March 24 - o Add all scores and divide by the number of...

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March 24, 2008 Central Tendency and Dispersion Summary measures o In addition to graphs and tables, we need summary statistics o Central tendency tells us the most typical or common score: Mean, median, mode o Dispersion tells us about differences in groups of cases Range, inter-quartile range, variance, standard deviation Central tendency: the mode o Mode can be calculated for any type of variable o It is your only option for a nominal-level measure or a true ordinal-level measure o It is the most common value o We can read it from a graph, or a frequency table o If there are two categories with equal or near-equal quantities at the mode, we have a bimodal distribution Central tendency: the median o The median is the 50% percentile – the middle score in a ranked list of values measured at the interval or ratio level o Half of all scores are above it; half are below it o Median position = (n+1)/2; (when cases are ranked in order) Central tendency: the mean o The arithmetic average ; For a sample μ For a population
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Unformatted text preview: o Add all scores and divide by the number of cases o This is what we refer to most often, and what we use most often in statistics o The mean carries the most information, but is sensitive to outliers o Formula (x with line over it = sigma*x sub i / n) =Σx i /N Dispersion o Dispersion statistics tell us how spread out or scattered the scores in a distribution are o This is important, because the central tendency alone doesn’t tell us enough o Though book discusses the variation ratio for nominal or ordinal data, we will focus only on measure for interval or ratio date Dispersion: the range o The range is the distance from the lowest to highest value Dispersion: Interquartile range o Quartiles are the 25 th , 50 th , and 75 th percentile (they divide the distribution in 4 equal segments) o IQR = X Q3 – X Q1 ; the difference between the 3 rd quartile and the 1 st quartile o If a quartile value falls between 2 cases, take their midpoint....
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