggregation

combining of individuals into groups (done in statistics)

aggregate-type proposition

asserts smt presumably true of the aggregate class/group, but not necessarily of each person

(use language like, on average)